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Title: Twentieth Century Standard Puzzle Book - Three Parts in One Volume
Author: Pearson, Cyril
Language: English
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Transcriber’s Notes
Text printed in italics has been transcribed _between underscores_,
bold face text =between equal signs=. Blackletter and spaced out text
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GOOD VALUE
GAMAGES
Latest Conjuring
By WILL GOLDSTON
_The Latest and Best Book Published_
[Illustration]
=_A Few Principal Items--_=
CHAPTER I.--Latest tricks with and without apparatus, many published
for the first time. Illustrated.
CHAPTER II.--Every new and startling illusion accurately explained
with illustrations.
CHAPTER III.--Latest methods for performing the “Mystic Kettle” that
boils on ice, including the “Magic Kettle,” the most remarkable
utensil to hold liquor. This little kettle can produce almost any
drink from milk to whisky. Illustrated.
CHAPTER IV.--Correct methods to escape from Handcuffs, Leg-irons,
Rope, Iron Collars, Padlocks, Sacks, Iron Trunks, Wooden Boxes,
Barrels, Iron Cages. Illustrated.
CHAPTER V.--Hand Shadows and how to work them. Illustrated.
Without a doubt the greatest and cheapest book ever published on
Magic.
ORDER IMMEDIATELY TO AVOID DISAPPOINTMENT
_Handsomely Bound in Cloth_, =2/-= Post Free, =2/3=
The Secrets of Magic
BY WILL GOLDSTON
[Illustration]
Over 100 pages and as many illustrations. This up-to-date work,
describing only the latest secrets and effects in conjuring, also
contains biographies of leading magicians.
This book is in its 4th Edition, and is without doubt a very useful
book, as it contains many valuable tricks and illusions never before
divulged.
Cloth Bound. Price =2/6=. Postage 3d.
A. W. GAMAGE, Ltd
HOLBORN
LONDON, E.C.
THE TWENTIETH CENTURY
=STANDARD PUZZLE
BOOK=
THREE PARTS IN ONE VOLUME
EDITED BY
A. CYRIL PEARSON, M.A.
AUTHOR OF
‘_100 Chess Problems_,’ ‘_Anagrams, Ancient and Modern_,’ _etc._
_PROFUSELY ILLUSTRATED_
SECOND IMPRESSION
LONDON
GEORGE ROUTLEDGE & SONS, LTD.
NEW YORK: E. P. DUTTON & CO.
=Also in Three Parts=
I.--MAGIC SQUARES, PICTURE PUZZLES, ENIGMAS, CHARADES, RIDDLES,
CONUNDRUMS, NUTS TO CRACK, SOLUTIONS.
II.--OPTICAL ILLUSIONS, FREAKS OF FIGURES, CHESS CAMEOS, SCIENCE AT
PLAY, CURIOUS CALCULATIONS, WORD AND LETTER PUZZLES, SOLUTIONS.
III.--WORD PUZZLES, MISSING WORDS, LETTER PUZZLES, ANAGRAMS, PICTURE
PUZZLES, PALINDROMES, SOLUTIONS.
=Also by the same Author=
PICTURED PUZZLES AND WORD PLAY. Profusely Illustrated. Crown 8vo.
Cloth.
=PART I.=
CONTENTS
PAGE
MAGIC SQUARES, PUZZLES, TRICKS, ENIGMAS I-1
CHARADES, ETC. I-80
RIDDLES AND CONUNDRUMS I-104
NUTS TO CRACK I-115
SOLUTIONS I-148
MAGIC SQUARES
No. I.--FOUR HUNDRED YEARS OLD!
In Albert Dürer’s day, as in Milton’s, “melancholy” meant
_thoughtfulness_, and on this ground we find on his woodcut,
“Melancholia, or the Genius of the Industrial Science of Mechanics,” a
very early instance of a Magic Square, showing that Puzzles had a
recognised place in mental gymnastics four hundred years ago.
[Illustration]
No. II.--A SIMPLE MAGIC SQUARE
Much time was devoted in olden days to the construction and elaboration
of Magic Squares. Before we go more deeply into this fascinating
subject, let us study the following pretty and ingenious method of
making a Magic Square of sixteen numbers, which is comparatively simple,
and easily committed to memory:--
+--+--+--+--+
| 1|15|14| 4|
+--+--+--+--+
|12| 6| 7| 9|
+--+--+--+--+
| 8|10|11| 5|
+--+--+--+--+
|13| 3|2 |16|
+--+--+--+--+
Start with the small square at the top left-hand corner, placing there
the 1; then count continuously from left to right, square by square, but
only insert those numbers which fall upon the diagonals--namely, 4, 6,
7, 10, 11, 13, and 16.
Then start afresh at the bottom right-hand corner, calling it 1, and
fill up the remaining squares in order, from right to left, counting
continuously, and so placing in their turn 2, 3, 5, 8, 9, 12, 14, and
15. Each row, column, diagonal, and almost every cluster of four has 34
as the sum of its numbers.
No. III.--ANOTHER MAGIC SQUARE
+--+--+--+--+--+
| 1|20|16|23| 5|
+--+--+--+--+--+
|15| 7|12| 9|22|
+--+--+--+--+--+
|24|18|13| 8| 2|
+--+--+--+--+--+
| 4|17|14|19|11|
+--+--+--+--+--+
|21| 3|10| 6|25|
+--+--+--+--+--+
In this Magic Square the rows, columns, and diagonals add up to 65, and
the sum of any two opposite and corresponding squares is 26.
ENIGMAS
1
A MYSTIC ENIGMA
He stood himself beside himself
And looked into the sea;
Within himself he saw himself,
And at himself gazed he.
Now when himself he saw himself
Within himself go round,
Into himself he threw himself,
And in himself was drowned.
Now if he had not been himself,
But other beast beside,
He would himself have cut himself
Nor in himself have died.
No. IV.--A NEST OF CENTURIES
+--+--+--+--+--+--+--+
|22|47|16|41|10|35| 4|
+--+--+--+--+--+--+--+
| 5|23|48|17|42|11|29|
+--+--+--+--+--+--+--+
|30| 6|24|49|18|36|12|
+--+--+--+--+--+--+--+
|13|31| 7|25|43|19|37|
+--+--+--+--+--+--+--+
|38|14|32| 1|26|44|20|
+--+--+--+--+--+--+--+
|21|39| 8|33| 2|27|45|
+--+--+--+--+--+--+--+
|46|15|40| 9|34| 3|28|
+--+--+--+--+--+--+--+
The numbers in this Magic Square of 49 cells add up in all rows,
columns, and diagonals to 175. The four corner cells of every square or
rectangle that has cell 25 in its centre, and cells 1, 7, 49, 43, add up
to 100.
2
One morning Chloe, to avoid the heat,
Sat in a corner of a shady seat.
Young Strephon, on the self-same errand bound,
This fairest flower of all the garden found.
Her peerless beauty set his heart aflame,
Three monosyllables expressed his aim.
At a respectful distance he conversed
About the weather; then became immersed
In other topics, lessening the while
The space between them, heartened by her smile.
The same three simple words, now joined in one,
Expressed their happy state at set of sun.
No. V.--THE MAKING OF A MAGIC SQUARE
An ideal Magic Square can be constructed thus:
Place 1, 2, 3, 4, 5 in any order in the five top cells, set an asterisk
over the third column, as shown in the diagram; begin the next row with
this figure, and let the rest follow in the original sequence; continue
this method with the other three rows.
PREPARATORY SQUARE NO. 1.
*
+--+--+--+--+--+
| 1| 3| 5| 2| 4|
+--+--+--+--+--+
| 5| 2| 4| 1| 3|
+--+--+--+--+--+
| 4| 1| 3| 5| 2|
+--+--+--+--+--+
| 3| 5| 2| 4| 1|
+--+--+--+--+--+
| 2| 4| 1| 3| 5|
+--+--+--+--+--+
PREPARATORY SQUARE NO. 2.
*
+--+--+--+--+--+
| 5|15| 0|10|20|
+--+--+--+--+--+
|10|20| 5|15| 0|
+--+--+--+--+--+
|15| 0|10|20| 5|
+--+--+--+--+--+
|20| 5|15| 0|10|
+--+--+--+--+--+
| 0|10|20| 5|15|
+--+--+--+--+--+
Make a similar square of 25 cells with 0, 5, 10, 15, 20, as is shown in
No. 2, placing the asterisk in this case over the fourth column of
cells, and proceeding as before, in an unchanging sequence. Using these
two preparatory squares, try to form a Magic Square in which the same
number can be counted up in forty-two different ways.
No. VI.--ANOTHER WAY TO MAKE A MAGIC SQUARE
Here is one of many methods by which a Magic Square of the first
twenty-five numbers can readily be made.
+--+
| 1|
+--+--+--+
| 2| | 6|
+==+==+==+==+==+
∥ 3|20| 7|24|11∥
+--+--+--+--+--+--+--+
| 4∥16| 8|25|12| 4∥16|
+--+--+--+--+--+--+--+--+--+
| 5| ∥ 9|21|13| 5|17∥ |21|
+--+--+--+--+--+--+--+--+--+
|10∥22|14| 1|18|10∥22|
+--+--+--+--+--+--+--+
∥15| 2|19| 6|23∥
+==+==+==+==+==+
|20| |24|
+--+--+--+
|25|
+--+
This is done by first placing the figures from 1 to 25 in diagonal rows,
as is shown above, and then introducing the numbers that are _outside_
the square _into_ it, by moving each of them five places right, left,
up, or down. A Magic Square is thus formed, the numbers of which add up
to 65 in lines, columns and diagonals, and with the centre and any four
corresponding numbers on the borders.
No. VII.--A MONSTER MAGIC SQUARE
Here is what may indeed be called a Champion Magic Square:--
+---+---+---+---+---+---+---+---+---+---+---+
| 23|464|459|457|109|111|108|110|132|133|130|
+---+---+---+---+---+---+---+---+---+---+---+
| 25| 41|436|435|433|432|196|195|241|242|200|
+---+---+---+---+---+---+---+---+---+---+---+
| 27| 45| 13|474|469|467| 82| 81| 72| 90| 91|
+---+---+---+===+===+===+===+===+===+===+===+
|461| 55| 15∥ 34|450|449|447|446|156|157|180|
+---+---+---+---+---+---+---+---+---+---+---+
|456| 56| 17∥ 42| 3|484|479|477| 66| 65| 68|
+---+---+---+---+---+===+===+===+===+===+===+
|137|428|471∥ 41| 5∥127|126|125|361|362|363|
+---+---+---+---+---+---+===+===+===+===+===+
|153|431|466∥ 31| 7∥347∥148|338|339|145|143|
+---+---+---+---+---+---+---+---+---+---+---+
|154|439| 98∥453|481∥325∥161|169|168|318|319|
+---+---+---+---+---+---+---+---+---+---+---+
|384|266|407∥445|476∥292∥293|191|190|299|298|
+---+---+---+---+---+---+---+---+---+---+---+
|383|268|406∥442|424∥270∥280|272|273|211|210|
+---+---+---+---+---+---+---+---+---+---+---+
|379|265|392∥172| 60∥248∥227|250|251|230|232|
+---+---+---+---+---+---+---+---+---+---+---+
|378|267|391∥173| 59∥226∥249|228|229|252|254|
+---+---+---+---+---+---+---+---+---+---+---+
|351|282|405∥176| 74∥204∥214|206|207|277|276|
+---+---+---+---+---+---+---+---+---+---+---+
|350|263|390∥177| 73∥182∥192|301|300|189|187|
+---+---+---+---+---+---+---+---+---+---+---+
|334|199| 77∥330|423∥171∥315|323|322|164|165|
+---+---+---+---+---+---+---+---+---+---+---+
|333|216| 96∥311|413∥149∥346|147|146|340|341|
+---+---+---+---+---+---+===+===+===+===+===+
|100|221| 76∥310|414∥369|359|360|124|123|122|
+---+---+---+---+---+===+===+===+===+===+===+
| 99|223| 75∥291|483| 1| 6| 8|419|420|417|
+---+---+---+---+---+---+---+---+---+---+---+
|104|202| 97∥452| 35| 36| 38| 39|329|328|305|
+---+---+---+===+===+===+===+===+===+===+===+
|105|238|473| 11| 16| 18|403|404|393|395|394|
+---+---+---+---+---+---+---+---+---+---+---+
|136|438| 49| 50| 52| 53|289|290|244|243|285|
+---+---+---+---+---+---+---+---+---+---+---+
|463| 21| 26| 28|376|374|377|375|353|352|355|
+---+---+---+---+---+---+---+---+---+---+---+
+---+---+---+---+---+---+---+---+---+---+---+
|131|373|371|357|356|372|382|370|335| 30| 22|
+---+---+---+---+---+---+---+---+---+---+---+
|225|284|287|246|245|288|261| 51| 58| 47|460|
+---+---+---+---+---+---+---+---+---+---+---+
| 83|401|400|396|398|399|397| 20| 12|440|458|
+===+===+===+===+===+===+===+===+---+---+---+
|181|326|327|306|307| 44| 37| 33∥470|430| 24|
+---+---+---+---+---+---+---+---+---+---+---+
| 67|422|421|416|415| 10| 2|443∥468|429| 29|
+===+===+===+===+===+===+---+---+---+---+---+
|364|365|366|118|117|116∥480|444∥ 14| 57|348|
+===+===+===+===+===+---+---+---+---+---+---+
|342|142|344|345|139∥138∥478|454∥ 19| 54|332|
+---+---+---+---+---+---+---+---+---+---+---+
|320|321|163|162|324∥160∥ 4|32 ∥387| 46|331|
+---+---+---+---+---+---+---+---+---+---+---+
|297|186|185|184|302∥193∥ 9| 40∥ 78|219|101|
+---+---+---+---+---+---+---+---+---+---+---+
|209|208|278|279|205∥215∥ 61| 43∥ 79|217|102|
+---+---+---+---+---+---+---+---+---+---+---+
|231|233|256|257|258∥237∥425|313∥ 93|220|106|
+---+---+---+---+---+---+---+---+---+---+---+
|253|255|234|235|236∥259∥426|312∥ 94|218|107|
+---+---+---+---+---+---+---+---+---+---+---+
|275|274|212|213|271∥281∥411|309∥ 80|203|134|
+---+---+---+---+---+---+---+---+---+---+---+
|188|296|295|294|183∥303∥412|308∥ 95|222|135|
+---+---+---+---+---+---+---+---+---+---+---+
|166|167|317|316|170∥314∥ 62|155∥408|286|151|
+---+---+---+---+---+---+---+---+---+---+---+
|144|343|141|140|337∥336∥ 72|174∥389|269|152|
+===+===+===+===+===+---+---+---+---+---+---+
|121|120|119|367|368|358∥ 71|175∥409|264|385|
+===+===+===+===+===+===+---+---+---+---+---+
|418| 63| 64| 69| 70|475|482|194∥410|262|386|
+---+---+---+---+---+---+---+---+---+---+---+
|304|159|158|179|178|441|448|451∥388|283|381|
+===+===+===+===+===+===+===+===+---+---+---+
|402| 84| 85| 89| 87| 86| 88|465|472|247|380|
+---+---+---+---+---+---+---+---+---+---+---+
|260|201|198|239|240|197|224|434|427|437|349|
+---+---+---+---+---+---+---+---+---+---+---+
|354|112|114|128|129|113|103|115|150|455|462|
+---+---+---+---+---+---+---+---+---+---+---+
Its 484 cells form, as they are numbered, a Magic Square, in which all
rows, columns, and diagonals add up to 5335, and it is no easy matter to
determine in how many other symmetrical ways its key-number can be
found.
When the cells outside each of the dark border lines are removed, three
other perfect Magic Squares remain.
Collectors should take particular note of this masterpiece.
No. VIII.--A NOVEL MAGIC SQUARE
A Magic Square of nine cells can be built up by taking any number
divisible by 3, and placing, as a start, its third in the central cell.
Thus:--
+--+--+--+
|28|29|24|
+--+--+--+
|23|27|31|
+--+--+--+
|30|25|26|
+--+--+--+
Say that 81 is chosen for the key number. Place 27 in the centre; 28,
29, in cells 1, 2; 30 in cell 7; 31 in 6; and then fill up cells 3, 4,
8, and 9 with the numbers necessary to make up 81 in each row, column,
and diagonal.
Any number above 14 that is divisible by 3 can be dealt with in this
way.
3
Enriched I am with much that’s fat,
Yet money I possess not;
Enlightening all who come to me,
True wisdom I express not.
I may be wicked, but protest
That sinful none have found me;
Though I destroy myself to be
Of use to those around me.
No. IX.--TWIN MAGIC SQUARES
Among the infinite number of Magic Squares which can be constructed, it
would be difficult to find a more remarkable setting of the numbers 1 to
32 inclusive than this, in which two squares, each of 16 cells, are
perfect twins in characteristics and curious combinations.
+--+--+--+--++--+--+--+--+
| 1| 8|29|28||11|14|23|18|
+--+--+--+--++--+--+--+--+
|30|27| 2| 7||21|20| 9|16|
+--+--+--+--++--+--+--+--+
| 4| 5|32|25||10|15|22|19|
+--+--+--+--++--+--+--+--+
|31|26| 3| 6||24|17|12|13|
+--+--+--+--++--+--+--+--+
There are at least forty-eight different ways in which 66 is the sum of
four of these numbers. Besides the usual rows, columns, and diagonals,
any square group of four, both corner sets, all opposite pairs on the
outer cells, and each set of corresponding cells next to the corners,
add up exactly to 66.
4
Of Spanish extraction, my hue
Is as dark as a negro can be;
I am solid, and yet it is true
That in part I am wet as the sea,
My second and first are the same
In all but condition and name;
My second can burst
The abode of my first,
And my whole from the underground came.
No. X.--A BORDERED MAGIC SQUARE
Here is a notable specimen of a Magic Square:--
+--+--+--+--+--+--+--+
| 4| 5| 6|43|39|38|40|
+--+==+==+==+==+==+--+
|49∥15|16|33|30|31∥ 1|
+--+--+==+==+==+--+--+
|48∥37∥22|27|26∥13∥ 2|
+--+--+--+==+--+--+--+
|47∥36∥29∥25∥21∥14∥ 3|
+--+--+--+==+--+--+--+
| 8∥18∥24|23|28∥32∥42|
+--+--+==+==+==+--+--+
| 9∥19|34|17|20|35∥41|
+--+==+==+==+==+==+--+
|10|45|44| 7|11|12|46|
+--+--+--+--+--+--+--+
The rows, columns, and diagonals all add up to exactly 175 in the full
square. Strip off the outside cells all around, and a second Magic
Square remains, which adds up in all such ways to 125.
Strip off another border, as is again indicated by the darker lines, and
a third Magic Square is left, which adds up to 75.
5
AN OLD ENIGMA
BY HANNAH MORE
I’m a strange contradiction: I’m new and I’m old,
I’m sometimes in tatters and sometimes in gold,
Though I never could read, yet letter’d I’m found,
Though blind I enlighten, though free I am bound.
I’m English, I’m German, I’m French, and I’m Dutch;
Some love me too dearly, some slight me too much.
I often die young, though I sometimes live ages,
And no Queen is attended by so many pages.
No. XI.--A LARGER BORDERED MAGIC SQUARE
Here is another example of what is called a “bordered” Magic Square:--
+--+--+--+--+--+--+--+--+--+
| 5|80|59|73|61| 3|63|12|13|
+--+==+==+==+==+==+==+==+--+
| 1∥20|55|30|57|28|71|26∥81|
+--+--+==+==+==+==+==+--+--+
| 4∥14∥31|50|29|60|35∥68∥78|
+--+--+--+==+==+==+--+--+--+
|76∥58∥46∥38|45|40∥36∥24∥ 6|
+--+--+--+--+--+--+--+--+--+
| 7∥65∥33∥43|41|39∥49∥17∥75|
+--+--+--+--+--+--+--+--+--+
|74∥64∥48∥42|37|44∥31∥18∥ 8|
+--+--+--+==+==+==+--+--+--+
|67∥10∥47|32|53|22|51∥72∥15|
+--+--+==+==+==+==+==+--+--+
|66∥56|27|52|25|54|11|62∥16|
+--+==+==+==+==+==+==+==+--+
|69| 2|23| 9|21|79|19|70|77|
+--+--+--+--+--+--+--+--+--+
These 81 cells form a complete magic square, in which rows, columns, and
diagonals add up to 369. As each border is removed fresh Magic Squares
are formed, of which the distinctive numbers are 287, 205, and 123. The
central 41 is in every case the greatest common divisor.
No. XII.--A CENTURY OF CELLS
Can you complete this Magic Square, so that the rows, columns, and
diagonals add up in every case to 505?
+----+----+----+----+----+----+----+----+----+-----+
|_91_| _2_| _3_|_97_| _6_|_95_|_94_| _8_| _9_|_100_|
+----+----+----+----+----+----+----+----+----+-----+
|_20_| | | |_16_|_15_| | | | _81_|
+----+----+----+----+----+----+----+----+----+-----+
|_21_| | | |_25_|_26_| | | | _30_|
+----+----+----+----+----+----+----+----+----+-----+
|_60_| | | |_66_|_65_| | | | _41_|
+----+----+----+----+----+----+----+----+----+-----+
|_50_|_49_|_48_|_57_|_55_|_56_|_54_|_43_|_42_| _51_|
+----+----+----+----+----+----+----+----+----+-----+
|_61_|_59_|_58_|_47_|_45_|_46_|_44_|_53_|_52_| _40_|
+----+----+----+----+----+----+----+----+----+-----+
|_31_| | | |_35_|_36_| | | | _70_|
+----+----+----+----+----+----+----+----+----+-----+
|_80_| | | |_75_|_76_| | | | _71_|
+----+----+----+----+----+----+----+----+----+-----+
|_90_| | | |_86_|_85_| | | | _11_|
+----+----+----+----+----+----+----+----+----+-----+
| _1_|_99_|_98_| _4_|_96_| _5_| _7_|_93_|_92_| _10_|
+----+----+----+----+----+----+----+----+----+-----+
We have given you a substantial start, and, as a further hint, as all
the numbers in the first and last columns end in 0 or 1, so in the two
next columns all end in 2 or 9, in the two next in 3 or 8, in the two
next in 4 or 7, and in the two central columns in 5 or 6.
6
HALLAM’S UNSOLVED ENIGMA
I sit on a rock while I’m raising the wind,
But the storm once abated I’m gentle and kind.
I’ve Kings at my feet, who await but my nod
To kneel in the dust on the ground I have trod.
Though seen to the world, I am known to but few,
The Gentile detests me, I’m pork to the Jew.
I never have passed but one night in the dark,
And that was with Noah alone in the ark.
My weight is three pounds, my length is a mile.
And when I’m discovered you’ll say, with a smile,
That my first and my last are the pride of this isle.
No. XIII.--A SINGULAR MAGIC SQUARE
In this Magic Square, not only do the rows, columns, and diagonals add
up to 260, but this same number is produced in three other and quite
unusual ways:--
+--+--+--+--+--+--+--+--+
|18|63| 4|61| 6|59| 8|41|
+--+--+--+--+--+--+--+--+
|49|32|51|14|53|12|39|10|
+--+--+--+--+--+--+--+--+
| 2|47|36|45|22|27|24|57|
+--+--+--+--+--+--+--+--+
|33|16|35|46|21|28|55|26|
+--+--+--+--+--+--+--+--+
|31|50|29|20|43|38| 9|40|
+--+--+--+--+--+--+--+--+
|64|17|30|19|44|37|42| 7|
+--+--+--+--+--+--+--+--+
|15|34|13|52|11|54|25|56|
+--+--+--+--+--+--+--+--+
|48| 1|62| 3|60| 5|58|23|
+--+--+--+--+--+--+--+--+
(1) Each group of 8 numbers, ranged in a circle round the centre; there
are six of these, of which the smallest is 22, 28, 38, 44, 19, 29, 35,
45, and the largest is 8, 10, 56, 58, 1, 15, 49, 63. (2) The sum of the
4 central numbers and 4 corners. (3) The diagonal cross of 4 numbers in
the middle of the board.
No. XIV.--SQUARING THE YEAR
On another page we give an interesting Magic Square of 121 cells based
upon the figures of the year 1892. Here, in much more condensed form, is
one more up to date.
+---+---+---+
|637|630|635|
+---+---+---+
|632|634|636|
+---+---+---+
|633|638|631|
+---+---+---+
The rows, columns, and diagonals of these nine cells add up in all cases
to the figures of the year 1902.
The central 634 is found by dividing 1902 by its lowest factor greater
than 2, and this is taken as the middle term of nine numbers, which are
thus arranged to form a Magic Square.
7
RANK TREASON
BY AN IRISH REBEL, 1798
The pomps of Courts and pride of Kings
I prize above all earthly things;
I love my country, but the King
Above all men his praise I sing.
The royal banners are displayed,
And may success the standard aid!
I fain would banish far from hence
The “Rights of Men” and “Common Sense;”
Confusion to his odious reign,
That Foe to princes, Thomas Payne.
Defeat and ruin seize the cause
Of France, its liberties and laws!
Where does the treason come in?
No. XV.--SQUARING ANOTHER YEAR
The following square of numbers is interesting in connection with the
year 1906.
+------+------+------+------+
|_A_ |_B_ |_C_ |_D_ |
| _476_| _469_| _477_| _484_|
+------+------+------+------+
|_E_ |_F_ |_G_ |_H_ |
| _483_| _478_| _470_| _475_|
+------+------+------+------+
|_I_ |_J_ |_K_ |_L_ |
| _471_| _474_| _482_| _479_|
+------+------+------+------+
|_M_ |_N_ |_O_ |_P_ |
| _480_| _481_| _473_| _472_|
+------+------+------+------+
Add the rows --ABCD, EFGH, IJKL, MNOP.
or the squares --ABEF, CDGH, IJMN, KLOP.
or semi-diagonals--AFIN, BEJM, CHKP, DGLO,
AFCH, BEGD, INKP, MJOL.
and the sum, in every case, is 1906.
No. XVI.--MANIFOLD MAGIC SQUARES
Here is quite a curious nest of clustered Magic Squares, which is worth
preserving:--
+--+--+--+--+--+--+--+--+--+--+--+
| 2|13|24|10|16| 2|13|24|10|16| 2|
+--+--+--+--+--+--+--+--+--+--+--+
| 9|20| 1|12|23| 9|20| 1|12|23| 9|
+--+--+--+--+--+==+==+==+==+==+--+
|11|22| 8|19| 5∥11|22| 8|19| 5∥11|
+--+--+--+--+--+--+--+--+--+--+--+
|18| 4|15|21| 7∥18| 4|15|21| 7∥18|
+--+--+--+--+--+--+--+--+--+--+--+
|25| 6|17| 3|14∥25| 6|17| 3|14∥25|
+--+--+--+--+--+--+--+--+--+--+--+
| 2|13|24|10|16∥ 2|13|24|10|16∥ 2|
+--+--+==+==+==+==+==+--+--+--+--+
| 9|20∥ 1|12|23∥ 9|20∥ 1|12|23∥ 9|
+--+--+--+--+--+==+==+==+==+==+--+
|11|22∥ 8|19| 5|11|22∥ 8|19| 5|11|
+--+--+--+--+--+--+--+--+--+--+--+
|18| 4∥15|21| 7|18| 4∥15|21| 7|18|
+--+--+--+--+--+--+--+--+--+--+--+
|25| 6∥17| 3|14|25| 6∥17| 3|14|25|
+--+--+--+--+--+--+--+--+--+--+--+
| 2|13∥24|10|16| 2|13∥24|10|16| 2|
+--+--+==+==+==+==+==+--+--+--+--+
| 9|20| 1|12|23| 9|20| 1|12|23| 9|
+--+--+--+--+--+--+--+--+--+--+--+
|11|22| 8|19| 5|11|22| 8|19| 5|11|
+--+--+--+--+--+--+--+--+--+--+--+
Every square of every possible combination of 25 of these numbers in
their cells, such as the two with darker borders, is a perfect Magic
Square, with rows, columns, and diagonals that add up in all cases to
65.
8
AN ENIGMA FOR CHRISTMAS HOLIDAYS
Formed half beneath and half above the earth,
We owe, as twins, to art our second birth.
The smith’s and carpenter’s adopted daughters,
Made upon earth, we travel on the waters.
Swifter we move as tighter we are bound,
Yet never touch the sea, or air, or ground.
We serve the poor for use, the rich for whim,
Sink if it rains, and if it freezes swim.
No. XVII.--LARGER AUXILIARY MAGIC SQUARES
A very interesting method of constructing a Magic Square is shown in
these three diagrams:--
+---+---+---+---+---+---+---+---+---+---+---+
| 1| 2| 3| 4| 5| 6| 7| 8| 9| 10| 11|
+---+---+---+---+---+---+---+---+---+---+---+
| 3| 4| 5| 6| 7| 8| 9| 10| 11| 1| 2|
+---+---+---+---+---+---+---+---+---+---+---+
| 5| 6| 7| 8| 9| 10| 11| 1| 2| 3| 4|
+---+---+---+---+---+---+---+---+---+---+---+
| 7| 8| 9| 10| 11| 1| 2| 3| 4| 5| 6|
+---+---+---+---+---+---+---+---+---+---+---+
| 9| 10| 11| 1| 2| 3| 4| 5| 6| 7| 8|
+---+---+---+---+---+---+---+---+---+---+---+
| 11| 1| 2| 3| 4| 5| 6| 7| 8| 9| 10|
+---+---+---+---+---+---+---+---+---+---+---+
| 2| 3| 4| 5| 6| 7| 8| 9| 10| 11| 1|
+---+---+---+---+---+---+---+---+---+---+---+
| 4| 5| 6| 7| 8| 9| 10| 11| 1| 2| 3|
+---+---+---+---+---+---+---+---+---+---+---+
| 6| 7| 8| 9| 10| 11| 1| 2| 3| 4| 5|
+---+---+---+---+---+---+---+---+---+---+---+
| 8| 9| 10| 11| 1| 2| 3| 4| 5| 6| 7|
+---+---+---+---+---+---+---+---+---+---+---+
| 10| 11| 1| 2| 3| 4| 5| 6| 7| 8| 9|
+---+---+---+---+---+---+---+---+---+---+---+
+---+---+---+---+---+---+---+---+---+---+---+
| 0| 11| 22| 33| 44| 55| 66| 77| 88| 99|110|
+---+---+---+---+---+---+---+---+---+---+---+
| 33| 44| 55| 66| 77| 88| 99|110| 0| 11| 22|
+---+---+---+---+---+---+---+---+---+---+---+
| 66| 77| 88| 99|110| 0| 11| 22| 33| 44| 55|
+---+---+---+---+---+---+---+---+---+---+---+
| 99|110| 0| 11| 22| 33| 44| 55| 66| 77| 88|
+---+---+---+---+---+---+---+---+---+---+---+
| 11| 22| 33| 44| 55| 66| 77| 88| 99|110| 0|
+---+---+---+---+---+---+---+---+---+---+---+
| 44| 55| 66| 77| 88| 99|110| 0| 11| 22| 33|
+---+---+---+---+---+---+---+---+---+---+---+
| 77| 88| 99|110| 0| 11| 22| 33| 44| 55| 66|
+---+---+---+---+---+---+---+---+---+---+---+
|110| 0| 11| 22| 33| 44| 55| 66| 77| 88| 99|
+---+---+---+---+---+---+---+---+---+---+---+
| 22| 33| 44| 55| 66| 77| 88| 99|110| 0| 11|
+---+---+---+---+---+---+---+---+---+---+---+
| 55| 66| 77| 88| 99|110| 0| 11| 22| 33| 44|
+---+---+---+---+---+---+---+---+---+---+---+
| 88| 99|110| 0| 11| 22| 33| 44| 55| 66| 77|
+---+---+---+---+---+---+---+---+---+---+---+
+---+---+---+---+---+---+---+---+---+---+---+
| 1| 13| 25| 37| 49| 61| 73| 85| 97|109|121|
+---+---+---+---+---+---+---+---+---+---+---+
| 36| 48| 60| 72| 84| 96|108|120| 11| 12| 24|
+---+---+---+---+---+---+---+---+---+---+---+
| 71| 83| 95|107|119| 10| 22| 23| 35| 47| 59|
+---+---+---+---+---+---+---+---+---+---+---+
|106|118| 9| 21| 33| 34| 46| 58| 70| 82| 94|
+---+---+---+---+---+---+---+---+---+---+---+
| 20| 32| 44| 45| 57| 69| 81| 93|105|117| 8|
+---+---+---+---+---+---+---+---+---+---+---+
| 55| 56| 68| 80| 92|104|116| 7| 19| 31| 43|
+---+---+---+---+---+---+---+---+---+---+---+
| 79| 91|103|115| 6| 18| 30| 42| 54| 66| 67|
+---+---+---+---+---+---+---+---+---+---+---+
|114| 5| 17| 29| 41| 53| 65| 77| 78| 90|102|
+---+---+---+---+---+---+---+---+---+---+---+
| 28| 40| 52| 64| 76| 88| 89|101|113| 4| 16|
+---+---+---+---+---+---+---+---+---+---+---+
| 63| 75| 87| 99|100|112| 3| 15| 27| 39| 51|
+---+---+---+---+---+---+---+---+---+---+---+
| 98|110|111| 2| 14| 26| 38| 50| 62| 74| 86|
+---+---+---+---+---+---+---+---+---+---+---+
It will be noticed that each row after the first, in the two upper
auxiliary squares, begins with a number from the same column in the row
above it, and maintains the same sequence of numbers. When the
corresponding cells of these two squares are added together, and placed
in the third square, a Magic Square is formed, in which 671 is the sum
of all rows, columns, and diagonals.
No. XVIII.--SQUARING BY ANNO DOMINI
Here is a curious form of Magic Square. The year 1892 is taken as its
basis.
+---+---+---+---+---+---+---+---+---+---+---+
|112|124|136|148|160|172|184|196|208|220|232|
+---+---+---+---+---+---+---+---+---+---+---+
|147|159|171|183|195|207|219|231|122|123|135|
+---+---+---+---+---+---+---+---+---+---+---+
|182|194|206|218|230|121|133|134|146|158|170|
+---+---+---+---+---+---+---+---+---+---+---+
|217|229|120|132|144|145|157|169|181|193|205|
+---+---+---+---+---+---+---+---+---+---+---+
|131|143|155|156|168|180|192|204|216|228|119|
+---+---+---+---+---+---+---+---+---+---+---+
|166|167|179|191|203|215|227|118|130|142|154|
+---+---+---+---+---+---+---+---+---+---+---+
|190|202|214|226|117|129|141|153|165|177|178|
+---+---+---+---+---+---+---+---+---+---+---+
|225|116|128|140|152|164|176|188|189|201|213|
+---+---+---+---+---+---+---+---+---+---+---+
|139|151|163|175|187|199|200|212|224|115|127|
+---+---+---+---+---+---+---+---+---+---+---+
|174|186|198|210|211|223|114|126|138|150|162|
+---+---+---+---+---+---+---+---+---+---+---+
|209|221|222|113|125|137|149|161|173|185|197|
+---+---+---+---+---+---+---+---+---+---+---+
Within this square 1892 can be counted up in all the usual ways, and
altogether in 44 variations. Thus any two rows that run parallel to a
diagonal, and have between them eleven cells, add up to this number, if
they are on opposite sides of the diagonal.
9
The sun, the sun is my delight!
I shun a gloomy day,
Though I am often seen at night
To dart across the way.
Sometimes you see me climb a wall
As nimble as a cat,
Then down into a pit I fall
Like any frightened rat.
Catch me who can--woman or man--
None have succeeded who after me ran.
No. XIX.--A MAGIC SQUARE OF SEVEN
+----+
| _1_|
+----+----+----+
| _8_| | _2_|
+----+----+----+----+----+
|_15_| | _9_| | _3_|
+====+====+====+====+====+====+====+
∥_22_|_47_|_16_|_41_|_10_|_35_| _4_∥
+----+----+----+----+----+----+----+----+----+
|_29_∥ _5_|_23_|_48_|_17_|_42_|_11_|_29_∥ _5_|
+----+----+----+----+----+----+----+----+----+----+----+
|_36_| ∥_30_| _6_|_24_|_49_|_18_|_36_|_12_∥ | _6_|
+----+----+----+----+----+----+----+----+----+----+----+----+----+
|_43_| |_37_∥_13_|_31_| _7_|_25_|_43_|_19_|_37_∥_13_| | _7_|
+----+----+----+----+----+----+----+----+----+----+----|----+----+
|_44_| ∥_38_|_14_|_32_| _1_|_26_|_44_|_20_∥ |_14_|
+----+----+----+----+----+----+----+----+----+----+----+
|_45_∥_21_|_39_| _8_|_33_| _2_|_27_|_45_∥_21_|
+----+----+----+----+----+----+----+----+----+
∥_46_|_15_|_40_| _9_|_34_| _3_|_28_∥
+====+====+====+====+====+====+====+
|_47_| |_41_| |_35_|
+----+----+----+----+----+
|_48_| |_42_|
+----+----+----+
|_49_|
+----+
This Magic Square of 49 cells is constructed with a diagonal arrangement
of the numbers from 1 to 49 in their proper order. Those that fall
outside the central square are written into it in the seventh cell
inwards from where they stand. It is interesting to find out the many
combinations in which the number 175 is made up.
10
WHAT MOVED HIM?
I grasped it, meaning nothing wrong,
And moved to meet my friend,
When lo! the stalwart man and strong
At once began to bend.
The biped by the quadruped
No longer upright stood,
But bowed the knee and bent his head
Before the carved wood.
No. XX.--CURIOUS SQUARES
These are two interesting Magic Squares found on an antique gong, at
Caius College, Cambridge:--
+--+--+--+ +--+--+--+
| 6|13| 8| | 7|14| 9|
+--+--+--+ +--+--+--+
|11| 9| 7| |12|20| 8|
+--+--+--+ +--+--+--+
|10| 5|12| |11| 6|13|
+--+--+--+ +--+--+--+
In the one nine numbers are so arranged that they count up to 27 in
every direction; and in the other the outer rows total 30, while the
central rows and diagonals make 40.
11
RINGING THE CHANGES
My figure, singular and slight,
Measures but half enough at sight.
I rode the waters day and night.
I tell the new in Time’s quick flight,
Or how old ages rolled in might.
Cut off my tail, it still is on!
Put on my head, and there is none!
No. XXI.--A MOORISH MAGIC SQUARE
Among Moorish Mussulmans 78 is a mystic number.
+--+--+--+--+
|40|10|20| 8|
+--+--+--+--+
| 7|21| 9|41|
+--+--+--+--+
|12|42| 6|18|
+--+--+--+--+
|19| 5|43|11|
+--+--+--+--+
Here is a cleverly-constructed Magic Square, to which this number is the
key.
The number 78 can be arrived at in twenty-three different
combinations--namely, ten rows, columns, or diagonals; four corner
squares of four cells; one central square of four cells; the four corner
cells; two sets of corresponding diagonal cells next to the corners; and
two sets of central cells on the top and bottom rows, and on the outside
columns.
No. XXII.--A CHOICE MAGIC SQUARE
Here is a Magic Square of singular charm:--
+==+==+==+==+==+==+==+==+==+
|31|36|29∥76|81|74∥13|18|11|
+--+--+--+--+--+--+--+--+--+
|30|32|34∥75|77|79∥12|14|16|
+--+--+--+--+--+--+--+--+--+
|35|28|33∥80|73|78∥17|10|15|
+==+==+==+==+==+==+==+==+==+
|22|27|20∥40|45|38∥58|63|56|
+--+--+--+--+--+--+--+--+--+
|21|23|25∥39|41|43∥57|59|61|
+--+--+--+--+--+--+--+--+--+
|26|19|24∥44|37|42∥62|55|60|
+==+==+==+==+==+==+==+==+==+
|67|72|65∥ 4| 9| 2∥49|54|47|
+--+--+--+--+--+--+--+--+--+
|66|68|70∥ 3| 5| 7∥48|50|52|
+--+--+--+--+--+--+--+--+--+
|71|64|69∥ 8| 1| 6∥53|46|51|
+==+==+==+==+==+==+==+==+==+
The 81 cells of this remarkable square are divided by parallel lines
into 9 equal parts, each made up of 9 consecutive numbers, and each a
Magic Square in itself within the parent square. Readers can work out
for themselves the combinations in the larger square and in the little
ones.
12
CANNING’S ENIGMA
There is a noun of plural number,
Foe to peace and tranquil slumber.
Now almost any noun you take
By adding “s” you plural make.
But if you add an “s” to this
Strange is the metamorphosis.
Plural is plural now no more,
And sweet what bitter was before.
XXIII.--THE TWIN PUZZLE SQUARES
+-+-+-+ +-+-+-+
|1|2|3| | |2|3|
+-+-+-+ +-+-+-+
| |5|6+====+4|5| |
+-+-+-+ +-+-+-+
|7|8| | |7|8|9|
+-+-+-+ +-+-+-+
Fill each square by repeating two of its figures in the vacant cells.
Then rearrange them all, so that the sums of the corresponding rows in
each square are equal, and the sums of the squares of the corresponding
cells of these rows are also equal; and so that the sums of the four
diagonals are equal, and the sum of the squares of the cells in
corresponding diagonals are equal.
13
There is an old-world charm about this Enigma:--
In the ears of young and old
I repeat what I am told;
And they hear me, old and young,
Though I have no busy tongue.
When a thunder-clap awakes me
Not a touch of terror takes me;
Yet so tender is my ear
That the softest sound I fear.
Call me not with bated breath,
For a whisper is my death.
No: XXIV.--MAGIC FRACTIONS
Here is an arrangement of fractions which form a perfect Magic Square:--
+-------+-------+-------+
| _³⁄₈_ | _⁵⁄₁₂_| _⁵⁄₂₄_|
+-------+-------+-------+
| _¹⁄₆_ | _¹⁄₃_ | _¹⁄₂_ |
+-------+-------+-------+
|_¹¹⁄₂₄_| _¹⁄₄_ | _⁷⁄₂₄_|
+-------+-------+-------+
If these fractions are added together in any one of the eight
directions, the result in every case is unity. Thus ³⁄₈ + ¹⁄₃ + ⁷⁄₂₄ =
1, ¹⁄₆ + ¹⁄₃ + ¹⁄₂ = 1, and so on throughout the rows, columns, and
diagonals.
14
“DOUBLE, DOUBLE, TOIL AND TROUBLE!”
“By hammer and hand
All arts do stand”--
So says an ancient saw;
But hammer and hand
Will work or stand
By my unwritten law.
Behold me, as sparks from the anvils fly,
But fires lie down at my bitter cry.
No. XXV.--MORE MAGIC FRACTIONS
We are indebted to a friend for the following elaborate Magic Square of
fractions, on the lines of that on the preceding page.
+-------+-------+-------+-------+-------+
|_¹⁹⁄₈₀_| _⁷⁄₂₀_| _¹⁄₄₀_|_¹¹⁄₈₀_| _¹⁄₄_ |
+-------+-------+-------+-------+-------+
|_¹³⁄₄₀_| _¹⁄₈_ | _⁹⁄₈₀_| _⁹⁄₄₀_|_¹⁷⁄₈₀_|
+-------+-------+-------+-------+-------+
| _¹⁄₁₀_| _⁷⁄₈₀_| _¹⁄₅_ | _⁵⁄₁₆_| _³⁄₁₀_|
+-------+-------+-------+-------+-------+
| _³⁄₁₆_| _⁷⁄₄₀_|_²³⁄₈₀_|_¹¹⁄₄₀_| _³⁄₄₀_|
+-------+-------+-------+-------+-------+
| _³⁄₂₀_|_²¹⁄₈₀_| _³⁄₈_ | _¹⁄₂₀_|_¹³⁄₈₀_|
+-------+-------+-------+-------+-------+
The composer claims that there are at least 160 combinations of 5 cells
in which these fractions add up to unity, including, of course, the
usual rows, columns, and diagonals.
15
Two brothers wisely kept apart,
Together ne’er employed;
Though to one purpose we are bent
Each takes a different side.
We travel much, yet prisoners are,
And close confined to boot,
Can with the fleetest horse keep pace,
Yet always go on foot.
No. XXVI.--A MAGIC OBLONG
On similar lines to Magic Squares, but as a distinct variety, we give
below a specimen of a Magic Oblong.
+--+--+--+--+--+--+--+--+
| 1|10|11|29|28|19|18|16|
+--+--+--+--+--+--+--+--+
| 9| 2|30|12|20|27| 7|25|
|--+--+--+--+--+--+--+--|
|24|31| 3|21|13| 6|26| 8|
|--+--+--+--+--+--+--+--|
|32|23|22| 4| 5|14|15|17|
+--+--+--+--+--+--+--+--+
The four rows of this Oblong add up in each case to 132, and its eight
columns to 66. Two of its diagonals, from 10 to 5 and from 28 to 23,
also total 66, as do the four squares at the right-hand ends of the top
and bottom double rows.
16
My name declares my date to be
The morning of a Christian year;
And motherless, as all agree,
And yet a mother, too, ’tis clear.
A father, too, which none dispute,
And when my son comes I’m a fruit.
And, not to puzzle overmuch,
’Twas I took Holland for the Dutch.
17
My head is ten times ten,
My body is but one.
Add just five hundred more, and then
My history is done.
Although I own no royal throne,
Throughout the sunny South in fame I stand alone.
No. XXVII.--A MAGIC CUBE
Much more complicated than the Magic Square is the Magic Cube.
First Layer from Top.
+---+---+---+---+---+
|121| 27| 83| 14| 70|
+---+---+---+---+---+
| 10| 61|117| 48| 79|
+---+---+---+---+---+
| 44|100| 1| 57|113|
+---+---+---+---+---+
| 53|109| 40| 91| 22|
+---+---+---+---+---+
| 87| 18| 74|105| 31|
+---+---+---+---+---+
Second Layer from Top.
+---+---+---+---+---+
| 2 | 58|114| 45| 96|
+---+---+---+---+---+
| 36| 92| 23| 54|110|
+---+---+---+---+---+
| 75|101| 32| 88| 19|
+---+---+---+---+---+
| 84| 15| 66|122| 28|
+---+---+---+---+---+
|118| 49| 80| 6| 62|
+---+---+---+---+---+
Third Layer from Top.
+---+---+---+---+---+
| 33| 89| 20| 71|102|
+---+---+---+---+---+
| 67|123| 29| 85| 11|
+---+---+---+---+---+
| 76| 7| 63|119| 50|
+---+---+---+---+---+
|115| 41| 97| 3| 59|
+---+---+---+---+---+
| 24| 55|106| 37| 93|
+---+---+---+---+---+
Fourth Layer from Top.
+---+---+---+---+---+
| 64|120| 46| 77| 8|
+---+---+---+---+---+
| 98| 4| 60|111| 42|
+---+---+---+---+---+
|107| 38| 94| 25| 51|
+---+---+---+---+---+
| 16| 72|103| 34| 90|
+---+---+---+---+---+
| 30| 81| 12| 68|124|
+---+---+---+---+---+
Lowest Layer.
+---+---+---+---+---+
| 95| 21| 52|108| 39|
+---+---+---+---+---+
|104| 35| 86| 17| 73|
+---+---+---+---+---+
| 13| 69|125| 26| 82|
+---+---+---+---+---+
| 47| 78| 9| 65|116|
+---+---+---+---+---+
| 56|112| 43| 99| 5|
+---+---+---+---+---+
Those who enjoy such feats with figures will find it interesting to work
out the many ways in which, when the layers are placed one upon another,
and form a cube, the number 315 is obtained by adding together the
cell-numbers that lie in lines in the length, breadth, and thickness of
the cube.
18
Sad offspring of a blighted race,
Pale Sorrow was my mother;
I’ve never seen the smiling face
Of sister or of brother.
Of all the saddest things on earth,
There’s none more sad than I,
No heart rejoices at my birth.
And with a breath I die!
No. XXVIII.--A MAGIC CIRCLE
The Magic Circle below has this particular property:--
32
61 94
52 38
191 4
+
28 193
26 44
98 67
16
The 14 numbers ranged in smaller circles within its circumference are
such that the sum of the squares of any adjacent two of them is equal to
the sum of the squares of the pair diametrically opposite.
19
Add a hundred and nothing to ten,
And the same to a hundred times more,
Catch a bee, send it after them, then
Make an end of a fop and a bore.
No. XXIX.--MAGIC CIRCLE OF CIRCLES
We have had some good specimens of Magic Squares. Here is a very curious
and most interesting Magic Circle, in which particular numbers, from 12
to 75 inclusive, are arranged in 8 concentric circular spaces and in 8
radiating lines, with the central 12 common to them all.
57 24 15 14
31 71 64 72
48 17 22 23
38 69 66 65
50 19 20 21
36 60 75 67
59 26 13 12
29 12 12 74
12 12
+
12 12
42 12 12 61
44 45 58 27
35 43 28 68
53 52 51 18
33 34 37 70
55 54 49 16
40 32 39 63
46 47 56 25
41 30
The sum of all the numbers in any of the concentric circular spaces,
with the 12, is 360, which is the number of degrees in a circle.
The sum of the numbers in each radiating line with the 12, is also 360.
The sum of the numbers in the upper or lower half of any of the circular
spaces, with half of 12, is 180, the degrees of a semi-circle.
The sum of any outer or inner four of the numbers on the radiating
lines, with the half of 12, is also 180.
No. XXX.--THE UNIQUE TRIANGLE
In the following triangle, if two couples of the figures on opposite
sides are transposed, the sums of the sides become equal, and also the
sums of the squares of the numbers that lie along the sides. Which are
the figures that must be transposed?
/\
/ \
/ 5 \
/ \
/ 4 6 \
/ \
/ 3 7 \
/ \
/ 2 1 9 0 \
------------------
20
They did not climb in hope of gain,
But at stern duty’s call;
They were united in their aim,
Divided in their fall.
21
Forsaken in some desert vast,
Where never human being dwelt,
Or on some lonely island cast,
Unseen, unheard, I still am felt.
Brimful of talent, sense, and wit,
I cannot speak or understand;
I’m out of sight in Church, and yet
Grace many temples in the land.
No. XXXI.--MAGIC TRIANGLES
Here is a nest of concentric triangles. Can you arrange the first 18
numbers at their angles, and at the centres of their sides, so that they
count 19, 38, or 57 in many ways, down, across, or along some angles?
[Illustration]
This curiosity is found in an old document of the Mathematical Society
of Spitalfields, dated 1717.
22
Allow me, pray, to go as first,
And then as number two;
Then after these, why, there you are,
To follow as is due.
But lest you never guess this queer
And hyperbolic fable,
Pray let there follow after that
Whatever may be able.
No. XXXII.--TWIN TRIANGLES
The numbers outside these twin triangles give the sum of the squares of
the four figures of the adjacent sides:--
/\
/ \
/ 7 \
/ \
135 / 2 3 \ 99
/ . . \
/ 9 . . 5 \
/ . . \
/ 1 8 6 4 \
------------------
. 117 .
. .
. .
. .
..
. .
. .
. .
. 137 .
------------------
\ 6 4 2 9 /
\ . . /
\ 5 . . 1 /
\ . . /
119 \ 7 8 / 155
\ /
\ 3 /
\ /
\/
The twins are also closely allied on these points:--
18 is the common difference of 99, 117, 135, and of 119, 137, 155.
19 is the sum of each side of the upper triangle.
20 is the common difference of any two sums of squares symmetrically
placed, both being on a line through the central spot.
21 is the sum of each side of the lower triangle.
10 is the sum of any two figures in the two triangles that correspond.
254 is the sum of 135, 119, of 117, 137, and of 90, 155.
By transposing in each triangle the figures joined by dotted lines, the
nine digits run in natural sequence.
No. XXXIII.--A MAGIC HEXAGON
We have dealt with Magic Squares, Circles, and Triangles. Here is a
Magic Hexagon, or a nest of Hexagons, in which the numbers from 1 to 73
are arranged about the common centre 37.
1 5 6 70 60 59 58
63 8
62 19 53 46 22 45 9
61 20 24 64
2 48 31 42 38 49 57
3 47 39 40 44 56
67 51 41 37 33 23 7
66 50 34 35 54 11
65 25 36 32 43 26 12
10 30 27 13
17 29 21 28 52 55 72
18 71
16 69 68 4 14 15 73
Each of these Hexagons always gives the same sum, when counted along the
six sides, or along the six diameters which join its corners, or along
the six which are at right angles to its sides. These sums are 259, 185,
and 111.
23
When I am in, its four legs have no motion;
When I am out, as fish it swims the ocean.
Then, if transposed, it strides across a stream,
Or adds its quality to eyes that gleam.
No. XXXIV.--MAGIC HEXAGON IN A CIRCLE
Inscribe six equilateral triangles in a circle, as shown in this
diagram, so as to form a regular hexagon.
[Illustration]
Now place the nine digits round the sides of each of the triangles, so
that their sum on each side may be 20, and so that, while there are no
two triangles exactly alike in arrangement, the squares of the sums on
the other sides may be alternately equal.
24
A PERSONAL ENIGMA
We can but see his sad reverse,
And while we say alas!
We hail his work so keen and terse,
With just a touch of gas.
No. XXXV.--A MAGIC CROSS
There are 33 different combinations of four of the numbers in the cells
of this magic cross which total up in each case to 26.
+----+----+
| _1_|_12_|
+----+----+----+----+
| _9_| _8_| _5_| _4_|
+----+----+----+----+
| _2_| _7_| _6_|_11_|
+----+----+----+----+
|_10_| _3_|
+----+----+
Those who care to work them out on separate crosses will find that there
is a very regular correspondence in the positions which the numbers
occupy.
25
What boy can live on with a prospect of age,
If you cut off his head at an early stage?
26
BY LORD MACAULAY
Here’s plenty of water, you’ll all of you say;
And minus the _h_ a thing used every day;
And here is nice beverage; put them together--
What is it with claws, but with never a feather?
No. XXXVI.--A CHARMING PUZZLE
Here is quite a charming little puzzle, which is by no means easy of
accomplishment:--
✦ ✦ ✦
✦ ✦ ✦
✦ ✦ ✦
Start from one of these nine dots, and without taking the pen from the
paper draw four straight lines which pass through them all. Each line,
after the first, must start where the preceding one ends.
27
A BROKEN TALE
The deil jumped
the clouds so high
That he bounded almost
right
the sky.
the trees
gates and fields and
He dodged with his tail
dragging
all these,
But, alas! made a terrible
bl,
For a twist in his tail
a rail,
hooked
And broke that appendage
as.
No. XXXVII.--LEAP-FROG
Place on a chess or draught-board three white men on the squares marked
_a_, and three black men on the squares marked _b_.
+---+---+---+---+---+---+---+
|_a_|_a_|_a_| |_b_|_b_|_b_|
+---+---+---+---+---+---+---+
The pieces marked _a_ can only move one square at a time, from left to
right, and those marked _b_ one square at a time, from right to left, on
to unoccupied squares; and any piece can leap over one of the other
colour, on to an unoccupied square. What is the least number of moves in
which the positions of the white and the black men can be reversed, so
that each square now occupied by a white is occupied by a black, and
each now occupied by a black holds a white piece?
28
To a word of assent join the first half of fright,
Then add what will never be seen in the night.
By such a conjunction we quickly attain
What most men have seen, but can’t see again.
29
My first is stately, proud, and grave,
My next will guard your treasure;
My whole, a slow but sturdy slave,
Will wait upon your pleasure.
No. XXXVIII.--SORTING THE COUNTERS
In the upper row of this diagram four white and four black counters are
placed alternately.
1 2 3 4 5 6 7 8 9 10
+---+---+---+---+---+---+---+---+---+---+
| ○ | ● | ○ | ● | ○ | ● | ○ | ● | | |
+---+---+---+---+---+---+---+---+---+---+
1 2 3 4 5 6 7 8 9 10
+---+---+---+---+---+---+---+---+---+---+
| | | ● | ● | ● | ● | ○ | ○ | ○ | ○ |
+---+---+---+---+---+---+---+---+---+---+
It is possible, by moving these counters two at a time, to arrange them
in four moves as they stand on the lower row. Can you do this?
Draughtsmen are handy for solving this puzzle, on a paper ruled as
above.
30
I am a word of letters six,
First link me with your mind;
Then shuffle me, and lo! I mix
With grief of noisy kind.
Shake me again, and you may fix
A cloak that hangs behind.
31
We are of use to every man
In walking, riding, rambling;
We join the gambols of the knave,
And play the knave in gambling!
No. XXXIX.--A TRANSFORMATION
Take five wooden matches, and bend each of them into a V. Place them
together, as is shown in the diagram, so that they take the form of an
asterisk, or a ten-pointed star.
[Illustration]
Lay them on some smooth surface, and without touching them transform
them into a star with five points.
32
Strange that a straggling tiresome weed
Will change its meaning quite,
And turn into a sign of grief
If we transpose it right;
And, stranger still, transposed again
Will tell of ease from grief or pain.
33
Find me two English verbs that ever
In a united state will blend,
Let one say “join,” the other “sever,”
While I divide them to the end.
No. XL.--DOMINO BUILDING
It is possible, with plenty of patience, to build up a whole set of
dominoes, so that they are safely supported on only two stones set up on
end.
[Illustration]
This, which might well seem impossible, is done by placing, as a
foundation, dominoes in the positions indicated by dotted lines. The
arch is then carefully constructed, as shown in the diagram, and for the
finish the four stones between the two foundation arches are drawn out,
and placed in pairs on end above, and finally, with the utmost care, the
other four are drawn away, and built in on the top. Thus the stones
indicated by the dotted lines at the base take their place within the
dotted lines above.
No. XLI.--FAST AND LOOSE
This diagram represents a shallow box, on the bottom of which twelve
counters or draughtsmen are lying loose.
[Illustration]
How can they be readjusted so that they will wedge themselves together,
and against the side of the box, and it can be turned upside down
without displacing them?
34
Taken entire
I’m full of fire.
With head away
A tax I pay.
If tail you bar
I turn from tar.
Headless again,
With tail restored.
Goddess of pain,
I sow discord.
No. XLII.--MAZY PROGRESS.
The diagram below is an exact reproduction of an old-fashioned maze, cut
in the ground near Nottingham. It is eighteen yards square, and the
black line represents the pathway, which is 535 feet in length.
[Illustration]
The point of this convoluted path is not so much to puzzle people, as to
show how much ground may be covered without diverging far from a centre,
or going over the same ground twice. As we advance along the line there
are no obstructions, and we find ourselves, after passing over the whole
of it, on the spot whence we set out.
35
Thrice three pins in shining line
Mary meant to fix;
Why did Mary turn the nine
Into thirty-six?
No. XLIII.--FOR CLEVER PENCILS
Start at _A_, and trace these figures with one continuous line,
finishing at _B_.
[Illustration]
You must not take your pencil from the paper, or go over any line twice.
36
A ring and a wing and three-fourths of a fog,
Will bring to your view a most obstinate dog.
37
Add fifty-seven to two-thirds of one,
Then take a fiddle,
And it will help to show you what is done,
To make this riddle.
38
I am a fish so neat and clever,
In pools and crystal streams I play,
To find me out my name you sever
As near the middle as you may.
No. XLIV.--TEST AND TRY
Those who have not seen it will find some real fun in the following
little experiment. Fix three matches as shown in the diagram, light the
cross match in the middle, and watch to see which of the ends will first
catch fire, or what will happen.
[Illustration]
39
I stand stock still, let who will hurry,
You cannot put me in a flurry,
Nor stir my stumps, for all your worry.
I am in haste, let none delay me
As fleetest couriers convey me.
You must transpose me ere you stay me.
40
Two to one, in case we hide,
You will find us in our site;
We are harmless side by side,
Parted we prepare to bite.
When united we divide,
When divided we unite.
No. XLV.--A CURIOUS PHENOMENON
Equal volumes of alcohol and water, when mixed, occupy less space than
when separate, to the extent indicated in this picture:
[Illustration]
If the sum of the volume of the two separate liquids is 100, the volume
of the mixture will be only 94. It is thought that the molecules of the
two liquids accommodate themselves to each other, so as to reduce the
pores and diminish the volume of the mixture.
41
Cut off my head, I’m every inch a king,
A warrior formed to deal a heavy blow;
Halve what remains, my second is a thing
Which nothing but my third can e’er make go.
My whole will vary as you take your line,
This less than human, that way all divine.
42
One half of me in solid earth you find,
The other half in ocean’s ample bed:
When in my whole we see these parts combined,
The earth remains, but all the sea is fled.
No. XLVI.--A HOME-MADE MICROSCOPE
The simplest and cheapest of all microscopes can easily be made at home.
The only materials needed are a thin slip of glass, on to which one or
two short paper tubes, coated with black sealing wax, are cemented with
the wax, a small stick, and a tumbler half full of water.
[Illustration]
Water is dropped gradually by aid of the stick into the cells, until
lenses are formed of the desired convexity, and objects held below the
glass will be more or less magnified.
43
Not ever changed unless unchanged,
Nor hanged unless beheaded;
Quick eyes may find in me arranged
Almost an angel bedded.
No. XLVII.--A PRETTY EXPERIMENT
For this curious experiment a glass bottle or decanter about half full
of water and a sound stalk of straw are needed.
[Illustration]
Bend the straw without breaking it, and put it, as is shown, into the
bottle, which can then be lifted steadily and safely by the straw, if it
is a sound one.
44
“WHAT THE DICKENS IS HIS NAME?”
_Merry Wives of Windsor._
A Russian nobleman had three sons. Rab, the eldest, became a lawyer, his
brother Mary was a soldier, and the youngest was sent to sea. What was
his name?
No. XLVIII.--A BOTTLED BUTTON
The button in a clear glass bottle, as is shown below, hangs attached by
a thread to the cork, which is securely sealed at the top.
[Illustration]
How can you sever the thread so that the button falls to the bottom
without uncorking or breaking the bottle?
45
A NEW “LIGHT BRIGADE”
Six before six before
Five times a hundred;
This must be brilliant, or
Solvers have blundered.
No. XLIX.--CLEARING THE WAY
Here is a pretty trick which requires an empty bottle, a lucifer match,
and a small coin.
[Illustration]
Break the wooden match almost in half, and place it and the coin in the
position shown above. Now consider how you can cause the coin to drop
into the bottle, if no one touches it, or the match, or the bottle.
46
Scorned by the meek and humble mind,
And often by the vain possessed,
Heard by the deaf, seen by the blind,
I give the troubled spirit rest.
47
To fifty for my half append
Two-thirds of one;
The other third my whole will end
When you have done.
No. L.--IS WATER POROUS?
Our belief that two portions of matter cannot occupy the same space at
the same time is almost shaken by the following experiment:
[Illustration]
If we introduce slowly some fine powdered sugar into a tumblerful of
warm water a considerable quantity may be dissolved in the water without
increasing its bulk.
It is thought that the atoms of the water are so disposed as to receive
the sugar between them, as a scuttle filled with coal might accommodate
a quantity of sand.
48
A DOUBLE SHUFFLE
See, the letters that I bring
Change their meaning quite;
Spell a hard and heavy thing,
Spell a soft and light.
No. LI.--A TEST OF GRAVITY
Set a stool, as is shown in the diagram below, about nine or ten inches
from the wall.
[Illustration]
Clasp it firmly by its two side edges, plant your feet well away from
it, and rest your head against the wall. Now lift the stool, and then
try, without moving your feet, to recover an upright position.
It will be as impossible as it is to stand on one leg while the foot of
that leg rests sideways against a wall or door.
No. LII.--BILLIARD MAGIC
Place a set of billiard balls as is shown in the diagram, the spot ball
overhanging a corner pocket, and the red and the plain white in a
straight line with it, leaving an eighth of an inch between the balls.
[Illustration]
How can you pot the spot white with the plain white, using a cue, and
without touching, or in any way disturbing, the red ball? There is not
room to pass on either side between the red ball and the cushion.
No. LIII.--THE NIMBLE COIN
Prepare a circular band of stiff paper, as is shown in the diagram, and
balance it, with a coin on the top, on the lip of a bottle.
[Illustration]
How can you most effectively transfer the coin into the bottle?
49
AN ENIGMA BY MUTATION
Search high or low, you’d find me where you list;
For not a place without me can exist.
I lose my head, and, seen with shoulders fair,
Become the very fairest of the fair.
Again I lose it, and, like some staunch hound,
The first and best amongst a pack am found.
And if at first both head and tail I lose
I am a portion such as all would choose.
No. LIV.--HIT IT HARD!
Place a strip of thin board, or a long wide flat ruler, on the edge of a
table, so that it just balances itself, and spread over it an ordinary
newspaper, as is shown in the illustration.
[Illustration]
You may now hit it quite hard with your doubled fist, or with a stick,
and the newspaper will hold it down, and remain as firmly in its place
as if it were glued to the table over it. You are more likely to break
the stick with which you strike than to displace the strip of wood or
the paper. Try the experiment.
50
AN ENIGMA BY SWIFT
We are little airy creatures
All of different voice and features.
One of us in glass is set,
One of us is found in jet.
Another you may see in tin,
And the fourth a box within.
If the others you pursue
They can never fly from you.
No. LV.--THE BRIDGE OF KNIVES
Here is an after-dinner balancing trick, which it is well to practise
with something less brittle than the best glass:--
[Illustration]
It will be seen that the blades of the knives are so cunningly
interlaced as to form quite a firm support.
51
A MEDLEY
Twice six is six, and so
Six is but three;
Three is just five you know,
What can we be?
Would you count more of us,
Nine are but four of us,
Ten are but three.
No. LVI.--DIFFERENT DENSITIES
Here is a pretty little experiment, which shows the effect of liquids of
different densities.
[Illustration]
Drop an egg into a glass vessel half full of water, it sinks to the
bottom. Drop it into strong brine, it floats. Introduce the brine
through a long funnel at the bottom of the pure water, and the water and
the egg will be lifted, so that the egg floats between the water and the
brine in equilibrium. The egg is denser than the water, and the brine is
denser than the egg.
52
THE MISSING LINK
A friend to all the human race
From emperor to peasant,
None is more missed when out of place,
More opportune when present.
Obedient to the general will
I yield to due control;
And yet the public twist me, till
They put me in a hole!
No. LVII.--COLUMBUS OUTDONE
Here is a very simple and effective little trick. Offer to balance an
egg on its end on the lip of a glass bottle.
[Illustration]
The picture shows how it is done, with the aid of a cork and a couple of
silver forks.
(From “La Science Amusante”).
53
Two words of equal length we here indite,
Which hold a famous father and his mate.
Embracing five, with fifty left and right,
The mother, looking both ways, keeps things straight.
Her husband, following a thousand quite,
With them has changed his sex, a funny fate,
And if this lady lose her head, she might,
Being a man, oppose the water-rate.
No. LVIII.--WHAT WILL HAPPEN?
The boy in this picture is blowing hard against the bottle, which is
between his mouth and the candle flame.
[Illustration]
What will happen?
54
In marble walls as white as milk,
Lined with a skin as soft as silk,
Within a fountain crystal clear
A golden apple doth appear.
No doors are there to this stronghold,
Yet thieves break in, and steal the gold.
No. LIX.--THE FLOATING NEEDLE
Here is a simple way to make a needle float on water:--
[Illustration]
Fill a wineglass or tumbler with water, and on this lay quite flat a
cigarette paper; place a needle gently on this, and presently the paper
will sink, and the needle will float on the water.
55
A one-syllable adjective I,
Indeterminate, misty, obscure:
Reduce me by five, and then try
How you like my attacks to endure.
I’m now a two-syllable noun,
My victims are hot and are cold;
In country more rife than in town,
I’m not such a pest as of old.
No. LX.--VIS INERTIÆ
Here is a pile of ten draughtsmen--one black among nine white.
[Illustration]
If I take another draughtsman, and with a strong pull of my finger send
it spinning against the column, what will happen?
56
DR. WHEWELL’S ENIGMA
A headless man had a letter to write,
He who read it had lost his sight.
The dumb repeated it word for word,
And deaf was the man who listened and heard.
57
AN ENIGMA FOR MOTORISTS
I am rough, I am smooth,
I am wet, I am dry;
My station is low,
My title is high.
The King my lawful master is,
I’m used by all, though only his.
No. LXI.--CUT AND COME AGAIN
How long would it take to divide completely a 2 ft. block of ice by
means of a piece of wire on which a weight of 5 lb. hangs?
[Illustration]
58
Without a dome, we are within a dome;
Homeless and roofless, we have roof and home.
Though frequent streams may flood our base and roof,
We rest unharmed, and always waterproof.
59
I’m the most fearful of fates upon earth,
Cut off my head and bright moments have birth,
Lop off my shoulders, and riddle my riddle;
Anything seems to be found in my middle.
No. LXII.--WHERE WILL IT BREAK?
When weak cords of equal strength are attached to opposite parts of a
wooden or metal ball which is suspended by one of them, a sharp, sudden
pull will snap the lower cord before the movement has time to affect the
ball; but a gentle, steady pull will cause the upper cord to snap, as it
supports the weight below it.
[Illustration]
60
I may be safe when honest ways prevail,
With no unworthy tricks or jobbery.
Cut off my head and fix it to my tail,
And I become at once rank robbery.
No. LXIII.--CATCHING THE DICE
Hold a pair of dice, and a cup for casting them, in one hand as is shown
in the diagram.
[Illustration]
Now, holding the cup fast, throw up one of the dice and catch it in the
cup. How can you best be sure of catching the other also in the cup?
61
Here is a metrical Enigma, which appeals with particular force to all
married folk, and to our cousins in America:
This is of fellowship the token,
Reverse it, and the bond is broken.
No. LXIV.--WILL THEY FALL?
Build up seven dominoes into a double arch, as is shown in the diagram
below, and place a single domino in the position indicated.
[Illustration]
Now put the fore-finger carefully through the lower archway, and give
this domino quite a smart tip up by pressing on its corner. What will
happen if this is done cleverly? Try it.
62
A monk in a moment, by violence heated,
Endangered the peace of his soul.
To atone for my second, my first he repeated
Just ten times a day on my whole.
No. LXV.--A TRANSPOSITION
Place three pennies in contact in a line as is shown below, so that a
“head” is between two “tails.”
[Illustration]
Can you introduce the coin with a shaded surface between the other two
in a straight line, without touching one of these two, and without
moving the other?
63
Two syllables this word contains:
Reverse them and then what remains?
* * * * *
With cap and pipe and goggles too
The comics hold him up to view,
Reverse his parts you would declare
A dog should not be quartered there.
64
Though I myself shut up may be,
My work is to set prisoners free.
No slave his lord’s commands obeys
With more insinuating ways.
All find me handy, sharp, and bright,
Where men in wit and wine delight;
While many keep me for their ease,
And turn and twist me as they please.
No. LXVI.--COIN COUNTING
Place ten coins in a circle, as is shown in this diagram, so that on all
of them the king’s head is uppermost.
====
= =
= 1 =
==== = = ====
= = ==== = =
= 10 = = 2 =
= = = =
==== ==== ==== ====
= = = =
= 9 = = 3 =
= = = =
==== ====
==== ====
= = = =
= 8 = = 4 =
= = = =
==== ==== ==== ====
= = = =
= 7 = = 5 =
= = ==== = =
==== = = ====
= 6 =
= =
====
Now start from any coin you choose, calling it 1, the next 2, and so on,
and turn the _fourth_, so that the tail is uppermost. Start again on any
king’s head, and again turn the fourth, and continue to do this until
all but one are turned.
Coins already turned are reckoned in the counting, but the count of
“four” must fall on an unturned coin.
Can you find a plan for turning all the coins but one in this way
without ever failing to count four upon a fresh spot, and to start on an
unturned coin?
No. LXVII.--THE BALANCED CORK
The diagram below shows how, using one hand only, and grasping a bottle
of wine by its body, the contents can be poured out without cutting or
boring the cork, or altogether removing it from the bottle.
[Illustration]
65
Transformed by art, and fond of port,
I blister in the sun;
But when I turn, and face the sport,
Away full tilt I run;
For if I double I am caught,
And that can be no fun.
66
A man without eyes saw plums on a tree,
He neither took plums nor plums left he.
No. LXVIII.--NUTS TO CRACK
A sharply-pointed knife with a heavy handle is stuck very lightly into
the lintel of a door, and the nut that is to be cracked is placed under
it, so that when the knife is released by a touch the nut is cracked.
[Illustration]
What simple and certain plan can you suggest for making sure that the
knife shall hit the nut exactly in the middle without fail?
67
A SINGULAR ENIGMA
Strange paradox! though my two halves are gone,
I still remain an undivided whole.
But were I double what I am, though one,
I then should be but half, upon my soul!
No. LXIX.--THE FLOATING CORKS
If we throw an ordinary wine cork into a tub of water it will naturally
float on its side. It is, however, possible to arrange a group of seven
such corks, without fastening them in any way, so that they will float
in upright positions.
[Illustration]
Place them together, as is shown in the illustration, and, holding them
firmly, dip them under the water till they are well wetted. Then,
keeping them exactly upright, leave go quietly, and they will float in a
compact bunch if they are brought slowly to the surface.
68
A PARADOX
I start with five thousand, and take nothing off,
Yet really in doing so nine-tenths I doff;
And it proves with no strain upon numbers or reason,
That the smaller are larger in size and in season.
No. LXX.--A LIGHT, STEADY HAND
As an exercise of patience and dexterity, try to balance a set of
dominoes upon one that stands upon its narrow end:--
[Illustration]
This is no easy matter, but a little patience will enable us to arrange
the stones in layers, which can with care be lifted into place and
balanced there.
69
With letters three indite my name,
Add one to show what I became,
Or try to tell what brought me fame.
No. LXXI.--WHAT IS THIS?
We expect to puzzle our readers completely by this diagram:--
[Illustration]
It is simply the enlargement by photography of part of a familiar
picture.
70
Eight letters respond to the quest
Of all for enjoyment athirst;
Two articles lead to the rest,
And the last of the rest is the first.
71
When letters five compose my name
I’m seldom seen but in a flame.
Take off one letter, then you see
That winter is the time for me.
Another take, and I appear
What many must be year by year.
No. LXXII.--TAKING THE GROUND FROM UNDER IT
Place a strip of smooth paper on a table so that it overhangs the side,
as is shown in the diagram. Stand a new penny steadily on edge upon the
paper.
[Illustration]
Take hold of the paper firmly, and give it a smart, steady pull. If this
is properly done it will leave the penny standing unmoved in its place.
72
A shining wit pronounced of late
That water in a freezing state
Is like an acting magistrate.
What was the quibble in his pate?
73
By something formed I nothing am,
Yet anything that you can name.
In all things false, yet ever true,
And still the same but never new;
Like thought I’m in a moment gone,
Nor can I ever be alone.
No. LXXIII.--A READY RECKONER
Two men, standing on the bank of a broad stream, across which they could
not cast their fishing lines, could not agree as to its width. A bet on
the point was offered and accepted, and the question was presently
decided for them by an ingenious friend who came along, without any
particular appliances for measurement.
He stood on the edge of the bank, steadied his chin with one hand, and
with the other tilted his cap till its peak just cut the top of the
opposite bank.
[Illustration]
Then, turning round, he stood exactly where the peak cut the level
ground behind him, and, by stepping to that spot, was able to measure a
distance equal to the width of the stream.
74
When you and I together meet,
Then there are six to see and greet.
If I and you should meet once more,
Our company would be but four.
And when you leave me all alone
I am a solitary one.
No. LXXIV.--THE CLIMBING HOOP
Paste or pin together the ends of a long strip of stiff paper so as to
form a hoop, and place on the table a board resting at one end upon a
book. Challenge those in your company to make the hoop run up the board
without any impulse.
[Illustration]
They must of course fail, but you can succeed by secretly fastening with
beeswax a small stone or piece of metal inside the hoop, as is indicated
in the diagram.
75
Invisible yet never out of sight,
I am indeed a centre of delight.
In quiet times I help to make things right,
Yet act as second in the fiercest fight.
No. LXXV.--THE SEAL OF MAHOMET
[Illustration]
This double crescent, called the Seal of Mahomet, from a legend that the
prophet was wont to describe it on the ground with one stroke of his
scimitar, is to be made by one continuous stroke of pen or pencil,
without going twice over any part of it.
76
Though I mingle with thieves,
And with all that deceives,
And never keep clear of depravity
Though possessed by a devil,
Or seen in a revel,
I do keep my centre of gravity.
77
There’s not a bird that cleaves the sky
With crest or plume more gay than I,
Yet guess me by this token:
That I am never seen to fly
Unless my wings are broken.
No. LXXVI.--MOVE THE MATCHES
Arrange 15 matches thus--
--------| --------| -------|
| | | | | |\ |
| | | |-------| | \ |
| | | | | | \ |
|-------- |-------- |-------
Remove 6 and what number will be left?
78
Split into three and mixed,
With Dives I am found.
Split into two and fixed
On four legs, flat or round.
In my most kindly sense unbroken,
Warm hearts and helpers I betoken.
79
I am high, I am low,
I am thick, I am thin,
I can keep out the snow,
But may let the rain in.
80
HIDDEN FRUIT
Go range through every clime, where’er
The patriot muse appears
He deeds of valour antedates,
His ban an army fears.
By midnight lamp each poet soul
Is plumed for flight sublime;
Pale monarch moon and shining stars
Witness his glowing rhyme!
Incited by the muse man goes
To grapple with his wrongs;
The poet cares not who makes laws,
If he may make the songs.
Can you discover ten fruits in these lines?
No. LXXVII.--LINES ON AN OLD SAMPLER
| |
--+-----------------------------------------+--
|~When I can plant with seventeen trees |
| Twice fourteen rows, in each row three;|
|A friend of mine I then shall please, |
| Who says he’ll give them all to me.~ |
--+-----------------------------------------+--
| |
81
The last of you before the end
Close to an inn we first must find,
If nothing follows all will tend
To hints that rankle in the mind.
No. LXXVIII.--DOMINO DUPLICITY
By the following ingenious arrangement of the stones a set of dominoes
appears to be unduly rich in doublets:--
+-------+ +-------+
| 1 1 | | 3 3 |
+---+---+---+-------+---+---+---+
| 1 | 1 5 | 5 0 | 0 3 | 3 |
| +---+---+---+---+-------+ |
| 6 | 6 | 5 5 | 0 | 0 6 | 6 |
+---+ +-------+ +-------+---+
| 6 | 6 | 4 4 | 4 | 4 6 | 6 |
| +---+---+---+---+-------+ |
| 2 | 2 4 | 4 | 4 | 4 5 | 5 |
+---+-------+ | +-------+---+
| 2 | 2 1 | 1 | 3 | 3 5 | 5 |
| +-------+---+---+-------+ |
| 0 | 0 1 | 1 3 | 3 2 | 2 |
+---+---+---+-------+---+---+---+
| 0 0 | | 2 2 |
+-------+ +-------+
It will be noticed that the charm of this arrangement is that the whole
figure contains a double set of quartettes, on which the pips are
similar.
82
Many men of many minds,
Many birds of many kinds,
Some are dun, and some are gray--
Which is this one? tell me, pray!
See him where the water shines,
But not perching on the pines.
No. LXXIX.--MORE DOMINO DUPLICITY
+-------+ +-------+ +-------+ +-------+
| 2 2 | | 0 0 | | 1 1 | | 3 3 |
+---+---+---+---+---+---+ +---+---+---+---+---+---+
| 2 | 2 3 | 3 0 | 0 | | 1 | 1 6 | 6 3 | 3 |
| +---+---+-------+ | | +-------+---+---+ |
| 6 | 6 | 3 | 3 1 | 1 | | 4 | 4 6 | 6 | 4 | 4 |
+---+ | +-------+---+ +---+-------+ | +---+
| 6 | 6 | 5 | 5 1 | 1 | | 4 | 4 0 | 0 | 4 | 4 |
| +---+---+-------+ | | +-------+---+---+ |
| 5 | 5 | 5 | 5 2 | 2 | | 2 | 2 0 | 0 | 5 | 5 |
+---+ | +-------+---+ +---+-------+ | +---+
| 5 | 5 | 0 | 0 2 | 2 | | 2 | 2 5 | 5 | 5 | 5 |
| +---+---+---+---+ | | +-------+---+---+ |
| 4 | 4 0 | 0 | 4 | 4 | | 1 | 1 5 | 5 | 6 | 6 |
+---+-------+ | +---+ +---+---+---+ | +---+
| 4 | 4 6 | 6 | 4 | 4 | | 1 | 1 3 | 3 | 6 | 6 |
| +-------+---+---+ | | +-------+---+---+ |
| 3 | 3 6 | 6 1 | 1 | | 0 | 0 3 | 3 2 | 2 |
+---+---+---+---+---+---+ +---+---+---+---+---+---+
| 3 3 | | 1 1 | | 0 0 | | 2 2 |
+-------+ +-------+ +-------+ +-------+
This again shows how the stones can be placed so that an ordinary set of
dominoes seems to be unduly rich in doublets.
83
We know how, by the addition of a single letter, our _cares_ can be
softened into a _caress_; but in the following Enigma a still more
contradictory result follows, without the addition or alteration of a
letter, by a mere separation of syllables:--
None can locate the subject of my riddle.
For all the world would seek its place in vain;
Cut it asunder almost in the middle,
And in our very midst its place is plain.
An aching void, an absolute negation,
Into the opposite extreme it breaks;
With just a gap to mark their new relation
Each letter still the same position takes.
No. LXXX.--TWO MORE PATTERNS
Here are two more perfect arrangements of a set of dominoes in
quartettes, so that the pips and blanks are similarly grouped and
repeated:--
+---+-------+-------+-------+---+ +---+-------+-------+-------+---+
| 3 | 3 0 | 0 5 | 5 2 | 2 | | 0 | 0 2 | 2 3 | 3 1 | 1 |
| +---+---+---+---+---+---+ | | +---+---+---+---+---+---+ |
| 3 | 3 | 0 | 0 | 5 | 5 | 2 | 2 | | 0 | 0 | 2 | 2 | 3 | 3 | 1 | 1 |
+---+ | | | | | +---+ +---+ | | | | | +---+
| 2 | 2 | 1 | 1 | 6 | 6 | | 4 | 4 | 5 | 5 | 0 | 0 |
+---+---+---+---+---+---+ +---+---+---+---+---+---+
| 2 | 2 | 1 | 1 | 6 | 6 | | 4 4 | 5 | 5 0 | 0 |
+---+ | | | | | +---+ +-------+ +-------+ |
| 1 | 1 | 4 | 4 | 3 | 3 | 0 | 0 | | 6 6 | 5 | 5 6 | 6 |
| +---+---+---+---+---+---+ | +---+---+---+---+---+---+
| 1 | 1 | 4 | 4 | 3 | 3 | 0 | 0 | | 6 | 6 | 5 | 5 | 6 | 6 |
+---+ | | | | | +---+ +---+ | | | | | +---+
| 6 | 6 | 5 | 5 | 4 | 4 | | 2 | 2 | 1 | 1 | 4 | 4 | 3 | 3 |
+---+---+---+---+---+---+ | +---+---+---+---+---+---+ |
| 6 6 | 5 5 | 4 4 | | 2 | 2 1 | 1 4 | 4 3 | 3 |
+-------+-------+-------+ +---+-------+-------+-------+---+
CHARADES
1
SIR WALTER SCOTT’S CHARADE
Sir Hilary fought at Agincourt,
Sooth! ’twas an awful day
And though in olden days of sport
The rufflers of the camp and court
Had little time to pray,
’Tis said Sir Hilary muttered there
Two syllables by way of prayer.
“My first to all the brave and proud
Who see to-morrow’s sun;
My next with her cold and quiet cloud
To those who find a dewy shroud
Before the day is won.
And both together to all bright eyes
That weep when a warrior nobly dies!”
No. LXXXI.--COUNTING THEM OUT
Arrange twelve dominoes as is shown in this diagram, and start counting
_in French_ from the double five, thus u, n, _un_; remove the stone you
thus reach, which has _one_ pip upon it, and start afresh with the next
stone, d, e, u, x, _deux_; this brings you to the stone with two pips;
then t, r, o, i, s, _trois_, brings you to that with _three_, and so on
until _douze_ brings you to twelve.
+---+---+---+---+---+---+---+---+---+---+---+---+
| 2 | 3 | 4 | 3 | 2 | 5 | 2 | 6 | 6 | 0 | 1 | 5 |
| | | | | | | | | | | | |
| 4 | 1 | 5 | 4 | 0 | 3 | 3 | 6 | 5 | 1 | 2 | 5 |
+---+---+---+---+---+---+---+---+---+---+---+---+
Always remove the stone as you hit upon each consecutive number.
Now who can re-arrange these same stones so that a similar result works
out in _English_, thus--o, n, e, _one_ (remove the stone), t, w, o,
_two_, and so on throughout?
2
A FAMILY CHARADE
A man with fourscore winters white
Sat dozing in his chair;
His frosted brow was quite my first,
Crowned with its silver hair.
My whole, when playing at his feet,
Sly glances upward stole;
My second, standing at his side,
Was father of my whole.
No. LXXXII.--TRICKS WITH DOMINOES
In this diagram the word EACH is formed by the use of a complete set of
stones, placing every letter in proper domino sequence.
+-------+-------+ +---+-------+ +---+-------+---+ +---+ +---+
| 6 5 | 5 3 | | 1 | 1 5 | | 1 | 1 1 | 1 | | 5 | | 0 |
+---+---+-------+ | +---+---+ | +-------+ | | | | |
| 6 | | 0 | | 5 | | 6 | | 2 | | 4 | | 3 |
| | +---+ | | +---+ +---+ +---+ +---+
| 0 +-------+ | 0 | | 2 | | 6 | | 4 +-------+ 3 |
+---+ 0 2 | | +---+---+ | | | | 4 3 | |
| 0 +-------+ | 4 | 4 2 | | 6 | | 4 +-------+ 3 |
| | +---+---+---+ +---+ +---+ +---+ +---+
| 0 | | 4 | | 2 | | 6 | | 2 | | 4 | | 3 |
+---+---+-------+ | | | | | +-------+ | | | | |
| 0 5 | 5 5 | | 6 | | 6 | | 3 | 3 2 | 2 | | 1 | | 1 |
+-------+-------+ +---+ +---+ +---+-------+---+ +---+ +---+
There are also the same number of pips in each letter. Can you construct
another English word under the same conditions? As a hint, the word that
we have in mind is plural.
3
Upon my face is not a single hair,
Although my beard uncut is growing there.
Men call me Shelley, though I can’t converse,
To me all tongues alike would be a curse.
I in my house must night and day abide,
And though quite well must keep my bed, outside.
For me no bell shall toll a funeral knell,
I’m doomed, like Shelley, dead to have no shell.
4
This amusing Charade is from the pen of a wise and witty Irish Bishop:--
True to the trumpet call of fame and duty
The soldier arms, and hastens to depart;
Nor casts one look behind, though love and beauty
Whisper _my first_ in tones that thrill his heart.
The war is o’er, with wealth and honour laden
The hero seeks the well-remembered Hall:
He woos and wins the unreluctant maiden,
And bids _my second_ o’er her blushes fall.
He takes her hand--a mist of rapture thickens
Before her eyes. Such bliss succeeding pain
O’ertasks her strength, and fainting nature sickens,
Until _my whole_ is rudely snapt in twain.
No. LXXXIII.--THE HOUR GLASS
This very beautiful specimen of a knight’s tour on the chess-board takes
its name from the figure formed by the tracery at its centre.
[Illustration]
An endless number of symmetrical patterns of varied design can be
formed, by a knight’s consecutive moves, with patience and ingenuity.
No. LXXXIV.--A STAR’S TOUR
Here is a pretty and very regular specimen of a knight’s tour on the
chess board.
[Illustration]
It is one of many variations which produce in the tracery a central
star.
5
MAKE IT KNOWN
My first she was a serving maid,
Who went to buy some tea;
How much she bought my second tells,
As all may plainly see.
Now when the answer you have found
Tell it to others too;
My whole will then to maids and men
Explain what ’tis you do.
No. LXXXV.--THE MARBLE ARCH
Here is a remarkably symmetrical specimen of a knight’s tour on the
chess board.
[Illustration]
It takes its name from the central archway, which this arrangement
forms.
6
My fourth is just ten times my first
When that takes on my second;
My third and second when reversed
Double my first are reckoned.
All this is empty, though my pen
So full may seem to show it;
Reverse my first and second, then
My whole becomes a poet.
7
O’er distant hills the rising moon
The evening mist dispersed:
And beaming radiant in the sky
She plainly showed _my first_.
A horseman guided by her light,
Approached with headlong speed
And as he rode _my second_ said
To urge his flagging steed.
His lady waited at the gate,
Though trysting hour was past.
She was _my whole_, because her lord
Was then _my third_ and last.
No. LXXXVI.--ANOTHER TOUR AMONG STARS
In No. LXXXIV we gave a pretty illustration of a knight’s tour, with a
central star.
[Illustration]
Here is a good course which shows in its symmetrical tracery a pair of
stars.
No. LXXXVII.--THE WINDMILL
Among the countless fanciful variations of the knight’s tour that are
possible, some have been so designed that more than a merely symmetrical
pattern is involved.
[Illustration]
Here is, for example, an excellent suggestion of the sails of a windmill
with their central fittings.
8
A TROPICAL CHARADE
My first’s a liquid or a solid snare,
My all is hot, or in a maiden’s hair;
My second just a track.
Transpose my first, and they will both declare
My all is now a black.
No. LXXXVIII.--LAZY TONGS
Here is a very distinctive specimen of the knight’s tour, in which the
design reminds us of the old-fashioned lazy-tongs, which stretched out
and then back, by opening or shutting their handles on finger and thumb.
[Illustration]
9
A FLORAL CHARADE
My first must be below the ground,
To do its proper duty;
Within my second may be found
Chaps that can boast no beauty;
Some simple garden holds the two combined,
Old-fashioned emblem of a candid mind.
No. LXXXIX.--CHESS ARITHMETIC
This beautiful symmetrical knight’s tour involves in its accomplishment
a pretty problem in arithmetic:--
[Illustration]
If we follow the course of the knight step by step, and number
consecutively the squares on which it rests at each move, we find that
there is a constant difference of 32 between the numbers on any two of
these squares that correspond in position on opposite sides of the
central line.
10
My first can be no joke to crack,
My second I adore;
Reverse her name, and you will see
Just what that maiden is to me.
My whole is grown where boys are black
Upon a sultry shore.
No. XC.--A SHORT KNIGHT’S TOUR
This short symmetrical knight’s tour can be tested on a corner of the
chessboard:--
[Illustration]
The knight can start from any square, and, taking the course indicated,
return on the twentieth move to the starting point.
11
BY GEORGE CANNING
Though weak my first is reckoned,
And game made of my second;
Yet both bade hosts defiance
When joined in close alliance.
12
As Lubin did my first, and, scythe in hand,
Espied his Phyllis by the hedgerow stand,
He called out to my next, in cheery tones and clear,
“Tell me, sweet all, you’ll fetch a pot of beer.”
No. XCI.--THE STOLEN PEARLS
A dishonest jeweller, who had a cross of pearls to repair for a lady of
title, on which nine pearls could be counted from the top, or from
either of the side ends to the bottom, kept back two of the pearls, and
yet contrived to return the cross re-set so that nine pearls could still
be counted in each direction, as at first. How was this done?
[Illustration]
13
A WORD OF WARNING
Says William to his thriftless wife,
“To _first_ unless you try,
Your wasteful ways will spoil our life.”
Her’s is a curt reply.
_Second_ and _third_ her answer give;
Full soon their fortunes fall,
Each of the hapless pair must live
And wander as my _all_.
14
A FINE CHARADE BY PRAED
Come from my first, ay, come;
The battle dawn is nigh,
And the screaming trump and the thundering drum
Are calling thee to die.
Fight, as thy father fought,
Fall, as thy father fell:
Thy task is taught, thy shroud is wrought,
So forward and farewell!
Toll ye my second, toll;
Fling high the flambeau’s light,
And sing the hymn for a parted soul
Beneath the silent night.
The helm upon his head,
The cross upon his breast,
Let the prayer be said, and the tear be shed
Now take him to his rest!
Call ye my whole, go call
The lord of lute and lay,
And let him greet the sable pall
With a noble song to-day.
Ay, call him by his name,
No fitter hand may crave
To light the flame of a soldier’s fame
On the turf of a soldier’s grave!
15
My first has cause in dread to hold
The foggy month November.
My next, when given to knights of old
Was held to mean “remember!”
16
With one line many do my first,
With two it can but meet;
My second, as its breakers burst,
Around my whole may beat.
17
She was my first; one happy day
She was my second,
And shewed my all. Now can you say
How this is reckoned?
18
My first it may a seaman save,
Or cause a fighter’s fall;
My next reminds us of the wave,
Or of unseemly brawl.
My whole is rather pert than brave,
And like a rubber ball.
19
Seen with a stolen spoon, my first was reckoned
Bad as my whole in moral tone.
Whether a number or alone my second
Touched by my third is turned to stone.
20
NOT A CATECHISM
My first a friend, companion, guide,
Is loving, staunch, and cheery;
My second has a cleansing side,
My third denotes a theory.
My whole, good luck! is held by few
To bore and make us weary.
21
My first is an insect,
My second a border;
My whole puts the face
Into tuneful disorder.
22
My first seldom crosses your path,
Though wheels and a body it hath;
My next from a clown
Much applause will bring down,
My whole was Goliath of Gath.
23
My first he sat upon my whole
And used it as my second.
His halves akin in Latin and
In English may be reckoned.
24
A PHONETIC FLORAL CHARADE
My first comes often to our mind
When for a saint we look.
My second sees the greetings kind
Of Bobby and the cook.
My whole in hothouse you may find,
Or pictured in a book.
25
Man cannot live without my first,
By day and night ’tis used;
My second is by all accursed,
By day and night abused.
My whole is never seen by day,
And never used by night,
’Tis dear to friends when far away,
But hated when in sight.
26
BY AN OXFORD OAR
I am my first, my second thou mayest be
In classic shades, where gently roll
The crystal waters of my whole
To seek the sea.
27
My first is worn by night and day,
And very useful reckoned;
London, or Bath, or Bristol may
With truth be styled my second.
Now if you cannot find me out
You lack my whole without a doubt.
28
My first now marks the soldier’s face,
Who was my next’s defender;
But when my whole attacked the place
It drove him to surrender.
29
My first is away from Paris, and may
Come round with a rap at your portal;
My second is Spanish, but quickly will vanish
If it turns to a nod from a mortal.
30
Often my first a B begins,
One always starts my second.
My all, though free from grosser sins,
Of little worth is reckoned.
31
My first is a kind of butter,
My second is a sort of cutter;
My whole, whether smaller or larger,
Was always a kind of charger.
32
My first is but lately promoted
To a place in our language, and quoted.
My second it lives in the sea.
On the hill-tops it flourishes free.
My whole I should certainly call
A delectable dainty for all.
33
AN ENIGMA-CHARADE
Take in my first, and you will find
It helps you to make up your mind.
Write to my second, and behold
You see into the secret told.
34
A QUAINT CHARADE
BY CHARLES JAMES FOX
My first is expressive of no disrespect,
But I never call you by it when you are by;
If my second you still are resolved to reject,
As dead as my whole I shall presently lie.
35
My first reversed will plainly show
An apple in its embryo.
Reverse my second, and we see
That which in sight can never be.
Replace them both, and write me down
Six letters that will spell a town.
36
My first is equal to the rest,
My second not so much;
My whole is better than the best,
Beyond compare nonsuch.
37
AN ITALIAN POET’S LOVE SONG
Hear me, my all: oh, be my first!
My second is a single;
If you say yes, then in my third
Our happy lives shall mingle.
38
A PARADOX
My first a simple verb, or half a verb, may be;
Almost the same my next, or half the same, we see.
My whole may weigh a ton or more, and yet be light,
Dull, and bereft of motion; swift, exceeding bright.
39
My first is found in fruit,
You take it for my second;
My whole in church to suit
Attentive ears is reckoned.
40
My _first_ is frugal, lean, and thin,
My _second_ leads to eve,
My _whole_ is hidden by a skin,
But not of sheep or beeve.
41
VERY PERSONAL
My first to us may point ’tis clear,
And what I say is true, sir!
My next to her your thoughts will steer,
My whole it is in view, sir!
42
My second in my first can speed
Across United States;
My third from Q’s pen we can read,
My whole has water-rates;
My first and second drive my first along,
My third and second drive a mind all wrong.
43
To puzzle solvers can I shine,
And so my first is writ.
With this my second did combine
To make a happy hit.
My whole, with both fixed in a line
Firm as I can, did fit.
44
A RUSTIC CHARADE
My first and second are my third,
My third my first and second may be;
My whole, if right you read the word,
May never have a wife or baby.
45
Let my second cut my first
Into slices thin;
Seek in Shakespeare for my whole,
Injured by his kin.
46
A FIRM GRIP
I may give you my first with my second,
Or my second may give with my first;
The one act as friendly is reckoned,
The other will rank with the worst.
If my whole through my second creeps over my first,
It will cling as a bond that no effort can burst.
47
My first is called a sin in name,
My third its simple cure;
My second puts an end to fame,
My whole in ease is sure.
48
In my first ’tis sweet to tarry
’Mid my second’s realms of bliss.
In the two, though none can marry,
All are subject to a kiss.
49
My first, which washes half a nation’s gums,
From foreign climes within my second comes:
And though, my whole, thine is no teacher’s part,
Thou art not science, but thou teachest art!
50
My first on country hedges grows,
My next is found in garden rows,
My third to make it more transpose,
My whole is one of London’s shows.
51
My first the best solver can never find out,
My second is looked for in vain;
My third may hide all from our view round about,
My whole must be weak, or in pain.
52
SORROW’S ANTIDOTE
My first does affliction denote,
Which my second is destined to bear;
My whole is the sweet antidote
That affliction to soothe and to share.
53
I see a sign of music not reversed, and then
My second and my third both pass beyond my ken.
54
My first has my second my third his mouth;
My whole was a tribe in the sunny south.
55
“QUOD” ERAT DEMONSTRANDUM
My second makes my ending,
My first is its reverse;
My whole bad men is sending
From court to quarters worse.
56
My first, though won and never lost,
Reversed is now before ye:
My second turns as red as blood
Upon a field of glory.
My whole is plain, yet you’ll confess
It is a wonder if you guess.
57
I get my second when I take my first,
And then my upright character is lost;
My whole gives quarters to a rat reversed,
Or is a refuge for the tempest tost.
58
My first is almost a cropper;
My second is often a propper;
My whole was entirely a whopper.
59
A FLORAL CHARADE
My first by poet’s eye was seen
Sad watching at the gates of heaven.
My next in tints of tender green
By Dickens with quaint art was given.
60
My first is nothing but a name
My second is more small;
My whole is of such slender fame
It has no name at all.
61
When second is of whole a fourth,
And first a fifth of second,
Then first by second multiplied
To make my whole is reckoned.
62
A CHARADE WITH A MORAL
My first is black, my second red,
My whole no man should take to bed.
63
My first upon their prey can dart,
My next can ne’er be down;
My whole performs a saucy part
In country or in town.
64
My first makes hills unpleasant
To every cyclist’s wheel.
My next is where they take you to
If in the streets you steal.
My whole is what I most dislike
When in the dumps I feel.
65
My first is the voice of heart-sorrows or joys,
My second, bar one, have been all of them boys,
My whole is made ill by the harsh raven’s noise.
66
QUITE SELF-CONTAINED
My first is in my second,
My third contains an ass;
And when my whole is reckoned
You see it is in glass.
67
Safe on Lucinda’s arm my first may rest,
And raise no tumult in Alonzo’s breast.
My second can the want of legs supply
To those that neither creep, nor walk, nor fly;
My whole is rival to the fairest toast,
And when most warmly welcomed suffers most.
68
My second, my first can control,
If his understanding is reckoned.
My second may not be my whole,
But my whole must be always my second.
69
AN OLD COCKNEY CHARADE
My first’s a little thing that hops,
My second comes with summer crops,
My whole is good with mutton chops.
70
A STRIKING CHARADE
My first I gently strike, and lo!
It soon becomes my second.
Indeed if this should not be so
My whole it is not reckoned.
71
PLANTING PEAS
“I think,” said Ted, “it will be wise
To set the peas this way;
For here they will face friendly skies,
And sun shines all the day.”
“Your first is good,” the gardener said,
“Peas thrive in sun and shower;
So now, good second, dig the bed
Where all can see them flower.”
Can you fit a word of two syllables to this Charade?
72
My first is found where wit and wine
Combine to grace the festal board;
My second where sad captives pine,
In dungeon of some tyrant lord.
My whole is ready for the doomed,
Twice tried by fire ere once consumed.
73
A BRAIN TWISTER
My first is half my second
And my third is half my first
My second and my third are good
To quench a mighty thirst.
RIDDLES AND CONUNDRUMS
1. Woman is my end, was my beginning, and you will find her in my midst.
2
I am an uncle, but it is not nice
To be saluted as an uncle twice.
Why not?
3. If a tailor and a goose are on the top of the Monument, which is the
quickest way for the tailor to get down?
4. My first is almost all, so is my second, and also my whole?
5
Those who have me do not desire me,
And yet they never wish to lose me,
Those who gain me have me no longer.
6. Why may a barrister’s fees be said to be cheap?
7
Two brothers are we, great burdens we bear,
By which we are heavily prest:
We are full all the day to endure wear and tear,
But empty when able to rest.
8. Peter Portman was so proud of his small feet that a wag started the
following riddle: “Why are Portman’s feet larger than any others in his
club?”
9
There is a word of letters four,
Take two away, and four remain;
Take three away, and five before
Your eyes you see as plain as plain.
10
To one syllable adjusted,
Running on the ground,
I have two, no longer trusted,
If you turn me round.
11. Why is a raven like a writing desk?
12. What do they do with peaches in California?
13. What is the utmost effort ever made by a piebald horse at a high
jump?
14
“In my first my second sat,
Then my third and fourth I ate.”
Under my first my second stood,
That’s your riddle: mine’s as good!
15. What are the differences between a gardener, a billiard-marker, a
precise man, and a verger?
16. Which can see most, a man with two eyes, or a man with one?
17. When you do not know the time, and “ask a policeman” what o’clock it
is, why are you like the Viceroy of India?
18. What is the question to which “yes” is the only possible reply?
19. What is that which will go up a pipe down, but will not go down a
pipe up; or will go down a pipe down, but not up a pipe up, and yet when
it has gone up a pipe or down a pipe, will go up or down?
20. Why was London for many years a wonderful place for carrying sound?
21. Why is a motor-car like swimming fish?
22. Who can decipher this?
1/6d. me a bloater.
23. Why is a moth flying round a candle like a garden-gate?
24
To half a dozen add half a score,
And you will plainly see
Just twenty, neither less nor more--
Now say, how can this be?
25. If I caught a newt why would it be a small one?
26. How can a lawyer’s fee be paid with only a threepenny piece?
27. When does the cannon ball?
28. Why should children go to bed soon after tea?
29. Which may weigh the most, Scotsmen or Irishmen?
30. Why cannot we have our hair cut?
31. Divide a hundred and fifty by half of ten, add two-thirds of ten,
and so you will find a town.
32. The following riddle is from the pen and fertile brain of Archbishop
Whately, who, it is said, offered in vain £50 for its solution:--
When from the Ark’s capacious round
Mankind came forth in pairs,
Who was it that first heard the sound
Of steps upon the stairs?
33. If Moses was the son of Pharaoh’s daughter, who was the daughter of
Pharaoh’s son?
34. I am a word of three syllables, and in all my fulness I represent
woman. Rob me of five letters and I am a man. Take away but four, I am
woman again. Remove only three, and I resume my manhood. What am I?
35. A cyclist on a night journey punctures his tyre, and finds that he
has forgotten his outfit for repairs. After wheeling the disabled
machine uphill for about two miles he registers a vow. What is it?
36
Some more than the mere whole my whole contains;
Remove that whole, and some of it remains!
37. Why were Younghusband’s pack-horses in Thibet like up-to-date motor
cars?
38
The public credit and the public shame
Differ in everything except in name.
39. Why is a telescope like a miser?
40. If I were in the sun, and you were out of it, what would it be?
41
I’m a word of four letters akin to the snow,
Just half of my first my third letter will show.
One fifth of my fourth my first you may call,
Of my second ’tis best to say nothing at all.
42. What is the chief and most natural thing for politicians to desire
to do when for the time they are out in the cold, awaiting a change of
Government?
43. I am long lasting, beginning at my end, ending with no beginning,
and my end and my beginning between them will bring you to an end.
44
With both feet crossed sit steady on a stool,
Then uncross one, and try to find a fool.
A RABBIT RUN
45. How far can a rabbit run into a square wood, with sides that each
measure a mile, if it keeps on a straight course and does not break
cover?
46
Often talked of, never seen,
Ever coming, never been,
Daily looked for, never here,
Still approaching in the rear.
Thousands for my presence wait,
But, by the decree of Fate,
Though expected to appear
They will never see me here.
47. I received my first because I was rash enough to say my second to my
third, when seeking re-election at my whole.
48
How is it, in this charming weather,
You and I can’t lunch together?
49
With a head, and without a head,
With a tail, and without a tail,
With a head without a tail,
With a tail without a head,
With a head and tail,
Without a head and tail.
50. “Ask me another,” she said, when he pressed her to name the happy
day. “I will,” he replied. “Why is the letter ‘d’ like the answer which
I seek from you?”
51
SWIFT’S RIDDLE
Two thirds of an ass, and a hole in the ground,
Will dress you a dinner worth many a pound.
TOM HOOD’S RIDDLE
52. Here is a riddle for which Tom Hood was responsible. Can you solve
it?
Twice to thine,
Once to mine,
With Congou make a gift divine.
53. Hold up your hand and you will see what you never have seen, never
can see, and never will see. What is this?
54. Can you tell the difference between the Emperor of Russia and an
ill-shod beggar?
55. Why did Eden Philpotts?
56. We have heard much of man’s imagined connection with the monkey,
through some missing link. What evidence can we gather from early
records of, at any rate, some verbal kinship with the patient ass?
57. My first is gold, my second is silver, my third is copper, and my
whole is tin.
58. What is highest when its head is off?
59. What word is there of six letters which can be so read that it
claims to be spelt with only one?
60. If a good oyster is a native, what is a bad one?
61. Why is John Bright?
62. If I walk into a room full of people, and place a new penny upon the
table in full view of the company, what does the coin do?
63. Jones, who had made it, and put it into his waistcoat pocket, lost
it. Brown picked it up, and lighted his cigar with it. Then they both
went to the train in it, and ran all the way.
64. Why cannot a deaf and dumb man tickle nine people?
65. When did “London” begin with an _l_ and end with an _e_?
66. I sent my second to my first, but many a whole passed before he came
back to me.
67. Which weighs most, the new moon or the full moon?
68. Here is a puzzle which is unique and most remarkable, and which
seems to be impossible, though it is absolutely sound:--
There is an English word of more than two letters, of which “la” is the
middle, is the beginning, and is the end, though there is but one “a”
and one “l” in the word. What is it?
69. Why is a bee like a rook?
70
A DARK REBUS
O
B =e= D
71
A MONKEY PUZZLER
If a monkey is placed before a cross, why does it at once get to the
top?
72
A RIDDLE BY COWPER
I am just two and two, warm and cold,
And the parent of numbers untold;
Lawful, unlawful, duty, fault,
Often costly, worthless bought.
A priceless boon, a matter of course,
Willingly yielded, taken by force.
The answer has been defined as “two heads and an application.”
HOW’S THAT, UMPIRE?
73. How can the Latin exhortation “Macte!” which may be roughly rendered
“Go on and prosper!” be applied at cricket to a batsman at a critical
moment?
BY TAPE MEASUREMENT
74. Are you good at topography? If so, can you discover and locate, from
this description of its surroundings, a town within 30 miles of London?
Half an inch before the trees, and half a foot and half a yard after
them, lead us to an English town.
75. We know how, by the addition of a single letter, our cares can be
softened into a caress; but in the following enigma a still more
contradictory result follows, without the addition or alteration of a
letter, by a mere separation of syllables:--
None can locate the subject of my riddle,
For all the world would seek its place in vain;
Cut it asunder almost in the middle,
And in our very midst its place is plain.
An aching void, an absolute negation,
Into the opposite extreme it breaks;
With just a gap to mark their new relation
Each letter still the same position takes.
76. MULTUM IN PARVO
What two letters describe in nine letters the position of one who has
been left alone in his extremity?
77. A CHANGE OF SEX
“Oh! would I were a man,” cried a schoolmistress, “that I might always
teach boys.”
We boys overheard her, and placed her with us. What did we thus turn her
into?
78. A STRIKING MATCH PUZZLE
How can you make a Maltese cross with less than twelve unbent and
unbroken matches?
79
Have we any reason to suppose that in very early times there were less
vowels than we have now?
80. A FRENCH RIDDLE
As Susette was sitting in the cool shadow of an olive grove at Mentone,
Henri came up and said to her, with his best bow, “Je sais que vous
n’avez pas mon premier, mais que vous êtes mon second, et je vous
donnerai mon tout!” What did he hold out to her?
81
On a church close to an old ruined priory, near Lewes, there is a
weathercock in the shape of a fish, probably an emblem of the faith.
What moral lesson does this relic of early days convey to us?
82
Take five from half of ten,
Set fifty in the middle,
Add twice five hundred then
To finish up the riddle,
And make it with your pen
As fit as any fiddle.
83. A PARADOX
“For the want of water we drank water, and if we had had water we should
have drank wine.”
Who can have said this, and what did they mean?
84. WHAT IS IT?
The poor have two, the rich have none,
Millions have many, you have one.
85
A thousand and one,
And a sixth part of twenty;
Some may have none,
But others have plenty!
86. GREAT SCOTT!
“Charge, Chester, charge! on, Stanley, on!”
Were the last words of Marmion.
Now, had I been in Stanley’s place
When Marmion urged him to the chase,
You would have thought, unless you knew,
That Scottish fray was Irish stew!
Shade of Sir Walter! What does all this mean?
87
I may be half of ten,
I may be nearly nine;
If eight contains me then
Two-thirds of six are mine.
A third of one, a fourth of four,
I am an eighth of many more.
88. QUITE A BEATITUDE
Let her be, or beat her,
Give her little ease;
Then in safety seat her
All among the bees.
89
Sharpen your wits till they are keen,
Then see if you can guess
What word it is that I have seen,
And spell it with an s!
90. RATHER PERSONAL
Take part of a foot,
And with judgment transpose.
You will find that you have it
Just under your nose.
NUTS TO CRACK
CRAZY LOGIC
1. Can you prove, by what we may call crazy logic, that madman is equal
to madam?
A BIT OF BOTANY
2. A rat with its teeth in the webbed feet of its prey was what the
squirrel saw one summer’s day, when he ran down from the tree-tops for a
cool drink in the pond below his nest. Can you find out from this the
name of the water-plant that was floating in the shade?
SIX SUNKEN ISLANDS
3. He set down the answer to that sum at random.
By bold policy Prussia became a leading power.
A great taste for mosaic has arisen lately.
The glad news was swiftly borne over England.
At dusk, year after year, the old man rambled home.
The children cried, hearing such dismal tales.
In each of these lines the name of an island is buried.
BURIED GEOGRAPHICAL NAMES
4. We could hide a light royal boat with a man or two; the skipper,
though, came to a bad end.
In this short sentence seven geographical names are buried, formed by
consecutive letters, which are parts always of more than one word. Can
you dig them out?
A TRANSPOSITION
5. What can you make of this? The letters are jumbled, but the words are
in due order.
Eltsheothwoedlaniscimtyyesrmh
Tsihptsnrtoniaisoetcra;
Ndaothetdandartssdensitemeb
Ehcatreeltnisitlpace.
6
ALL IN A ROW
Three little articles all in a line
Lead to a thousand, expressing,
If with another all these you combine
What can be never a blessing.
7
ASK A POLICEMAN
Ask a policeman, possibly he knows,
In uniformed array.
If not, an added letter plainly shows
How little he can say.
8
RULING LETTERS
We rule the world, we letters five,
We rule the world, we do;
And of our number three contrive
To rule the other two.
MIND YOUR STOPS
9. How would you punctuate the following sentence?
Maud like the pretty girl that she was went for a walk in the meadows.
10. ANSWER BY ECHO
What were they who paid three guineas
To hear a tune of Paganini’s?
11. BREAKING A RECORD
Only eight different letters are used in the construction of this
verse:--
Sad as the saddest end is his,
He hath insensate died.
He sinned, and that his Satan is
That standeth at his side.
Wishing to break this record, we have put together a rhyming verse of
similar length, in which only _five_ letters are used. They are these:
(18 times) ^eeeeeeeeeeeeeeeeee^.
(20 times) ^nnnnnnnnnnnnnnnnnnnn^.
(18 times) ^tttttttttttttttttt^.
(16 times) ^iiiiiiiiiiiiiiii^.
(15 times) ^sssssssssssssss^.
12. A CATCH SENTENCE
If is is not is and is not is is what is it is not is and what is it is
is not if is not is is? Can you punctuate this so that it has meaning?
13. CATCHING A HINT
Passing one day by train through a station I caught sight of two words
upon a large advertisement, which seemed cut out for puzzle purposes;
and before long I had framed the following riddle:
Bisect my first, transpose its first half, and between this and its
second half insert what remains if you take my second from my first. The
result is as good to eat as my first and second are to drink.
14. IS IT GRAMMAR?
It is difficult at first sight to grasp the meaning of this apparently
simple sentence:--“Time flies you cannot they pass at such irregular
intervals.” How does it read?
15. ROYAL MEMORIES
In Queen Victoria’s Jubilee year I went to the South Kensington Museum.
As I entered, looking at my watch, I thought of the good Queen. After
some hours of quiet enjoyment I came away, again looking at my watch,
and was reminded that the Prince Consort was not alive to share the
Jubilee joys. At what time, and for how long was I in the Museum?
16. A SEASONABLE MOTTO
CCC
---
SAW
17. AN OLD LATIN LEGEND
+------------------+
| AMANS TAM ERAT |
| HI DESINT HERO |
|AD DIGITO UT MANDO|
+------------------+
What is the interpretation?
18. THINGS ARE NOT WHAT THEY SEEM
Does the following statement imply that there is a curative virtue in
rose-coloured rays?
“I know that roseate hues preserve.”
19. DOCTOR FELL
“Keep the patients warm and quiet;
Solids are not well;
Let all sops be now their diet,”
So said Doctor Fell.
To what objection was this diet open?
20. DISLOCATED WORDS
These thirty-six letters form an English sentence:--
SAR BAB SAR BAB SAR BAB
SAR BAB SAR BAB SAR ARA
What can it be?
21. BROAD WILTSHIRE
“Igineyvartydreevriswutts.”
Can you interpret this sentence, spoken by a sturdy farmer in the corn
market?
22. FIND A RHYME
Try to find a rhyme to Chrysanthemum.
23. ABOUT THE EGGS
Did you hear that pathetic tale of the three eggs?
24. AN ANCIENT LEGEND
+--------------+
|Doun tooth ers|
| A sy |
| Ouw ould bed |
| One by. |
+--------------+
25. A FAMILY PARTY
HERE LIE
Two grandmothers, and their two granddaughters;
Two husbands, and their two wives;
Two fathers, and their two daughters;
Two mothers, and their two sons;
Two maidens, and their two mothers;
Two sisters, and their two brothers;
Yet but ---- in all lie buried here.
How many does the ---- represent?
26. A SIMPLE CHARM
A superstitious couple in the country who heard mysterious noises at
night in their house, sought the advice of a “wise woman” in the
neighbourhood. She gave them on paper the following charm, which would,
she assured them, counteract their evil star, and solve the mystery:--
ground
turn evil star.
What was its significance?
27. MADE IN FRANCE
We are five varied vowels of foreign sound,
Supported by one consonant between us.
Three letters now in four, where may be found
Another trio, quite a silly genus.
28. A PARADOX
What in his mind no man can find
Four symbols will display;
But only one remains behind
If one we take away.
29. THE BARBER’S JOKE
A barber placed prominently in his window the following notice:--
What do you think
I will shave you for nothing and give you a drink.
Attracted by this, a man went into the shop, and was shaved, but instead
of receiving any liquid refreshment, he was surprised by a demand for
the usual payment.
What was the barber’s explanation?
30. A FLIGHT OF FANCY
+-------------------------+
| G E N U I N E J A M |
| A |
| I C A R U M. |
+-------------------------+
This label, said to have been found among the ruins of old Rome, seems
to bear a very early reference to the birth of Icarus, the flying man;
or perhaps to some flying machine named after him, but not yet
perfected. Can this be so?
31. A SPELL
Two _c_’s, an _h_, an _n_, a _p_,
Three _a_’s, a _u_, an _i_, an _e_,
Tell us what English word are we?
32. JOHNSON’S CAT
Johnson’s cat went up a tree,
Which was sixty feet and three;
Every day she climbed eleven,
Every night she came down seven.
Tell me, if she did not drop,
When her paws would touch the top.
33. THE EXPANDING NINES
Some of us may perhaps remember Titania’s promise to Bottom in _A
Midsummer Night’s Dream_:
“I have a venturous fairy, that shall seek
The squirrel’s hoard, and fetch thee new nuts.”
Here is a little puzzle so fresh and curious that it will tempt the
fancy of those who find it added to our hoard:
A third of six behind them fix,
A third of six before;
Thus make two nines, when all combines,
Exactly fifty-four.
34. ACROSS THE MOAT
Form a square with four matches. Outside this, at an equal distance all
round, form another square with twelve matches, just so far away that
the space between them cannot be spanned by a match. With two matches
only, form a firm bridge from the outer to the inner square.
35. IS IT BANTING?
We start when the ninth hour is past,
Then there’s an end of you.
A vengeful goddess shows at last
What antifat will do.
36. QUITE A FAMILY PARTY
The telephone-bell roused Mrs P.W. from her after-luncheon nap, and her
husband’s voice came to her ears, from his office in the city:--“I am
bringing home to dinner my father’s brother-in-law, my brother’s
father-in-law, my father-in-law’s brother, and my brother-in-law’s
father.”
“Right!” she replied, knowing his quaint ways, “I shall be prepared.”
For how many guests did she provide?
37. THE WILY WAYFARER
“Give me as much money as I have in my hand,” said Will Slimly to the
landlord of a country inn, “and I will spend sixpence with you.” This
was done, and repeated twice with the cash that was still in hand, and
then the traveller was penniless. How much had he at first, and how much
did the landlord contribute to Will’s refreshment?
38. A CLEVER CONSTRUCTION
How can four triangles of equal size be formed with six similar matches?
39. A KNOTTY POINT
When first the marriage knot was tied
Between my wife and me,
My age as oft repeated hers
As three times three does three;
But when ten years and half ten years
We man and wife had been,
Her age came then as near to mine
As eight does to sixteen.
What age was hers, what age was mine,
When we were wed, from this divine.
40. A DIVISION SUM
“Take this half-crown,” said the vicar at a village festival, “and
divide it equally between those two fathers and their two sons, but give
nothing of less value than a penny to either of them.”
The schoolboy, who was a sharp lad, changed the half-crown, and divided
it equally among them. How was this possible?
41. A CROOKED ANSWER
Tom (_yawning_) to Nell--“I wish we could play lawn-tennis!”
Nell (_annoyed_).--“Odioso ni mus rem. Moto ima os illud nam?”
Can you make head or tail, in Latin or in English, of her reply?
42. THE PEELER’S SMILE
Two policemen stood behind a hedge, watching for motor-car scorchers.
One looked up the road, the other looked down it, so as to command both
directions.
“Bill,” said one, without turning his head, “what are you smiling at?”
How could he tell that his mate was smiling?
43. THE NIMBLE NINES
Twenty-seven with three nines
You and I can score;
Anyone one on other lines
Can extend them more.
Who can write them to be seen
Equal only to sixteen?
44. A TRYING SENTENCE
That that is is that that is not is not is not that it it is.
45. SHORT AND SWEET
What is this?
A L L O.
46. SUPPLY THE CONSONANTS
AN ENGLISH PROVERB
i e a o a a a e a a i
47. IT LOOKS BLACK
| | | | | | | | | | | | |
Add thirteen more strokes, and make--what?
48. THE CORONER’S CHOICE
Can a coroner, after signing his name, write his official position in
more ways than one?
HOW MANY PIPS?
Here is a good and simple card trick. Ask anyone to choose three cards
from a pack, and to place them face downwards on the table. Then,
beginning to count with the number of pips on each card laid down, let
him place other cards upon these, one heap at a time, until in every
case he counts up to 15, adding mentally 1 as he places down each card.
When he has completed the three heaps, take from him the remaining
cards, and count them. Their number, less 4, will always be the number
of pips on the three chosen cards. An ace counts 11, and a court card
10.
Thus, if he has chosen a 7, a 10, and an ace (11), he must cap these
with 8, 5, and 4 cards respectively. There will then be 32 cards left,
and 32 - 4 = 28, which is the sum of 7, 10, and 11.
ROUND THE MONKEY
Now for a few words about an old friend, familiar to most of us. If a
monkey sits on a post holding one end of a string, and continually moves
to face a man who holds the other end, and who walks round the post,
does that man walk round the monkey?
R. A. Proctor, the astronomer, treated the question thus, some years ago
in _Knowledge_:--“In what way does going round a thing imply seeing
every side of it? Suppose a man shut his eyes, would that make any
difference? Or suppose the man stood still, and the monkey turned round,
so as to show the man its front and back, would the stationary man have
gone round the monkey?”
We commend this ancient and puzzling subject of controversy to our
readers. Our own opinion is that the man _does_ walk round the monkey,
in the commonly accepted meaning of the words, but “who shall decide
when doctors disagree?”
BURIED ANIMALS
Here are a few cleverly buried animals:
“Come hither, mine friend,” said the monk, eyeing him kindly, “be a very
good boy, step through the furze bravely, and seek the lost riches.”
_Ermine_; _monkey_; _beaver_; _zebra_; _ostrich_.
We, as electricians, proclaim the electric motor cab a boon to London.
_Weasel_; _baboon_.
QUESTIONS WELL ANSWERED
What could not the cruet stand?
Seeing an apostle spoon.
Why did the barmaid champagne?
Because the stout porter bitter.
A TABLE OF AFFINITY
When it was reported that M. de Lesseps and his son were to marry
sisters, the _Rappel_ suggested these possible complications. Lesseps
the younger will be his father’s brother-in-law, and his wife will be
her own sister’s sister-in-law.
If Lesseps the elder has a son, and Lesseps the younger has a daughter,
and these marry, then the daughter of Lesseps the younger will be her
father’s sister-in-law, and the son of Lesseps the elder will be the
son-in-law of his brother. The son of the second marriage will have two
grandfathers, Lesseps the elder and the younger, so that old Lesseps
will become his own son’s brother.
MARY QUITE CONTRARY
Mary had a little lamb,
With feet as black as soot;
And into Mary’s bread and milk
He put his little foot.
Now Mary was an honest girl,
And scorned a hollow sham;
So the one word that Mary said
Was mother to the lamb!
MACARONIC VERSE
LATIN
“Is acer,” sed jacto his mas ter at te,
“Cantu passus sum jam?” “Notabit,” anser de;
“Mi jam potis empti, solis tento me,
For uva da lotas i vere vel se!”
ENGLISH
“I say, sir,” said Jack to his master at tea,
“Can’t you pass us some jam?” “Not a bit,” answered he,
“My jam pot is empty, so listen to me,
For you’ve had a lot as I very well see!”
HAM SANDWICHES
We most of us know the good old double-barrelled riddle, “Why need we
never starve in the desert?” “Because of the sand which is there.” “How
did the sandwiches get there?” “Ham settled there, and his descendants
bred and mustered.” This clever metrical solution is by Archbishop
Whately:--
A traveller o’er the desert wild
Should ne’er let want confound him,
For he at any time can eat
The sand which is around him.
It might seem strange that he should find
Such palatable fare,
Did we not know the sons of Ham
Were bred and mustered there.
A GOOD MOTTO
We know that Latin motto, with its clever double meaning, suggested for
a retired tobacconist, “_Quid rides_”--why do you smile?--or _quid_
rides. Here is another, proposed many years ago, for a doctor of
indifferent repute:--
Take some device in your own way,
Neither too solemn, nor too gay;
Three ducks suppose, white, grey, and black,
And let your motto be “Quack! Quack!”
ON ONE NOTT
There was a man who was Nott born,
His sire was Nott before him;
He did Nott live, he did Nott die,
His tombstone was Nott o’er him.
ON JOHN SO
So died John So,
So, so, did he so?
So did he live, and So did he die,
So, so, did he so?
So let him lie!
STRANGE SIGHTS
The importance of proper punctuation is very happily illustrated by the
following lines:--
I saw a peacock with a fiery tail
I saw a blazing comet pour down hail
I saw a cloud enwrapped with ivy round
I saw an oak tree swallow up a whale
I saw the boundless sea brimful of ale
I saw a Venice glass fifteen feet deep
I saw a well full of mens’ tears that weep
I saw wet eyes among the things that I saw
Were no sore eyes nor any other eye-sore.
A QUAINT INSCRIPTION
There is a curiously constructed inscription over the door of the
cloister of the Convent of the Carmelites at Caen, which runs thus:--
D di Si scap ac ab as
um vus mon ulare cepit tris.
T sæ Dæ ul in in an
The lines are in honour of one Simon Stock of that order, and they may
be freely rendered:--
W ho Si first beg pr
hen ly mon an his eaching.
T wi De howled to sc t
NONSENSE VERSE
IMPROMPTU, BY AN OLD DIVINE
If down his throat a man should choose
In fun to jump or slide,
He’d scrape his shoes against his teeth,
Nor soil his own inside.
Or if his teeth were lost and gone,
And not a stump to scrape upon,
He’d see at once how very pat
His tongue lay there by way of mat,
And he would wipe his feet on that!
EDGAR POE’S RIDDLE
Edgar A. Poe addressed the following puzzle-valentine to a lady, adding,
“You will not read the riddle, though you do the best you can do:”--
For her this rhyme is penned whose luminous eyes,
Brightly expressive as the twins of Leda,
Shall find her own sweet name, that nestling lies
Upon the page, enwrapped from every reader.
Search narrowly the lines--they hold a treasure
Divine--a talisman--an amulet
That must be worn at heart. Search well the measure.
The first letter of the first line, the second of the second, the third
of the third, and so on spell the lady’s name--Frances.
AN ILLUSION OF TYPE
A curious optical illusion is illustrated by printing a row of ordinary
capital letters and figures which are symmetrical, thus:--
[Illustration: SSSSSXXXXX3333388888]
If we glance at them casually it does not strike us that their upper
parts are smaller than the lower, but if we turn the paper upside down
we are at once surprised to see how marked the difference really is.
AN EXCHANGE OF COMPLIMENTS
At a tavern one night
Messrs More, Strange, and Wright
Met, good cheer and good thoughts to exchange.
Says More, “Of us three
The whole town will agree
There is only one knave, and that’s _Strange_!”
“Yes,” says Strange, rather sore,
“I’m sure there’s one _More_,
A most terrible knave, and a bite,
Who cheated his mother,
His sister, and brother.”
“Oh yes,” replied More, “that is _Wright_!”
ΗΚΙΣΤΑ ΛΙΨ
HE KISSED HER LIPS
(_According to the daily Press, a good old-fashioned kiss lately lost
favour in some quarters._)
Though a billiard player’s miss
Cannot meet or make a kiss;
Though a modern school of misses
Be not in the cue for kisses;
Chloe’s lips are not amiss,
Kismet! _I have_ met a kiss.
QUESTIONS WELL ANSWERED
We must not fail to register these two Questions Well Answered, which it
is hard to match for excellence:--
Q.--Why did the fly fly?
A.--Because the spider spied her!
And
Q.--Why did the lobster blush?
A.--Because it saw the salad dressing!
The following puzzling lines were the outburst of the wanton wit of a
lover, in his effort to play off one lady against another, and so retain
two strings to his bow:--
I don’t want the one that I don’t want to know
That I want the one that I want;
But the one that I do want wants me to go
And give up the one I don’t want.
Why I don’t want the one that I don’t want to know
That I want the one that I want,
Is because, if the one that I want can’t be so,
I shall want the one I don’t want.
Charles Lamb was responsible for the following ingenious perversion of
words, when the Whig associates of the Prince Regent were sore at not
obtaining office:--
Ye politicians tell me pray
Why thus with woe and care rent?
This is the worst that you can say,
Some wind has blown the wig away,
And left the hair apparent!
We may assume that this was the germ of the riddle “What is the
difference between the Prince of Wales, a bald-headed man, and a
monkey?” One is the _heir-apparent_, the second has no _hair apparent_,
and the third is a _hairy parent_.
GRAMMAR OF A SORT
When is whiskey an adverb?
_When it qualifies water._
When does a cow become a pronoun?
_When it stands for Mary._
Can the conjunction “and” be used otherwise than as a connecting link?
Yes, as in the puzzle sentence, “It was and I said not or,” which, if no
comma is placed after “said,” no one can read easily at sight.
A TONGUE TWISTER
The tragedy “William Tell” was to be played many years ago at the old
Drury Lane Theatre, and an actor, familiarly known as Will, asked the
exponent of the part of Tell, on the eve of its production, whether he
thought the play would tell with the critics and the public.
The following question and answer passed between them, in which only two
different words were used, in an intelligible sequence of twenty-five
words:--
_Will._--“The question has arisen Tell, ‘will Will Tell tell?’ Will Tell
tell Will ‘will Will Tell tell?’”
_Tell._--“Tell _will_ tell Will ‘will Will Tell tell?’ ‘Will Tell _will_
tell!’”
THE LADY AND THE TIGER
Many of our readers will enjoy this very clever rendering of a
well-known Limerick:--
There was a young lady of Riga,
Who smiled as she rode on a tiger.
They returned from the ride
With the lady inside,
And the smile on the face of the tiger!
Puella Rigensis ridebat,
Quam tigris in tergo vehebat;
Externa profecta,
Interna revecta,
Sed risus cum tigre manebat!
ANOTHER TONGUE TWISTER
Six sieves of sifted thistles,
Six sieves of unsifted thistles,
And six thistle sifters.
To be repeated six times rapidly and articulately.
NOVEL DEFINITION OF A MAN’S HAT
Darkness that may be felt.
IS IT LATIN?
The following cryptic notice was posted recently on the green baize
notice-board of a West-End Club:--
O nec ango in ab illi
Ardor pyram id contestata
Potor ac an non.
Si deis puto nat times
Ora res tu sed.
For some time its message was a mystery, until the sharp eyes of a
member deciphered in what seemed to be real Latin, and was made up of
Latin words, this English sentence, appropriate to the place:--“One can
go in a billiard or pyramid contest at a pot or a cannon. Side is put on
at times, or a rest used.”
FOR THE CHILDREN
A QUESTION
How much wood would a wood-chuck chuck,
If a wood-chuck could chuck wood?
THE REPLY
The wood that a wood-chuck would chuck
Is the wood that a wood chuck could chuck,
If the wood-chuck that could chuck would chuck,
Or a wood-chuck could chuck wood!
A QUAINT CONCEIT
The Capitol was saved of old
By geese with noisy bill;
More sage than silly, birds so bold
Should have a mission still.
Time was when roving on the loose,
A goose would raise my dander;
But now I feel each proper goose
Should have her propaganda!
A LACK OF HOPS!
A man fond of his joke, and speaking of Lenten fare to a friend in a
letter, wrote:--
I had a fish
In a dish
From an Archbish----
leaving it to his ingenuity to complete the broken line. The reply was a
clever solution to the puzzle:--
I had a fish
In a dish
From an Archbish----
’Op is not here
For he gave me no beer!
FOR THE CHILDREN
The following simple calculation will be amusing to children:--If an
even number of coins or sweets are held in one hand, and an odd number
in the other, let the holder multiply those in the right hand by 2, and
those in the left hand by 3, and add together the two results. If this
is an even quantity the coins or sweets in the right hand are even, and
in the left odd; if it is odd the contrary is the case.
PETER PIPER’S WIFE
(_To be read or said rapidly._)
Betty bit a bit o’ butter,
Bitter bit!
But a better bit o’ butter
Betty bit!
PHONETIC VERSE
“_A haunt each mermaid knows_”
Eh horn teach myrrh made nose,
Buy seize wear awl groat ales;
Hear chilled wrens port inn rose,
Seek your gain steals oar wails.
Sum son there yell oh hare,
Sums whim threw sigh leant baize;
Sow form sand fay says fare
Shy never knight sand daze.
PORSON’S EPIGRAM
Porson wrote a Latin epigram on a Fellow of one of the Colleges who
always pronounced the _a_ of Euphrates short. This was wittily
translated thus:--
With fear on the Euphrates shore
The wild waves made him shiver.
But he thought to pass more quickly o’er,
So he _abridged_--the river!
ALL THE ALPHABET
All the letters of the alphabet are used in these lines, which have such
an easy flow:--
“God gives the grazing ox his meat,
And quickly hears the sheep’s, low cry.
But man, who tastes his finest wheat,
Should joy to lift His praises high.”
A FRENCH TONGUE TWISTER
A French mother, as she gives to her child a cup of tea to allay its
cough, says:--
“Ton thé t’a-t-il oté ta toux?”
(Thy tea, has it removed thy cough?)
This sentence, repeated rapidly, is warranted to tire the nimblest
tongue.
QUEER QUESTIONS AND QUAINT REPLIES
Why does the cannon ball?
Because the Vickers Maxim
(the vicar smacks him!)
Why is the river Itchen?
Because there is a current in its bed.
WAS IT SCANDAL?
Dick and Harry meet in a dim hotel passage:--
_Dick._--Did you hear that story about No. 288?
_Harry_ (_all ears_).--No; what was it?
_Dick._--Oh, it’s too gross, too gross entirely!
_Harry._--Tell away. I’ll try to stand it.
_Dick._--Well; 288 _is_ two gross, isn’t it?
AN INCONSEQUENT ECHO
Byron in his “Bride of Abydos” is responsible for the following
strangely inconsequent echo:--
Hark to the hurried question of Despair,
“Where is my child?” and Echo answers,
“Where?”
A well-conducted echo would assuredly have seconded the cry of Despair
by repeating the final syllables “my child!”
AN APPROPRIATE ANSWER
Why did the Razorbill raise her bill?
To let the sea urchin see her chin!
CRICKET LATIN
Bene audax.
_Well bowled!_
MACARONIC VERSE
Here is a modern specimen of Macaronic verse:--
Luce metat ipse sutor
(Cantas Orci madentes!)
“Qua forum an empti putor
Potor tria quarto pes!”
Which reads into English thus:--
Lucy met a tipsy suitor
(Can’t a saucy maiden tease!)
“Quaff o’ rum an empty pewter
Pot, or try a quart o’ peas!”
MACARONIC PROSE
LATIN
Puris agem, suetis a sylva bella vi olet indue mos is pura sueta far,
amar vel verre ex que sit.
ENGLISH READING
Pure is a gem, sweet is a silver bell, a violet in dewy moss is purer,
sweeter far, a marvel very exquisite.
THE LONG AND THE SHORT OF IT
These quaint lines were once addressed to a very tall barrister, named
Long, when he was briefless:--
“Longè longorum longissime, Longe, virorum,
Dic mihi, te quæso, num Breve quicquid habes?”
MOORE’S RIDDLE
Thomas Moore, the poet, is responsible for the following rude riddle,
and its reply:--
Why is a pump like Viscount Castlereagh?
Because it is a slender thing of wood,
That up and down its awkward arms doth sway,
And coolly spout, and spout, and spout away,
In one weak, washy, everlasting flood!
BIGGAR AND BIGGER
Mrs Biggar had a baby. Which was the bigger? The baby was a little
Biggar!
Which was the bigger, Mr Biggar or the baby? Mr Biggar was father
Biggar!
Mr Biggar died; was the baby then bigger than Mrs Biggar? No, for the
baby was fatherless!
MAGIC CARD SQUARE
Place the sixteen court cards from an ordinary pack in the form of a
square, so arranged that no row, no column, and neither of the diagonals
shall contain more than one card of each suit, and one of each rank.
As the solution presents no difficulty, but merely calls for patience
and attention, we will leave it to the ingenuity of our readers.
THE ANNO DOMINI PUZZLE
A Scottish tradesman had made, as he supposed, about £4,000, but his old
clerk produced a balance-sheet which plainly showed £6,000 to his
credit. It came upon the old gentleman as quite a disappointing shock
when presently the puzzle was solved by the discovery that in the
addition the year of Our Lord had been taken into account!
A PUBLIC SINK
The following ingenious play upon words dates from the days when a
promise was made that the Thames pollution should cease in five years:--
In shorter time, kind sir, contrive
To purify our drink;
For while your figure is a Five
Our river is a Cinq!
ENGLISH AS SHE IS SPOKE
“Mr Smith presents his compliments to Mr Brown, and I have got a hat
that is not his, and he has got a hat that is not yours, so no doubt
they are the expectant ones!”
PICKING FROM _PUNCH_
This play upon words appeared many years ago in the pages of _Punch_,
and is worth preserving:--
To win the maid the poet tries,
And sonnets writes to Julia’s eyes.
She likes a verse, but, cruel whim,
She still remains _averse_ to him.
FRENCH ALLITERATION
“Si six scies scient six cigares, six cent six scies scient six cent six
cigares.”
_To be said trippingly without a trip._
If 6 saws cut 6 cigars, 606 saws cut 606 cigars.
MIND YOUR STOPS!
Here is a good illustration of the nonsense that may easily result from
the misuse of punctuation:--
Every lady in the land
Has twenty nails on each hand;
Five and twenty on hands and feet,
This is true without deceit.
A NOVEL DERIVATION
“Yes,” said an Eton captain of the boats to his uncle, the admiral, “I
can quite believe that the British Jack Tar takes his name from that
Latin verb, which is so suggestive of a life on the ocean wave,
_jactari_, to be tossed about.”
AN AERATED BISHOP
A bishop of Sodor and Man found himself entered in the visitor’s book of
a French hotel as “L’évêque du siphon et de l’homme!”
A HAPPY THOUGHT
They cannot be complete in aught
Who are not humourously prone;
A man without a merry thought
Can hardly have a funny bone.
OUGH!
Though the tough cough and hiccough
Make me hoarse,
Through life’s dark lough I plough
My patient course.
CUM GRANO SALIS
I know Eno, you know too,
Fact is we all three know.
We know Eno, he knows you.
You know I know Eno!
OLD AND SOUND ADVICE
NICHOLAS, 1828.
He who a watch would wear
This must he do;
Pocket his watch, and watch
His pocket too!
COLD-DRAWN CONCLUSIONS
Why is a lame dog like a blotting-pad?
A lame dog is a slow pup.
A slope up is an inclined plane.
An ink-lined plane is a blotting-pad!
THE LAST OF MARY
Mary had a little lamp,
Filled with benzoline;
Tried to light it at the fire,
Has not since benzine!
A BURIED WORD
It is difficult to imagine that the very incarnation of what is wild and
forbidding is buried in those words of peace and promise, “On Christmas
Eve you rang out Angel peals,” until we find in them the consecutive
letters “ourangoutang!”
EVE’S APPLE
How many apples were eaten by Adam and Eve? We know that Eve 81, and
that Adam 812, total 893. But Adam 8142 please his wife, and Eve 81242
please Adam, total 89,384. Then again Eve 814240 fy herself, and Adam
8124240 fy himself, total 8,938,480!
U C I D K
(_You see I decay!_)
“Surely, good sir, you follow me?
It is as plain as A B C.”
“Repeat it in a treble clef,
For I am rather D E F!”
BURIED BY ACCIDENT
Quite unconscious that he was burying a cat in his melodious lines Moore
wrote:--
“How sweet the answer Echo makes
To music at night...!”
A LAWYER’S PROPOSAL
Fee simple and the simple fee,
And all the fees in tail,
Are nothing when compared with thee,
Thou best of fees, fe-male!
A BROAD GRIN
“Sesquipedalia verba,” words a foot and a half long, were condemned by
Horace in his “Ars Poetica.” Had he known English, what would he have
said of “smiles,” a word so long that there is a mile between its first
and last letters?
SWISS HUMOUR
A Swiss lad asked me, as I stopped quite breathless on an Alpine height,
“Do you prefer ‘monter’ to ‘descendre?’” I declared a preference for
downhill, but he most convincingly replied, “I prefer ‘mon thé’ to ‘des
cendres!’” (my tea to cinders).
QUESTIONS WELL ANSWERED
Why did the penny stamp?
_Because the threepenny bit._
Why did the sausage roll?
_Because it saw the apple turn-over._
MEN OF LETTERS
A budding author something new
Submitting, signed himself X Q.
The editor the essay read,
And begged he might be X Q Z!
PUZZLES ON THE PAVEMENT
An angry street arab, who seems to have caught the infection of our
letter puzzles, was heard recently to call out to a gutter-snipe, “You
are a fifty-one ar!” (LIAR.)
PHONETIC ANSWERS
Why may you pick an artist’s pocket?--Because he has _pictures_.
What is the solace for a mind deprest?--_Deep rest_.
A FLIGHT OF FANCY
There was a man from Yankeeland
Who round a walnut tree
Did run so fast--that lissome man--
His own back he could see!
BURNS IN SABOTS
“Guigne a beau de qui sabot de
Nid a beau de t’elle?”
DOG LATIN
Here are all the elements of a rat hunt, expressed in Latin words:--“Sit
stillabit,” sed amanto hiscat, “sta redde, sum misi feror arat trito
unda minus, solet me terna ferret in micat.” They read into English, if
differently pointed, thus:--Sit still a bit, said a man to his cat, stay
ready, some mice I fear, or a rat try to undermine us, so let me turn a
ferret in, my cat.
EARLY RITUAL
It is said that at first Adam thought Eve angelical, but there came a
time when they both took to vestments.
LEST WE FORGET
If a man says that he forgets what he does not wish to remember, does he
mean to say that he does not remember what it is that he wishes to
forget; or that he is able to forget that which he does not wish to
remember?
QUAINT ANGLO-FRENCH QUESTION AND REPLY
Pas qu’il ma, ou qu’il pas?
_Marwood!_
SOME POPULAR DEFINITIONS
_Cricket._ _Lawn Tennis._ _Football._
Lords Ladies Legs
Stumps Jumps Bumps.
REAL DOG LATIN
Pax in bello.
_The dogs of war._
A QUAINT EPITAPH
Here in S X I lies.
Killed by X S I dies.
A PHONETIC REPLY
What is the French for teetotaler?--Thé tout à l’heure!
A FREE RENDERING
Varietas pro Rege.
_Change for a sovereign!_
A FREE TRANSLATION
“Splendide mendax.”
Lying in State.
A WORD AND A BLOW
When Dunlop, in playful mood, said that no one could make a good pun on
his name, a smart bystander at once exclaimed, “Lop off the end, and the
thing is done!”
DOG LATIN (FOR SCHOOLBOYS)
Mitte meos super omnes ad candam aut esse homines mortui.
The Dog Latin may be rendered thus: “Send my overalls to the tailor to
be mended.”
HIS L. E. G.
Some printer’s devil must have been at work when the proof-reader found
“The Legend of the Cid,” set up in type as “The leg end of the Kid!”
SOLUTIONS
No. V.--THE MAKING OF A MAGIC SQUARE
The perfect Magic Square, for which we have given the construction of
two preparatory squares, is formed by placing one of these over the
other, so that the numbers in their corresponding cells combine, as is
shown below.
PREPARATORY SQUARE NO. 1.
*
+--+--+--+--+--+
| 1| 3| 5| 2| 4|
+--+--+--+--+--+
| 5| 2| 4| 1| 3|
+--+--+--+--+--+
| 4| 1| 3| 5| 2|
+--+--+--+--+--+
| 3| 5| 2| 4| 1|
+--+--+--+--+--+
| 2| 4| 1| 3| 5|
+--+--+--+--+--+
PREPARATORY SQUARE NO. 2.
*
+--+--+--+--+--+
| 5|15| 0|10|20|
+--+--+--+--+--+
|10|20| 5|15| 0|
+--+--+--+--+--+
|15| 0|10|20| 5|
+--+--+--+--+--+
|20| 5|15| 0|10|
+--+--+--+--+--+
| 0|10|20| 5|15|
+--+--+--+--+--+
THE PERFECT MAGIC SQUARE.
+--+--+--+--+--+
| 6|18| 5|12|24|
+--+--+--+--+--+
|15|22| 9|16| 3|
+--+--+--+--+--+
|19| 1|13|25| 7|
+--+--+--+--+--+
|23|10|17| 4|11|
+--+--+--+--+--+
| 2|14|21| 8|20|
+--+--+--+--+--+
No less than 57,600 Magic Squares can be formed with twenty-five cells
by varying the arrangement of these same figures, but not many are so
perfect as our specimen, in which sixty-five can be counted in
forty-two ways. These comprise each horizontal row; each perpendicular
row; main diagonals; blended diagonals from every corner (such as 6,
with 14, 17, 25, 3; or 15, 18, with 21, 4, 7); centre with any four
equidistant in outer cells; any perfect St George’s cross (such as 18,
22, 1, 15, 9); and any perfect St Andrew’s cross (such as 6, 22, 13, 5,
19).
No. XII.--A CENTURY OF CELLS
Here is the solution of the ingenious Magic Square of 100 cells with 36
cells unfilled. The rows, columns, and diagonals all add up to 505.
+--+--+--+--+--+--+--+--+--+---+
|91| 2| 3|97| 6|95|94| 8| 9|100|
+--+--+--+--+--+--+--+--+--+---+
|20|82|83|17|16|15|14|88|89| 81|
+--+--+--+--+--+--+--+--+--+---+
|21|72|73|74|25|26|27|78|79| 30|
+--+--+--+--+--+--+--+--+--+---+
|60|39|38|64|66|65|67|33|32| 41|
+--+--+--+--+--+--+--+--+--+---+
|50|49|48|57|55|56|54|43|42| 51|
+--+--+--+--+--+--+--+--+--+---+
|61|59|58|47|45|46|44|53|52| 40|
+--+--+--+--+--+--+--+--+--+---+
|31|69|68|34|35|36|37|63|62| 70|
+--+--+--+--+--+--+--+--+--+---+
|80|22|23|24|75|76|77|28|29| 71|
+--+--+--+--+--+--+--+--+--+---+
|90|12|13|87|86|85|84|18|19| 11|
+--+--+--+--+--+--+--+--+--+---+
| 1|99|98| 4|96| 5| 7|93|92| 10|
+--+--+--+--+--+--+--+--+--+---+
Notice that the top and bottom rows contain all the numbers from 1 to 10
and from 91 to 100; the two rows next to these range from 11 to 20 and
from 81 to 90; the two next from 21 to 30 and from 71 to 80; the two
next from 31 to 39 and 60 to 70, excluding 61, but including 41; and the
two central rows the numbers run from 42 to 59, with 40 and 61.
No. XXIII.--TWIN PUZZLE SQUARES
The following diagram shows how the twin Magic Squares are evolved from
our diagram:--
+-+-+-+ +-+-+-+
|1|5|6| |2|3|7|
+-+-+-+ +-+-+-+
|2|6|7+====+3|4|8|
+-+-+-+ +-+-+-+
|3|7|8| |4|5|9|
+-+-+-+ +-+-+-+
The sums of the corresponding rows in each square are now equal, and the
sums of the squares of the corresponding cells of these rows are equal.
The sums of the four diagonals are also equal, and the sum of the
squares of the cells in corresponding diagonals are equal. The sum of
any two numbers symmetrically placed with respect to the connecting link
between the 7 and the 3 is always 10.
No. XXX.--THE UNIQUE TRIANGLE
The figures to be transposed in triangle A are 9 and 3 and 7 and 1.
/\ /\
/ \ / \
/ 5 \ / 5 \
/ \ / \
/ 4 6 \ / 4 6 \
/ \ / \
/ 3 7 \ / 9 1 \
/ \ / \
/ 2 1 9 8 \ / 2 7 3 8 \
------------------ ------------------
A B
Then in triangle B, the sum of the side is in each case 20, and the sums
of the squares of the numbers along the sides is in each case 126.
No. XXXI.--MAGIC TRIANGLES
The subjoined diagram shows the order in which the first 18 numbers can
be arranged so that they count 19, 38, or 57 in many ways, down, across,
or along some angles, 19 in 6 ways, 38 in 12, and 57 in 14 ways.
[Illustration]
Thus, for examples--
7 + 12 = 14 + 5 = 4 + 15 = 19
7 + 11 + 14 + 6 ------- = 38
7 + 14 + 4 + 5 + 12 + 15 = 57
No. XXXIV.--MAGIC HEXAGON IN A CIRCLE
The figures in the Magic Hexagon must be arranged as is shown in this
diagram:--
126
5 2 7 3 8 5
8 2 4 6 3 7
114 114
4 6 9 1 8 2
3 1 9 7 5 4 1 9 6
1 3 7 9 8 6 7 3 4
8 2 3 9 1 9
126 126
6 4 4 1 8 2
5 5 6 7 2 5
114
It will be seen that the sum of the four digits on each side of each
triangle is twenty, and that, while their arrangements vary, the total
of the added squares of the numbers on the alternate sides of the
hexagon are equal.
No. XXXVI.--A CHARMING PUZZLE
✦ ✦ ✦
✦ ✦ ✦
✦ ✦ ✦
To pass through these nine dots with four continuous straight lines,
start at the top right-hand corner, and draw a line along the top of
the square and _beyond its limits_, until its end is in line with the
central dots of the side and base. Draw the second line through these,
continuing it until its end is below and in line with the right-hand
side of the square; draw the third line up to the starting-point, and
the fourth as a diagonal, which completes the course.
No. XXXVII.--LEAP-FROG
On a chess or draught-board three white men are placed on squares marked
_a_ and three black men on squares marked _b_ in the diagram--
+---+---+---+---+---+---+---+
|_a_|_a_|_a_| |_b_|_b_|_b_|
+---+---+---+---+---+---+---+
1 2 3 4 5 6 7
Every _a_ can move from left to right one square at a time, and every
_b_ from right to left, and any piece can leap over one of another
colour on to an unoccupied square. They can reverse their positions
thus:--
If we number the cells or squares consecutively, and notice that at
starting the vacant cell is No. 4, then in the successive moves the
vacant cells will be 3, 5, 6, 4, 2, 1, 3, 5, 7, 6, 4, 2, 3, 5, 4. Of the
moves thus indicated six are simple, and nine are leaps.
No. XXXVIII.--SORTING THE COUNTERS
The counters are changed in four moves only, moving two at a time as
follows:--
1 2 3 4 5 6 7 8 9 10
+---+---+---+---+---+---+---+---+---+---+
| ○ | ● | ○ | ● | ○ | ● | ○ | ● | | |
+---+---+---+---+---+---+---+---+---+---+
1 2 3 4 5 6 7 8 9 10
+---+---+---+---+---+---+---+---+---+---+
| | | ● | ● | ● | ● | ○ | ○ | ○ | ○ |
+---+---+---+---+---+---+---+---+---+---+
Move 2 and 3 to 9 and 10.
„ 5 and 6 to 2 and 3.
„ 8 and 9 to 5 and 6.
„ 1 and 2 to 8 and 9.
No. XXXIX.--A TRANSFORMATION
To change the ten-pointed star of wooden matches into one of five points
without touching it, let a little water fall into the very centre, as it
lies on quite a smooth surface, and in a few moments, under the action
of the water, it will gradually assume the shape shown in the second
diagram, of a five-pointed star.
[Illustration]
This is a very simple and effective after-dinner trick. Small matches
move best.
No. XLI.--FAST AND LOOSE
The twelve counters or draughtsmen lying loosely at the bottom of a
shallow box can be arranged so that they wedge themselves together and
against the side thus:--
[Illustration]
Place one for the moment in the centre, and six round it. Hold these
firmly in their places with the left hand, and fix the other five round
them, as is shown in the diagram. Then remove the temporary centre, and
fill in with it the vacant place. All will then be in firm contact, and
the box may be turned upside down without displacing them.
No. XLIII.--FOR CLEVER PENCILS
This diagram, shows how a continuous course is possible without taking
pencil from paper, or going twice over any line.
[Illustration]
We have purposely left spaces wide enough to make the solution perfectly
clear.
No. XLVIII.--A BOTTLED BUTTON
[Illustration]
The diagram below shows how the thread within the bottle is severed so
that the button falls, without uncorking the bottle or breaking it.
Nothing is needed but a lens to focus the rays of the sun, which pass
through the glass without heating it, and burn the thread.
No. XLIX.--CLEARING THE WAY
In order to cause the coin to fall into the bottle without touching
coin, match, or bottle, let a drop or two of water fall upon the bent
middle of the match.
[Illustration]
Very soon, under the action of the water, the two ends of the match will
open out so that the coin which was resting on them falls between them
into the bottle.
No. LII.--BILLIARD MAGIC
The diagram we give below shows the ingenious trick by which the plain
white, if struck gently with a cue, will, aided by the tumbler, pot the
spot white ball without in any way disturbing the red.
[Illustration]
The balls to start with are an eighth of an inch apart, and there is not
room for a ball to pass between the cushions and the red. Place the
tumbler close to spot white.
No. LIII.--THE NIMBLE COIN
The most effective way to transfer the coin from the top of the circular
band of paper into the bottle is to strike a smart blow with a cane, or
any small stick, on the inside of the paper band. There is not time for
the coin to be influenced in the same direction, and it falls plumb into
the neck of the bottle.
[Illustration]
No. LVIII.--WHAT WILL HAPPEN?
When the boy shown in this picture blows hard at the bottle which is
between his mouth and the candle flame, the divided air current flows
round the bottle, reunites, and extinguishes the flame.
[Illustration]
No. LX.--VIS INERTIÆ
If, by a strong pull of my finger, I launch the draughtsman that is on
the edge of the table against the column of ten in front of it, the
black man, which is just at the height to receive the full force of the
blow, will be knocked clean out of its place, while the others will not
fall. This is another illustration of the _vis inertiæ_.
[Illustration]
No. LXI.--CUT AND COME AGAIN
A block of ice would _never_ be divided completely by a loop of wire on
which hangs a 5 ℔ weight. For as the wire works its way through, the
slit closes up by refreezing, and the weight falls to the ground with
the wire, leaving the ice still in a single block.
[Illustration]
No. LXIII.--CATCHING THE DICE
It is quite easy to throw the upper of this pair of dice into the air
and catch it in the cup, but the other is more elusive. As you throw it
upward with sufficient force you will also throw the die that has been
already caught out of the cup.
[Illustration]
The secret of success lies in dropping the hand and cup rapidly
downwards, quitting hold at the same moment of the die, which then falls
quietly into the cup held to receive it.
No. LXIV.--WILL THEY FALL?
When the single domino shown in the diagram in front of the double
archway, is quite smartly tipped up by the forefinger carefully inserted
through the lower arch, the stone which lies flat below another _is
knocked clean out_, while none of the other stones fall, another
practical illustration of _vis inertiæ_.
[Illustration]
For this very curious trick, club dominoes, thick and large, should be
used. Some patience and experience is needed, but success at last is
certain.
No. LXV.--A TRANSPOSITION
You will be able to place the shaded coin between the other two in a
straight line without touching one of these, and without moving the
other, if you place a finger firmly on the king’s head and then move the
shaded coin an inch or two to the right, and flick it back against the
coin you hold. The other “tail” coin will then spring away far enough to
allow the space that is required.
[Illustration]
No. LXVI.--COIN COUNTING
After reaching and turning the coin which you first call “four,” _miss
three coins_, and begin then a fresh set of four; repeat this process to
the end.
No. LXVIII.--NUTS TO CRACK
Hold a cup of water so that it will wet the handle of the knife, then
remove it, and place the nut exactly on the spot where the drop of water
falls from the handle.
No. LXXI.--WHAT IS THIS?
The photographic enlargement is simply a much magnified reproduction of
Mr Chamberlain’s eye and eyeglass, exactly as they appear in the picture
which we give below, taken from its negative. A strong condensing lens
will reproduce the original effect, which can also be obtained by
holding the enlargement at a distance.
[Illustration]
[Illustration]
No. LXXV.--THE SEAL OF MAHOMET
[Illustration]
This double crescent may be drawn by one continuous line, without
passing twice over any part, by starting at _A_, passing along the curve
_AGD_, from _D_ along _DEB_, from _B_ along _BFC_, and from _C_ along
_CEA_.
No. LXXVI.--MOVE THE MATCHES
If fifteen matches are arranged thus--
--------| --------| -------|
| | | | | |\ |
| | | |-------| | \ |
| | | | | | \ |
|-------- |-------- |-------
and six are removed, ten is the number that remains, thus--
------- ------- |\ |
| | | \ |
| |------ | \ |
| | | \ |
| |------ | \|
or one hundred may remain, thus:--
-------| -------|
| | | | |
| | | | |
| | | | |
| |------- |-------
No. LXXVII.--LINES ON AN OLD SAMPLER
This diagram shows the arrangement in which seventeen trees can be
planted in twenty-eight rows, three trees in each row:--
[Illustration]
No. LXXXI.--COUNTING THEM OUT
Here is an arrangement of dominoes which enables us to count out the
first twelve numbers, one after the other, by their spelling:--
+---+---+---+---+---+---+---+---+---+---+---+---+
| 2 | 3 | 4 | 3 | 2 | 5 | 2 | 6 | 6 | 0 | 1 | 5 |
| | | | | | | | | | | | |
| 4 | 1 | 5 | 4 | 0 | 3 | 3 | 6 | 5 | 1 | 2 | 5 |
+---+---+---+---+---+---+---+---+---+---+---+---+
Start with the double five, and, touching each stone in turn, say o, n,
e, _one_; remove the stone with one pip, and go on, t, w, o, _two_;
remove the two, and say t, h, r, e, e, _three_, and so on till you
reach at last the twelve.
Playing cards can be used, counting knave, queen, as eleven, twelve. It
makes quite a good trick if you place the cards face downwards in the
proper order, and then, saying that you will call up each number in
turn, move the cards one at a time to the other end, spelling out each
number as before, either aloud or not, and turning up and throwing out
each as you hit upon it. If you do not call the letters aloud it adds to
the mystery if you are blindfolded.
No. LXXXII.--TRICKS WITH DOMINOES
This is the other combination of stones and their pips which fulfils the
conditions, and forms the word AGES.
+---+-------+---+ +-------+-------+ +---+-------+---+ +-------+-------+
| 6 | 6 5 | 5 | | 6 4 | 4 0 | | 1 | 1 1 | 1 | | 0 5 | 5 3 |
| +-------+ | +---+---+-------+ | +-------+ | +---+---+-------+
| 0 | | 4 | | 6 | | 6 | | 4 | | 0 |
+---+---+---+---+ | | +-------+ +---+---+ +---+ | +-------+---+
| 0 0 | 4 4 | | 3 | | 4 2 | | 6 6 | | 2 | 2 2 | 2 |
+---+---+---+---+ +---+ +---+---+ +---+---+ +---+ +---+-------+ |
| 0 | | 4 | | 3 | | 2 | | 6 | | 0 | | 5 |
| | | | | +-------+ | | +-------+ | +-------+---+---+
| 1 | | 3 | | 3 | 3 1 | 1 | | 2 | 2 3 | 3 | | 1 5 | 5 5 |
+---+ +---+ +---+-------+---+ +---+-------+---+ +-------+-------+
+-------+-------+ +---+-------+ +---+-------+---+ +---+ +---+
| 6 5 | 5 3 | | 1 | 1 5 | | 1 | 1 1 | 1 | | 5 | | 0 |
+---+---+-------+ | +---+---+ | +-------+ | | | | |
| 6 | | 0 | | 5 | | 6 | | 2 | | 4 | | 3 |
| | +---+ | | +---+ +---+ +---+ +---+
| 0 +-------+ | 0 | | 2 | | 6 | | 4 +-------+ 3 |
+---+ 0 2 | | +---+---+ | | | | 4 3 | |
| 0 +-------+ | 4 | 4 2 | | 6 | | 4 +-------+ 3 |
| | +---+---+---+ +---+ +---+ +---+ +---+
| 0 | | 4 | | 2 | | 6 | | 2 | | 4 | | 3 |
+---+---+-------+ | | | | | +-------+ | | | | |
| 0 5 | 5 5 | | 6 | | 6 | | 3 | 3 2 | 2 | | 1 | | 1 |
+-------+-------+ +---+ +---+ +---+-------+---+ +---+ +---+
In both cases a complete set of stones is used, which are arranged in
proper domino sequence, and everyone of the eight letters carries
exactly forty-two pips.
No. XCI--THE STOLEN PEARLS
The dishonest jeweller reset the pearls in a cross so that its arms were
a stage higher up. It will be seen that by this arrangement nine pearls
can still be counted in each direction.
[Illustration]
ENIGMAS
1. Self-assassin, a neddy. Saw an ass in an eddy!
2. To get her: Together.
3. A candle.
4. Liquorice.
5. A book.
6. One solver proposes _raven_, croaking before a storm; once an object
of worship; seldom seen; forbidden in Leviticus as food; alone with Noah
when its mate was sent forth; weighing about 3 lbs; the name of a small
South Carolina island, having as its first and last letters R and N; the
Royal Navy.
Another finds in _K_ the key, as that letter with _no ar_ is alone in
_ark_. With much ingenuity he shows that the last line calls for a
second letter, and that the letters _K_ and _G_ can be traced
throughout almost all Hallam’s “lights;” _Kilogram_ being nearly 3 lbs.,
and _Knot_ a mile; while either _K.G._ (Knight of the Garter) or _King_
would fit the final line.
7. The lines become “rank treason” if the corresponding lines of the two
stanzas are read together, thus:--
The pomps of Courts and pride of Kings
I fain would banish far from hence,
and so on throughout.
8. A pair of skates.
9. A shadow.
10. A chair.
11. The changes that are rung are one, eno, Noe, neo, eon, on, none.
12. Cares, caress.
13. Echo.
14. Strike.
15. A pair of spurs.
16. A.D.A.M.; Adam; a dam; Adam; a damson; a dam.
17. The CID, the Castilian hero whose fame was at its height in the
middle of the eleventh century.
18. A sigh.
19. Coxcomb.
20. Jack and Jill.
21. A man’s felt hat.
22. Measurable.
23. Chair, char, arch.
24. Sala (G.A.S.), which reversed is _alas_.
25. Page, (p)age.
26. C (sea), A (hay), T (tea).
27. A BROKEN TALE
The deil jumped over the clouds so high
That he bounded almost right over the sky.
Over gates and fields, and under the trees
He dodged, with his tail dragging over all these,
But, alas! made a terrible blunder,
For a twist in his tail hooked under a rail,
And broke that appendage asunder.
28. Yesterday. _Most_ excludes Adam, and _ter_ is half of _terror_.
29. Donkey.
30. Mental, lament, mantle.
31. His heels.
32. Tares, tears, a rest.
33. Connecticut.
34. Grate, rate, rat, ate.
35. Mary, in fanciful mood, on her thirty-sixth birthday, decorated her
pincushion thus--XXXVI.
36. Opinionist.
37. Violin (LVII + on).
38. Trout (tr--out).
39. Post--stop.
40. A pair of scissors in a case.
41. Dog.
42. Mainland.
43. Changed.
44. The name of the Russian nobleman’s third son, the boy who went to
sea, was Yvan. As the name of the eldest, Rab, who became a lawyer, was
Bar reversed, and that of the soldier son Mary was Army as an anagram,
so Yvan’s name resolves itself into Navy, his profession.
45. VIVID.
46. Nothing.
47. London.
48. Rock, cork.
49. Place, lace, ace, lac.
50. a, e, i, o, u, y.
51. The solution of the enigma which begins:--
“Twice six is six, and so
Six is but three;
Three is just five you know,
What can we be?”
is the number of letters of the alphabet used in spelling a number. Thus
twice six, or _twelve_, is composed of six letters, and so on.
52. A button.
53. LEVEL--MADAM.
54. An egg.
55. Vague.
56.
A headless man had a letter to write,
(The letter O, i.e. _nothing_.)
He who read it had lost his sight,
(He read _nothing_.)
The dumb repeated it word for word,
(He said _nothing_.)
And deaf was he who listened and heard.
(He heard _nothing_.)
57. Highway.
58. A set of false teeth.
59. The “fearful fate” enigma is slaughter; cut off its head and we have
laughter; lop off its shoulders and we find aught.
60. Speculation--peculations.
61. The word “united” is “of fellowship the token,” and the requirement
“reverse it, and the bond is broken” refers only to the two central
letters. When this is reversed the word “untied” is formed.
62. Average.
63. German--manger.
64. Corkscrew.
65. _Tar_ is transformed by _Art_, and as a sailor is fond of port, and
blisters in the sun. When it turns to run it becomes _Rat_, and when it
doubles it is _Tartar_, and is caught.
66.
A man with one eye two plums must have seen,
One perfectly ripe, the other quite green.
The former he took, and ate it with pleasure,
The other he left to ripen at leisure.
67. A widower who has lost two wives.
68. The grape-vine on the Marquis of Breadalbane’s estate, Killin, N.B.,
which bears more than 5000 bunches of grapes, of which only 500,
properly thinned out, are allowed to mature, so that the fewer and
smaller bunches bear finer fruit.
69. Poe, poet, poetry.
70. Theatres. The articles _the_ and _a_ lead on to the other four
letters _tres_, and these form the word _rest_, if the _t_ is
transferred to the end.
71. Scold, cold, old.
72. Justice, (_just_--_ice_).
73. A shadow.
74. VI., IV., I.
75. The letter I.
76. The letter V.
77. An army.
78. _A rich table_; _chair_, _table_; _charitable_.
79. High-low.
80. Orange, pear, date, banana, peach, plum, lime, lemon, mango, apple.
81. Innuendo.
82. Snipe, of which _pines_ is an exact anagram.
83.
None can locate the subject of my riddle,
For all the world would seek its place in vain,
Cut it asunder almost in the middle,
And in our very midst its place is plain
is solved by _nowhere_, _now here_.
CHARADES
1. Good-night (knight).
2. Grandson.
3. Oyster.
4. Stay-lace.
5. Ann--ounce.
6. VOID, OVID.
7. Disconsolate (disc--on--so--late).
8. Ginger--Nigger. (G.E.R. Great Eastern Railway).
9. Honesty (hone, below the razor).
10. Nutmeg.
11. Waterloo.
12. Whether (whet--her).
13. Mendicant (mend I can’t).
14. Campbell.
15. Foxglove.
16. Anglesea.
17. Shewed.
18. Sparrow, often a gutter percher!
19. Dishonest (dish--one--st).
20. Dogmatism.
21. Anthem.
22. Gigantic (gig--antic).
23. Toad (_ad_ is Latin for _to_).
24. Cineraria (sinner--area).
25. Ignis--fatuus, or Will-o’-the-wisp (ignis, fire--fatuus, a fool).
26. Isis (sis in Latin, _thou mayest be_).
27. Capacity.
28. Scarcity.
29. Pardon.
30. Humbug.
31. Ramrod.
32. Dumpling.
33. Into.
34. Herring.
35. Dublin (bud--nil).
36. Peerless.
37. Beatrice.
38. Beam--_be_ is half of the word _verb_, _am_ is half of _same_, and
_be_ and _am_ are similar in sense.
39. Pulpit.
40. Spare--rib.
41. Usher.
42. The ship _Carmania_.
43. Candid.
44. Husbandman.
45. Hamlet.
46. Handcuff.
47. Sinecure.
48. Infancy.
49. Teachest.
50. Hippodrome.
51. Invalid.
52. Woman.
53. Kensington.
54. Benjamin.
55. Stipendiary.
56. Wonder.
57. Cabin.
58. Falstaff.
59. Periwinkle.
60. Nameless.
61. Fourscore.
62. Hatred.
63. Catsup.
64. Molestation.
65. Omen.
66. Isinglass.
67. Muffin.
68. Footman.
69. Sparrow-grass.
70. Matchless.
71. Planted.
72. Toast-rack.
73. Half-and-half, if properly punctuated.
RIDDLES AND CONUNDRUMS
1. Washerwoman.
2.
“Call me an uncle, then you speak me fair,
Call me an _uncle_-_an_ uncle if you dare!”
3. Pluck the goose.
4. Also.
5. A lawsuit.
6. Because they are bargains.
7. A pair of shoes.
8. Because whenever he goes out he can put his portmanteaux (Portman
toes) into his boots.
9. FIVE.
10. Rail--liar.
11. Because it slopes with a flap!
12. In California they eat all the peaches they can, and can all they
can’t!
13. The utmost effort ever made by a piebald (or by any) horse at a high
jump is _four feet from the ground_!
14. Insatiate (in--sat--I--ate).
The clever couplet--
Under my first my second stood.
That’s your riddle: mine’s as good!
was intended to point out that the enigma
In my first my second sat,
Then my third and fourth I ate
was _understood_, and to frame at the same time a fresh one of similar
sort.
15. A gardener minds his peas, a billiard-marker his cues, a precise man
his p’s and q’s, and a verger his keys and pews.
16. A man with one eye can see more than a man with two, for in addition
to all else he can see the other man’s two eyes, which can only see his
one.
17. When you ask a policeman what o’clock it is, you are like the
Viceroy of India, because you are _as king for the time_.
18. “What does Y E S spell?” is the question to which “yes” is the only
possible reply.
19. An umbrella.
20. London for many years was a wonderful place for sound, for you could
laugh at 5 p.m. at Waterloo Junction, and by walking briskly across the
river be in time for the late Echo at Charing Cross.
21. Because it may be smelt!
22. The full reading of “1s. 6d. me a bloater” is “Bob Tanner sent me a
bloater.”
_Note._--If any solver should ask, “But where is the ‘sent’?” we reply,
“The scent was in the bloater!”
23. The solution of the prime conundrum “Why is a moth flying round a
candle like a garden gate?” is--Because if it keeps on it singes its
wings (its hinges it swings).
24. (Twe)lve--twe(nty) = twenty.
25. Because it would be my newt (minute).
26. The steps by which, in paying my debt to a lawyer, a threepenny
piece swells to the needed six and eightpence are these:--
Three pence is one and two pence;
One and two pence is fourteen pence;
Fourteen pence is six and eight pence!
27. When the Vickers Maxim (vicar smacks him).
28. Children should go to bed soon after tea because when “t” is taken
away _night_ is _nigh_.
29. Scottish may be lighter than Irish men, for while Irishmen may be
men of Cork, Scotsmen may be men of Ayr.
30. Because barbers do not cut hair any longer!
31. Colenso.
32. This is Archbishop Whately’s riddle, and a solution, suggested long
after his offer of £50 had expired:--
When from the Ark’s capacious round
Mankind came forth in pairs,
Who was it that first heard the sound
Of boots upon the stairs?
To him who cons the matter o’er,
A little thought reveals,
He heard it first who went before
Two pairs of soles and eels!
33. If Moses was the son of Pharaoh’s daughter, _he_ was the daughter of
Pharaoh’s son.
34. The word of three syllables which represents woman or man
alternately by three contractions is heroine--hero--her--he.
35. Solution to-morrow!
36. Wholesome.
37. They were jolly well tired!
38. The stocks.
39. Because it makes a far--thing present.
40. If I were in the sun, and you were out of it, it would be a _sin_.
41. COLD.
42. Take _off_--_ice_.
43. Enduring.
44. Uncross the “t” of “a foot,” and it becomes “a fool.”
45. A rabbit can run into a square wood with sides that each measures a
mile, keeping always in a straight line, _until it reaches the middle of
the wood_, when it must begin to run out of it!
46. To-morrow.
47. Scar--bo--rough.
48.
Though I in time for lunch may be,
U cannot come till after T.
49. A wig.
50. Because _we_ cannot be _wed_ without it.
51. A spit.
52. Wit (double you--I--tea).
53. Holding up your hand you will see what you never have seen, never
can see, and never will see--namely, the little finger as long as the
finger next to it!
54. The Emperor of Russia issues manifestoes. An ill-shod beggar
manifests toes without his shoes!
55. To show Walsham How a good bishop is made.
56. There was certainly a tribe of Man--asses.
57. L. s. d.
58. A pillow.
59. Abused (a--b--used).
60. A settler.
61. Because John Burns.
62. It looks round!
63. A minute.
64. A deaf and dumb man cannot tickle nine persons, because he can only
gesticulate (just tickle eight!).
65. London always began with an _l_, and end always began with an _e_!
66. Season.
67. The new moon, for the full moon is much lighter.
68. Island (_la_ is the middle, _is_ is the beginning, _and_ is the
end!).
69. Because! (_bee caws_).
70. The reading of the Dark Rebus
O
B =e= D
is--a little blackie in bed with nothing over him.
71. If a monkey is placed before a cross it at once gets to the top, for
APE is then APEX.
72. The answer to this riddle, defined as “two heads and an
application,” is _a kiss_.
73. The Latin expression of encouragement “macte” may be applied in its
English equivalent _in-crease_ to a batsman when an umpire says of him
“not out” after a risky run.
74. The place which answers to the description “Half an inch (ch) before
the trees (elms), half a foot (fo), and half a yard (rd) after them
leads us to an English town,” is _Chelmsford_.
75. The subject of the riddle, which none can locate, is _nowhere_. Cut
asunder almost in the middle, it breaks into the opposite extreme, and
becomes _now here_!
76. The two letters which in nine letters describe the position of one
who has been left alone in his extremity are a _b_ and one _d_.
_Abandoned._
77. Usher (us--her).
78. You can make a Maltese cross with less than twelve unbent and
unbroken matches, by striking only one match and dropping it down his
back. If the first fails, try another!
79. We may suppose that there were less vowels than we have now in the
early days of _Noe_, when _u_ and _i_ were not there.
80. An orange (or--ange).
81. The moral taught to us by the old emblem of a weathercock in the
shape of a fish on a church near Lewes is, “It is vain to aspire!”
82. FIDDLE.
83. The words “for the want of water we drank water, and if we had had
water we should have drank wine,” were spoken by the crew of a vessel
that could not cross the harbour bar for want of water, and who had no
wine on board.
84.
The poor have two, the rich have none,
Millions have many, you have one,
is solved by O.
85. Money.
86. Had _I_ been in Stanley’s place when Marmion cried “On, Stanley,
on!” the resulting word _on_-_i_-_on_ would have made the Scottish fray
seem more like Irish stew.
87. The figure O.
88.
Let her be, or beat her,
Give her little ease;
Then in safety seat her
All among the bees,
is solved by _A Queen Bee_. The _Bee_ is made up of the letter _b_, in
Greek called _beta_, and two little _e_s.
89. Its.
90. Inch--chin.
NUTS TO CRACK
1. CRAZY LOGIC
Can you prove that madman = madam is solved thus:--
A madman is a man beside himself. Therefore a madman = two men.
Madam is a woman. Woman is double you O man (w-o-man). Therefore madam =
two men.
And as things which are equal to the same are equal to one another,
therefore madman = madam.
Q. E. D.
(_Quite easily Done._)
2. A BIT OF BOTANY
The water-plant is the _Frogbit_, which floats and spreads on the
surface of ponds and pools.
3. The six islands buried in the lines--
He set down the answer to that sum at random.
By bold policy Prussia became a leading power.
A great taste for mosaic has arisen lately.
The glad news was swiftly borne over England.
At dusk, year after year, the old man rambled home.
The children cried, hearing such dismal tales.
are Sumatra, Cyprus, Formosa, Borneo, Skye, Malta.
4. The seven geographical names “buried” in the sentence, “We could hide
a light royal boat with a man or two; the skipper, though, came to a
bad end,” are Deal, Troy, Witham, Esk, Perth, Baden, Aden.
5. The jumbled letter lines read thus:--
Let those who deal in mystic rhymes
This transposition trace;
And to _The Standard_ send betimes
Each letter in its place.
6.
Three little articles all in a line
Lead to a thousand, expressing,
If with another all these you combine,
What can be never a blessing--
is solved by ANATHEMA (an-a-the-M-a).
7.
Ask a policeman, possibly he knows
In uniformed array
If not, an added letter plainly shows
How little he can say--
is solved by adding n _to uniformed_--_uninformed_.
8. The Ruling letters in:--
We rule the world, we letters five,
We rule the world, we do!
And of our number three contrive
To rule the other two--
are B. U. T. (beauty), and Y. Z. (wise head).
9. Many might punctuate the sentence, “Maud like the pretty girl that
she was went for a walk in the meadows” by merely putting a full stop at
the end of it. But why not make a _dash after Maud_?
10. The answer by Echo to
What were they who paid three guineas
To hear a tune of Paganini’s
is _Pack o’ ninnies_!
11. The verse in which only five different letters are used is--
It is nineteen tennis nets,
Nine in tents in tints intense.
Ten sent in inset in sets,
See it, test it, it is sense!
12. The catch sentence: “If is is not is and is not is is what is it is
not is and what is it is is not if is not is is?” becomes intelligible
if it is punctuated thus: If “is” is not “is,” and “is not” is “is,”
what is it “is not” is, and what is it “is” is not, if “is not” is “is?”
13. The words on the placard were PALE ALE, and these through the steps
described become PA-LE AP-LE, APPLE.
14. The reading of “Time flies you cannot they pass at such irregular
intervals,” is as though it ran “You cannot time flies, they pass at
such irregular intervals.”
ROYAL MEMORIES
15. I was reminded of Queen Victoria as I entered the South Kensington
Museum at _five minutes to one_, because I noticed that the hands of my
watch were so placed as to represent a very perfect V.
When I left the building it was _twenty-five minutes and forty-five
seconds to six_, and then the hands, with the help of the seconds hand
which crossed it, formed a very perfect A, and so reminded me of Prince
Albert.
16. The solution of
CCC
---
SAW
is “the season was backward.”
17. THE OLD LATIN LEGEND
+------------------+
| AMANS TAM ERAT |
| HI DESINT HERO |
|AD DIGITO UT MANDO|
+------------------+
reads off into excellent English thus:--
“A man’s tame rat hides in the road; dig it out man, do!”
18. The statement “I know that roseate hues preserve” does not imply
that there is any curative virtue in rose-coloured rays, but asserts “I
know that Rose ate Hugh’s preserve!”
19. The following exception was taken to Dr Fell’s diet for the sick of
all sops:--
“Sure the doctor’s wits are failing,”
Cried a saucy wag.
“Allsopp’s ale the sick and ailing
To their bier will drag.”
20. The English dislocated sentence formed by these thirty-six
letters:--
SAR BAB SAR BAB SAR BAB
SAR BAB SAR BAB SAR ARA
is, “A bar as a barb bars Barbara’s Barabbas.”
21. The Wiltshire farmer’s sentence--
“Igineyvartydreevriswutts”
when interpreted runs, “I gave him forty-three for his oats.”
22. Here is a tolerable rhyme to Chrysanthemum:--
Through gardens where appear
Beds of chrysanthemum,
We pass at eve to hear
Our choir their anthem hum.
23. This was, in brief, the pathetic tale of the three eggs--“_Two
bad!_”
24. THE ANCIENT LEGEND
+--------------+
|Doun tooth ers|
| A sy |
| Ouw ould bed |
| One by |
+--------------+
reads thus:--“Do unto others as you would be done by.”
25. There were but six persons in the vault which contained two
grandmothers and their two grand-daughters; two husbands and their two
wives; two fathers and their two daughters; two mothers and their two
sons; two maidens and their two mothers; two sisters and their two
brothers. Two widows had each one son, and each married the son of the
other, and had a daughter by the marriage.
26. The supposed charm--
ground
turn evil star
given by the wise woman to a nervous couple, to counteract their evil
star, and account for mysterious noises, is merely “Rats live
underground,” _turn_ being a direction to the solver.
27. The word composed of five varied vowels of foreign sound, with but
one consonant between them, is oiseau, the French for bird. The three
letters which flow in four are eau, water, which flows in the River
Oise, and the other trio spell oie, a goose, which is found therein.
28. The Paradox--
What in his mind no man can find
Four symbols will display;
But only one remains behind
If one we take away--
is solved by _Bone_.
29. The barber who had placed in his window the notice--
“What do you think
I will shave you for nothing and give you a drink”
explained, to the man who expected a free shave and a cool drink, that
the interpretation was really this:--“What? Do you think I will shave
you for nothing, and give you a drink?”
30. The curious Latin label--
+-------------------------+
| G E N U I N E J A M |
| A |
| I C A R U M. |
+-------------------------+
has no reference to Icarus, or to flying machines. Its proper place was
on a cask of “Genuine Jamaica Rum.”
31. The puzzle word is ipecacuanha.
32.
Johnson’s cat went up a tree,
Which was sixty feet and three;
Every day she climbed eleven,
Every night she came down seven.
Tell me, if she did not drop,
When her paws would touch the top--
is solved thus:--As each day and night the cat climbed up eleven feet,
and came down seven, the daily upward gain was four feet, and thirteen
days would bring her fifty-two feet up the tree. Then on the fourteenth
day she mounted the remaining eleven feet, and was at the top, so that
no coming down seven feet is to be taken into account, and she attains
her place _in fourteen days_.
33.
A third of six behind them fix,
A third of six before;
Thus makes two nines, when all combines,
Exactly fifty-four--
is solved:--
IX NINE (the two nines.)
(S is a third of six) SIX NINES = 54.
34. To bridge the moat, or space between the two squares which one match
cannot span, place one match across one of the corners of the outer
square, and the other from this to the inner square.
35.
We start when the ninth hour is past,
Then there’s an end of you.
A vengeful goddess shows at last
What Antifat will do--
is solved by _attenuate_ (at ten-u-Ate, goddess of vengeance).
36. Mrs P.W. had only one guest to provide for. Her husband had invited
his father’s brother-in-law, Jones, who was his brother’s father-in-law,
because Mr P.W.’s brother had married Jones’ daughter, and his
father-in-law’s brother, because he had himself married Jones’ niece,
and also his brother-in-law’s father, as Mr P.W.’s sister married Jones’
son.
37. This sharp customer started with _fivepence farthing_, and gradually
extracted from the landlord’s pocket a shilling and three farthings
towards the eighteenpence which he spent in refreshments.
38. To form four triangles of equal size with six similar matches, place
three of them in a triangle on the table, and hold or balance the other
three above these, so as to form the skeleton of a pyramid.
39. The following couplet solves this question:--
Forty-five-years I had seen
When my bride was but fifteen
40. The lad gave tenpence each to a grandfather, his son, and his
grandson.
41. Nell’s reply to Tom, when he said, with a yawn, “I wish we could
play lawn-tennis!” “Odioso ni mus rem. Moto ima os illud nam,” was not
Latin, but good sound English. Read each word in its order _backwards_,
and you have-- “Oh! so do I in summer. Oh, Tom! am I so dull, I man?”
42. The policeman who was looking up the road for motor-car scorchers
was able to see that his mate, who was looking down the road, was
smiling, because they stood face to face.
43.
Twenty-seven with three nines
You and I can score;
Anyone on other lines
Can extend them more.
Who can write them to be seen
Equal only to sixteen?--
is solved thus:--Two of the three nines are reversed, and then
96
-- = 16.
6
44. The trying sentence, “that that is is that that is not is not is not
that it it is,” is cleared thus by proper punctuation:--That that is,
is; that that is not, is not. Is not that it? It is.
45. A L L O is “Nothing after all.”
46. The proverb with missing consonants is--Give a dog a bad name and
hang him.
47. If to the thirteen upright strokes--
| | | | | | | | | | | | |
thirteen more are added, the word HOTTENTOT may be formed.
48. A coroner could, after signing his name, write down his official
position with _c or one r_.
=PART II.=
CONTENTS
PAGE
OPTICAL ILLUSIONS II-1
FREAKS OF FIGURES II-20
CHESS CAMEOS II-26
SCIENCE AT PLAY II-58
CURIOUS CALCULATIONS II-114
WORD AND LETTER PUZZLES II-147
SOLUTIONS II-167
OPTICAL ILLUSIONS
No. I.--SWALLOWED!
Take a small card and place it on its longer edge upon the dotted line.
Now set the picture in a good light on the table, and let your head drop
gradually towards the card until you almost touch it with your nose. You
will see the bird fly into the jaws of the snake!
[Illustration]
AMUSING PROBLEMS
THE CARPENTER’S PUZZLE
1. A carpenter was called in to mend a hole in a wooden floor. The gap
was two feet wide, and twelve feet long, while the only board at hand
was three feet wide, and eight feet long.
+----------------+
| Fig. 1. |
| |
| |
+----------------+
+------------------------+
| Fig. 2. |
| |
+------------------------+
This had been put aside as useless, but, on catching sight of it, the
carpenter ran his rule over it and said that he could make a perfect
fit, and cover all the hole by cutting the board into two pieces. How
did he do this?
No. II.--AN ILLUSION OF ROTATION
This most interesting optical illusion was devised by Professor Thompson
some years ago:--
[Illustration]
[Illustration]
If the illustration is moved by hand in a small circle on the level,
with such motion as is given in rinsing out a bowl, the circles of the
larger diagram will seem to revolve in the direction in which the paper
is moved, while the cogs of the smaller diagram will apparently turn
slowly in the opposite direction.
No. III.--WHIRLING WHEELS
Here is another combination of the clever illusion of the whirling
wheels.
[Illustration]
If a rapid rotating motion is given to the diagram, each circle will
seem to revolve, and the cog wheel in the centre will appear to move
slowly round in the opposite direction.
GOLDEN PIPPINS
2. A man leaves an orchard of forty choice apple trees to his ten sons.
On the first tree is one apple, on the second there are two, on the
third three, and so on to the fortieth, on which there are forty.
Each son is to have four of the trees, and on them an equal number of
the apples. How can they thus apportion the trees, and how many apples
will each son have? Here is one way:--
1 2 3 4 5 6 7 8 9 10
20 19 18 17 16 15 14 13 12 11
21 22 23 24 25 26 27 28 29 30
40 39 38 37 36 35 34 33 32 31
-----------------------------
82 82 82 82 82 82 82 82 82 82
Can you find another perfect solution?
No. IV.--AN ILLUSION OF MOTION
We call very particular attention to this fascinating illustration of
the fact that the mind and eye may receive and register false
impressions under quite simple conditions:--
[Illustration]
Hold this at rather more than reading distance, upright, and move it
steadily up and down. The dark line will soon seem to slide up and down
upon the perpendicular line. It will be better seen if drawn to pattern
on a card.
No. V.--ARE THEY PARALLEL?
As the eye falls upon the principal lines of this interesting diagram,
an immediate impression is formed that they are not parallel.
[Illustration]
This, however, is a most curious illusion, created in the mind entirely
by the short sloping lines, as is found at once by the simple test of
measurement.
AN AWKWARD FIX
3. With no knowledge of the surrounding district, I was making my way to
a distant town through country roads, guided by the successive
sign-posts that were provided.
Coming presently to four cross-roads I found to my dismay that some one
had in mischief uprooted the sign-post and thrown it into the ditch. In
this perplexing fix how could I find my way? A bright thought struck me.
What was it?
LINKED SWEETNESS LONG DRAWN OUT
4. As I stood on the platform at a quiet country station, an engine,
coming along from my left at thirty miles an hour, began to whistle when
still a mile away from me. The shrill sound continued until the engine
had passed a mile and a half to my right. For how long was I hearing its
whistle?
No. VI.--ILLUSION OF LENGTH
In this curious optical illusion the lines are exactly equal in length.
\ /
\ /
>--------------------<
/ \
/ \
/ \
/ \
<-------------------->
\ /
\ /
The eye is misled by the effect which the lines drawn outward and inward
at their ends produce upon the mind and sight.
ELASTIC QUARTERS
5.
In room marked A two men were placed,
A third he lodged in B;
The fourth to C was next assigned,
The fifth was sent to D.
In E the sixth was tucked away,
F held the seventh man;
For eighth and ninth were G and H,
Then back to A he ran.
Thence taking one, the tenth and last,
He lodged him safe in I;
Thus in nine rooms ten men found place,
Now can you tell me why?
EXCLUDED DAYS
6. Are there any particular days of the week with which no new century
can begin?
No. VII.--ILLUSION OF HEIGHT
These straight lines, at right angles to each other, are, though they do
not seem to be, exactly equal in length.
[Illustration]
This and similar illusions are probably due to the variation of the
vague mental standard which we unconsciously employ, and to the fact
that the mind cannot form and adhere to a definite scale of measurement.
DRIVING POWER
7. Why has a spliced cricket bat such good driving power? and why is the
“follow through” of the head of a golf club so telling in a driving
stroke?
THE BUSY BOOKWORM
8. On my bookshelf in proper order stand two volumes. Each is two inches
thick over all, and each cover is an eighth of an inch in thickness. How
far would a bookworm have to bore in order to penetrate from the first
page of Vol. I. to the last page of Vol. II.?
No. VIII.--ILLUSION OF DIRECTION
Can you decide at a glance which of the two lines below the thick band
is a continuation of the line above it?
[Illustration]
Make up your mind quickly, and then test your decision with a straight
edge.
A TERRIBLE TUMBLE
9. From what height must a man fall out of an airship--screaming as he
goes overboard--so as to reach the earth before the sound of his cry?
_N.B._--Resistance of the air, and the acoustical fact that sound will
not travel from a rare to a dense atmosphere, are to be disregarded.
IN A PREDICAMENT
10. Imagine a man on a perfectly smooth table surface of considerable
size, in a vacuum, where there is no outside force to move him, and
there is no friction. He may raise himself up and down, slide his feet
about, double himself up, wave his arms, but his centre of gravity will
be always vertically above the same point of the surface.
How could he escape from this predicament, if it was a possible one?
No. IX.--THINGS ARE NOT WHAT THEY SEEM
It is difficult, even after measurement, to believe that these figures
are of the same size.
[Illustration]
But they will stand the test of measurement.
A CLIMBING MONKEY
11. A rope passes over a single fixed pulley. A monkey clings to one end
of the rope, and on the other end hangs a weight exactly as heavy as the
monkey. The monkey presently starts to climb up the rope. Will he
succeed?
GAINING GROUND
12. Seeing that the tension on a pair of traces tends as much to pull
the horse backward as it does to pull the carriage forward, why do the
traces move on at all?
No. X.--THE SHIFTING BRICK
A very curious and interesting form of optical illusion is well
illustrated by what may be called “the shifting brick.”
[Illustration]
The central brick, drawn to show all its edges, as though it were made
of glass, will assume the form indicated by one or other of the smaller
bricks at its right and left, according to the way in which the eyes
accommodate themselves for the moment to one pattern or to the other. If
you do not see this at first, look steadily for awhile at the pattern
you desire.
ASK A CYCLIST
13. Why does a rubber tyre leave a double rut in dust, and a single one
in mud?
TODHUNTER’S UNIQUE PUZZLE PROBLEM
14. If two cats, on opposite sides of a sharply sloping roof, are on the
point of slipping off, which will hold on the longest?
No. XI.--AN ILLUSION WITH COINS
If you place four coins in the positions shown at the top of this
diagram, and attempt, or challenge some one to attempt, without any
measuring, to move the single coin down in a straight line until the
spaces from C to D on either side exactly equal the distance from A to
B--
[Illustration]
It must drop as far as is shown here, which seems to the unaided eye to
be too far.
This excellent illusion can be shown as an after-dinner trick with four
napkin-rings.
No. XII.--THE FICKLE BARREL
Here is another excellent optical illusion. Look attentively at the
diagram below, and notice in which direction you apparently look into
it, as though it were an open cask.
[Illustration]
Now shake the paper, or move it slightly, and you will find, more often
than not, that you seem to see into it in quite the opposite direction.
HEADS I WIN!
15. I hold a penny level between my finger and thumb, and presently let
it fall from the thumb by withdrawing my finger. It makes exactly a
half-turn in falling through the first foot. If it starts “heads,” how
far must it fall to bring it “heads” to the floor?
HE DID IT!
16. “They call these safety matches,” said Funnyboy at his club one day,
“and say that they strike only on the box. Don’t believe it! I can
strike them quite easily on my boot.”
No sooner said than done. He took out a match, struck it on his boot,
and--phiz!--it was instantly alight. The box was handed round, and match
after match was struck by the bystanders on their boots, but not one of
them could succeed.
“You don’t give the magic touch,” said Funnyboy, as he gaily struck
another. How did he do it?
No. XIII.--A STRANGE OPTICAL ILLUSION
[Illustration]
[Illustration]
How many cubes can you see as you look at the large diagram? The two
smaller ones should be looked at first alternately, and they will assist
the eye to see at one time six, and at another time seven, very distinct
cubes.
No. XIV.--A CIRCULAR ILLUSION
This curious optical illusion is not easily followed by eye to the
finish of the several lines.
[Illustration]
Each short line is, in fact, part of the circumference of a circle, and
the circles when completed will be found to be accurately concentric. It
would seem at first sight that the lines are taking courses which would
eventually meet at some point common to them all.
A CYCLE SURPRISE
17. We commend this curious point to the special attention of
cyclists:--
A bicycle is stationary, with one pedal at its lowest point. If this
bicycle is lightly supported, and the bottom pedal is pulled backward,
what will happen?
No. XV.--THE GHOST OF A COIN
[Illustration]
A most remarkable optical illusion is produced by the blending of the
dark and light converging rays of this diagram. Stand with your back to
the light, hold the page, or better still, the diagram copied on a card,
by the lower right-hand corner, give it a continuous revolving movement
in either direction, and the visible ghost of a silver coin, sometimes
as large as sixpence, sometimes as large as a shilling, will appear!
Where can it come from?
ROUGH AND READY
18. A merchant has a large pair of scales, but he has lost his weights,
and cannot at the moment replace them. A neighbour sends him six rough
stones, assuring him that with them he can weigh any number of pounds,
from 1 to 364. What did each stone weigh?
No. XVI.--A TAME GOOSE
Here is a pretty form of our first illusion:--
[Illustration]
Place the edge of a card on the dotted line, look down upon it in a good
light, and, as you drop your face till it almost touches the card, you
will see the goose _move towards the sugar_ in the little maiden’s hand.
REJECTED ADDRESSES
19. A wheel is running along a level road, and a small clot of mud is
thrown from the hindermost part of the rim. What happens to it? Does it
ever renew its acquaintance with the wheel that has thus rejected it?
No. XVII.--ILLUSION OF LENGTH
Here is another method by which an optical illusion of length is very
plainly shown:--
A B
+--------------+
/ \
/ \
/ \
/ \
+------------------------+
A B
+--------------+
\ /
\ /
\ /
\ /
+----+
Judged by appearances, the line A B in the larger figure is considerably
longer than the line A B below it, but tested by measurement they are
exactly equal.
THE CARELESS CARPENTER
20. A village carpenter undertook to make a cupboard door. When he began
to put it in its place it was too big, so he took it back to his
workshop to alter it. Unfortunately he now cut it too little. What could
he do? He determined to cut it again, and it at once became a good fit.
How was this done?
No. XVIII.--PERPENDICULAR LINES
Here is another excellent illustration that seeing is not always
believing.
[Illustration]
No one could suppose at first sight that these four lines are perfectly
straight and parallel, but they will stand the test of a straight edge.
The divergent rays distract the vision.
BY THE COMPASS
21. If from the North Pole you start sailing in a south-westerly
direction, and keep a straight course for twenty miles, to what point of
the compass must you steer to get back as quickly as possible to the
Pole?
No. XIX.--ILLUSION OF PERSPECTIVE
The optical illusion in the picture which we reproduce is due to the
defective drawing of the two men on the platform. In actual size upon
the paper the further man looks much taller than the other.
[Illustration]
Measurement, however, shows the figures to be exactly of a height. This
illusion is due to the fact that the head of the further man is quite
out of perspective. If he is about as tall as the other, and on level
ground, both heads should be about on the same line. As drawn, he is, in
fact, a monster more than eight feet high.
DICK IN A SWING
22. If Dick, who is five feet in height, stands bolt-upright in a swing,
the ropes of which are twenty feet long, how much further in round
numbers do his feet travel than his head in describing a semi-circle?
No. XX.--OUR BLIND SPOT
Here is an excellent and very simple illustration of a well-known
optical curiosity:--
[Illustration]
Hold this picture at arm’s length in the right hand, hold the left hand
over the left eye, and draw the picture towards you gradually, looking
always at the black cross with the right eye. The black disc will
presently disappear, and then come into sight again as you continue to
advance the paper.
A POSER
23. Can you name nine countries in Europe of which the initial letters
are the same as the finals?
FREAKS OF FIGURES
A HANDY SHORT CUT
Here is a delightfully simple way in which market gardeners, or others
who buy or sell weighty produce, can check their invoices for potatoes
or what not.
Say, for example, that a consignment weighs 6 tons, 10 cwts., 1 qr.
Then, since 20 cwts. are to a ton as 20s. are to a pound, and each
quarter would answer on these lines to 3d., we can at once write down £6
10s. 3d., as the price at £1 the ton. On this sure basis any further
calculation is easily made.
No. XXI.--THE PERSISTENCE OF VISION
[Illustration: HOW TO SEE THE GHOST]
Look steadily, in a good light, for thirty seconds at the cross in the
eye of the pictured skull; then look up at the wall or ceiling, or look
fixedly at a sheet of paper for another thirty seconds, when a
ghost-like image of the skull will be developed.
NOT SO FAST!
A gardener, when he had planted 100 trees on a line at intervals of 10
yards, was able to walk from the first of these to the last in a few
seconds, for they were set _on the circumference of a circle_!
No. XXII.--THE PERSISTENCE OF VISION
Here is another example of what is known as the persistence of vision:--
[Illustration]
Look fixedly for some little time at this grotesque figure, then turn
your eyes to the wall or ceiling, and you will in a few seconds see it
appear in dark form upon a light ground.
A PUZZLE NUMBER
The sum of nine figures a number will make,
Of which just a third will remain
If fifty away from the whole you should take,
Thus turning a loss to a gain.
It needs something more than mere arithmetic to discover that the
solution to this puzzle is XLV, the sum of the nine digits, for if the L
is removed, XV, the third of XLV, remains.
No. XXIII.--ANOTHER PARALLEL FREAK
Here is another curious illusion:--
[Illustration]
The four straight lines are perfectly parallel, but the contradictory
herring-bones disturb the eye.
THE MAGIC OF FIGURES
If our penny had been current coin in the first year of the
Christian era, and had been invested at compound interest at
five per cent., it would have amounted in 1905 to more than
£132,010,000,000,000,000,000,000,000,000,000,000,000.
This gigantic sum would afford an income of £101,890,000,000,000,000,000
every second to every man, woman, and child in the world, if we take its
population to be 1,483,000,000 souls!
Absurdly small in contrast to these startling figures is the modest
eight shillings which the same penny would have yielded in the same time
at simple interest.
No. XXIV.--ILLUSION OF LENGTH
Here in another form is shown the illusion of length.
[Illustration]
At first sight it seems that the two upright lines are distinctly longer
than the line that slopes, but it is not so.
WHAT IS YOUR AGE?
Here is a neat method of discovering the age of a person older than
yourself:--
Subtract your own age from 99. Ask your friend to add this remainder to
his age, and then to remove the first figure and add it to the last,
telling you the result. This will always be the difference of your ages.
Thus, if you are 22, and he is 35, 99 - 22 = 77. Then 35 + 77 = 112. The
next process turns this into 13, which, added to your age, gives his
age, 35.
No. XXV.--THE HONEYCOMB ILLUSION
In this diagram one hundred and twenty-one circular spots are grouped in
a diamond.
[Illustration]
If we half close our eyes, and look at this through our eye-lashes, we
find that it takes on the appearance of a section of honeycomb, with
hexagonal cells.
MULTIPLICATION NO VEXATION
Here is a ready method for multiplying together any two numbers between
12 and 20.
Take one of the two numbers and add it to the unit digit of the other.
Beneath the sum thus obtained, but one place to the right, put the
product of the unit digits of the two original numbers.
The sum of these new numbers is the product of the numbers that were
chosen. Thus:--
19 × 13. (19 + 3) = 22
(9 × 3) = 27
---
247
No. XXVI.--CHESS CAMEO
By Dr GOLD
_A Chess Joke_
BLACK
+---+---+---+---+---+---+---+---+
| |.b.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| p |...| k |...| |.K.| |
+---+---+---+---+---+---+---+---+
| |.n.| |.P.| |...| |...|
+---+---+---+---+---+---+---+---+
|.P.| |...| p |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| N |...| N |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| B |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
Black has made an illegal move. He must replace this, and move his king
as the penalty. White then mates on the move.
[1]SHOT IN A PYRAMID
Here is a method for determining the total number of balls in a solid
pyramid built up on a square base:--
Multiply the number of shot on one side of the base line by 2, add 3,
multiply by the number on the base line, add 1, multiply again by the
number on the base, and finally divide by 6. Thus, if the base line is
12--
12 × 2 + 3 = 27; 27 × 12 + 1 = 325; 325 × 12 = 3900; and 3900 ÷ 6 = 650,
which is the required number.
[1] _N.B._--This title does not imply a tragedy.
No. XXVII.--CHESS CAMEO
By A. CYRIL PEARSON
_A Chess Puzzle_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |.p.| |...| |.p.| p |
+---+---+---+---+---+---+---+---+
| |.P.| |.P.| |.k.| |...|
+---+---+---+---+---+---+---+---+
|...| |.p.| K |.N.| P |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| p |...| R |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.N.| |...| |
+---+---+---+---+---+---+---+---+
| |.q.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White might have given mate on the last move. White now to retract his
move, and mate at once.
_Show by analysis the mating position._
No. XXVIII.--CHESS CAMEO
By J. G. CAMPBELL
_A very Clever Device_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| p |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |.P.| |.p.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| K |...| p |...| |.B.| |
+---+---+---+---+---+---+---+---+
| P |...| |.P.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.p.| p |
+---+---+---+---+---+---+---+---+
| |.P.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| K |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play and draw.
COMIC ARITHMETIC
“Now, boys,” said Dr Bulbous Roots to class, “you shall have a
half-holiday if you prove in a novel way that 10 is an even number.”
Next morning, when the doctor came into school, he found this on the
blackboard:--
SIX = 6
IX = 9
---------
By subtraction S = -3
SEVEN = 7
S = -3
------------
Therefore EVEN = 10
Q. E. D.
(_Quite easily done!_)
The half-holiday was won.
No. XXIX.--CHESS CAMEO
By E. B. COOK
_A Fine Example_
BLACK
+---+---+---+---+---+---+---+---+
| |.k.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.R.| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| K |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| p |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and draw.
No. XXX.--CHESS CAMEO
By A. F. MACKENZIE
_A Prize Problem_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |.r.| |...| |.b.|
+---+---+---+---+---+---+---+---+
|.p.| |...| |...| |.P.| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |.q.|
+---+---+---+---+---+---+---+---+
|.N.| b |...| |...| |...| K |
+---+---+---+---+---+---+---+---+
| p |.P.| |.k.| P |...| R |...|
+---+---+---+---+---+---+---+---+
|...| |.p.| P |.p.| |.B.| R |
+---+---+---+---+---+---+---+---+
| |...| n |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.N.| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in two moves.
There are twelve variations in this beautiful problem.
MAGIC MULTIPLICATION
It will interest all who study short cuts and contrivances to know that
a novice at arithmetic who has mastered simple addition, and can
multiply or divide by 2, but by no higher numbers, can, by using all
these methods, multiply any two numbers together easily and accurately.
This is how it is done:--
Write down the numbers, say 53 and 21, divide one of them by 2 as often
as possible, omitting remainders, and multiply the other by 2 the same
number of times; set these down side by side, as in the instance given
below, and wherever there is an _even_ number on the division side,
strike out the corresponding number on the multiplication side. Add up
what remains on that side, and the sum is done. Thus:--
53 21
26 (42)
13 84
6 (168)
3 336
1 672
------
1113
which is 53 multiplied by 21.
No. XXXI.--CHESS CAMEO
BY A. W. GALITZKY
_A Prize Problem_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |.B.| q |.n.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| p |
+---+---+---+---+---+---+---+---+
| |...| N |...| R |...| P |.P.|
+---+---+---+---+---+---+---+---+
|...| |...| |...| k |...| |
+---+---+---+---+---+---+---+---+
| |...| b |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| n |...| |...| |.K.| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in two moves.
No. XXXII.--CHESS CAMEO
BY S. LOYD
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |.N.| |.p.| |.p.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.p.| |...| |
+---+---+---+---+---+---+---+---+
| |...| |.k.| N |.q.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.n.| |...| |
+---+---+---+---+---+---+---+---+
| |.K.| |...| |.B.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in two moves.
No. XXXIII.--CHESS CAMEO
BY B. G. LAWS
_A Prize Problem_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.q.| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| n |.p.| |.p.| p |...| k |
+---+---+---+---+---+---+---+---+
| N |...| P |...| k |.b.| |.R.|
+---+---+---+---+---+---+---+---+
|...| n |...| |.B.| |...| R |
+---+---+---+---+---+---+---+---+
| |...| |.r.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in two moves.
PERFECT NUMBERS
The following particulars about a very rare property of numbers will be
new and interesting to many of our readers:--
The number 6 can only be divided without remainder by 1, 2, and 3,
excluding 6 itself. The sum of 1 + 2 + 3 is 6. The only exact divisors
of 28 are 1, 2, 4, 7, and 14, and the sum of these is 28; 6 and 28 are
therefore known as perfect numbers.
The only other known numbers which fulfil these conditions are 496;
8128; 33,550,336; 8,589,869,056; 137,438,691,328; and
2,305,843,008,139,952,128.
This most remarkable rarity of perfect numbers is a symbol of their
perfection.
No. XXXIV.--CHESS CAMEO
BY EMIL HOFFMANN
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| q |...| |.B.|
+---+---+---+---+---+---+---+---+
|.R.| |...| |...| |.Q.| n |
+---+---+---+---+---+---+---+---+
| |...| |...| k |...| |...|
+---+---+---+---+---+---+---+---+
|.b.| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |.R.| |...| |...|
+---+---+---+---+---+---+---+---+
|.p.| |...| B |...| n |...| b |
+---+---+---+---+---+---+---+---+
| K |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in two moves. There are no less than twelve
variations!
No. XXXV.--CHESS CAMEO
BY J. POSPICIL
_A Prize Problem_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |.N.| |...|
+---+---+---+---+---+---+---+---+
|...| N |...| |...| |...| p |
+---+---+---+---+---+---+---+---+
| |...| n |...| B |.p.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.k.| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.K.| |...| |...| P |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| P |.n.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.Q.| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in two moves.
AMICABLE NUMBERS
Somewhat akin to perfect numbers are what are known as amicable numbers,
of which there is a still smaller quantity in the realm of numbers.
The number 220 can be divided without remainder only by 1, 2, 4, 5, 10,
11, 22, 44, 55, and 110, and the sum of these divisors is 284. The only
divisors of 284 are 1, 2, 4, 71, and 142, and the sum of these is 220.
The only other pairs of numbers which fulfil this curious mutual
condition, that the sum of the divisors of each number exactly equals
the other number, are 17,296 with 18,416, and 9,363,584 with 9,437,056.
No other numbers, at least below ten millions, are in this way
“amicable.”
No. XXXVI.--CHESS CAMEO
BY H. J. C. ANDREWS
_A Prize Problem_
BLACK
+---+---+---+---+---+---+---+---+
| |...| K |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.Q.| |
+---+---+---+---+---+---+---+---+
| |.B.| |...| |...| |.R.|
+---+---+---+---+---+---+---+---+
|...| |...| k |.N.| |.b.| R |
+---+---+---+---+---+---+---+---+
| P |...| |...| |...| P |...|
+---+---+---+---+---+---+---+---+
|...| k |...| p |...| |...| |
+---+---+---+---+---+---+---+---+
| B |...| |.P.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in two moves.
No. XXXVII.--CHESS CAMEO
BY ALFRED DE MUSSET
_A Gem of the First Water_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| n |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| N |...| |.k.|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |.N.| |...| |.K.|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.R.| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
A SWARM OF ONES
1 × 9 + 2 = 11
12 × 9 + 3 = 111
123 × 9 + 4 = 1111
1234 × 9 + 5 = 11111
12345 × 9 + 6 = 111111
123456 × 9 + 7 = 1111111
1234567 × 9 + 8 = 11111111
12345678 × 9 + 9 = 111111111
No. XXXVIII.--CHESS CAMEO
BY FRANK HEALEY
_A Masterpiece_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |.B.| N |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.P.| |...| |.p.| |.p.| |
+---+---+---+---+---+---+---+---+
| |...| K |...| k |.b.| P |...|
+---+---+---+---+---+---+---+---+
|.Q.| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.n.| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
DIVINATION BY FIGURES
There is a pleasant touch of mystery in the following method of
discovering a person’s age:--Ask any such subjects of your curiosity to
write down the tens digit of the year of their birth, to multiply this
by 5, to add 2 to the product, to multiply this result by 2, and finally
to add the units digit of their birth year. Then, taking the paper from
them, subtract the sum from 100. This will give you their age in 1896,
from which their present age is easily determined.
No. XXXIX.--CHESS CAMEO
BY FRANK HEALEY
_The “Bristol Prize Problem”_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| n |...| |...| N |.p.| |
+---+---+---+---+---+---+---+---+
| |.N.| |...| |...| Q |...|
+---+---+---+---+---+---+---+---+
|...| b |.k.| P |...| |...| |
+---+---+---+---+---+---+---+---+
| p |...| p |...| |.p.| |...|
+---+---+---+---+---+---+---+---+
|.P.| |.P.| |...| R |...| |
+---+---+---+---+---+---+---+---+
| |...| |.P.| |...| P |.K.|
+---+---+---+---+---+---+---+---+
|.B.| |...| R |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
FUR AND FEATHERS
As I came in after a day among the birds and rabbits, the keeper asked
me--“Well, sir, what sport?” I replied, “36 heads and 100 feet.” It took
him some time to calculate that I had accounted for 22 birds and 14
rabbits.
No. XL.--CHESS CAMEO
BY J. E. CAMPBELL
_Splendid Strategy_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |.N.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| p |.p.| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.B.| |.k.| p |.P.| |.n.| Q |
+---+---+---+---+---+---+---+---+
| |...| p |.N.| |.P.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| B |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| K |.R.| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
JUGGLING WITH THE DIGITS
The nine digits can be arranged to form fractions equivalent to
1 1 1 1 1 1 1
- - - - - - -
3 4 5 6 7 8 9
thus:--
5823 1 7956 1 2973 1 2943 1 5274 1
----- = - ----- = - ----- = - ----- = - ----- = -
17469 3 31824 4 14865 5 17658 6 36918 7
9321 1 8361 1
----- = - ----- = -
74568 8 75249 9
No. XLI.--CHESS CAMEO
BY W. GRIMSHAW
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.N.| |...| K |...| |...| |
+---+---+---+---+---+---+---+---+
| |.b.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| k |...| |...| |
+---+---+---+---+---+---+---+---+
| |.P.| p |.p.| p |.P.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.P.| P |
+---+---+---+---+---+---+---+---+
| |.Q.| |...| |...| R |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
No. XLII.--CHESS CAMEO
BY S. LOYD
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| P |...|
+---+---+---+---+---+---+---+---+
|...| |.K.| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |.p.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.p.| |
+---+---+---+---+---+---+---+---+
| |.Q.| |...| |.N.| k |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
A MOTOR PROBLEM
This motor problem will be new and amusing to many readers:--
Let _m_ be the driver of a motor-car, working with velocity _v_. If a
sufficiently high value is given to _v_, it will ultimately reach _pc_.
In most cases _v_ will then = _o_. For low values of _v_, _pc_ may be
neglected; but if _v_ be large it will generally be necessary to square
_pc_, after which _v_ will again assume a positive value.
By a well-known elementary theorem, _pc_ + _lsd_ = (_pc_)², but the
squaring may sometimes be effected by substituting _x_³ (or × × ×) for
_lsd_. This is preferable, if _lsd_ is small with regard to _m_. If
_lsd_ be made sufficiently large, _pc_ will vanish.
Now if _jp_ be substituted for _pc_ (which may happen if the difference
between _m_ and _pc_ be large) the solution of the problem is more
difficult. No value of _lsd_ can be found to effect the squaring of
_jp_, for, as is well-known, (_jp_)² is an impossible quantity.
No. XLIII.--CHESS CAMEO
BY J. G. CAMPBELL
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| p |...| Q |
+---+---+---+---+---+---+---+---+
| |...| |.k.| N |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.N.| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| P |...| B |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.P.| p |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |.K.| |.B.|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
No. XLIV.--CHESS CAMEO
BY FRANK HEALEY
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |.K.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |.R.| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |.P.| k |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |.Q.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
A NEAT METHOD OF DIVISION
To divide any sum easily by 99, cut off the two right-hand figures of
the dividend and add them to all the others. Set down the result of this
in line below, and then repeat this process until no figures remain on
the left to be thus dealt with.
Now draw a line down between the tens and hundreds columns, and add all
up on the left of it, thus:--
8694 | 32 120 | 78
87 | 26 1 | 98
1 | 13 | 99
| 14 ------------
------------- 121 and 99 over.
8782 and 14 over. In other words, 122.
The last number on the right of the lines shows always the remainder. If
this should appear as 99 (as in the second example above), add one to
the number on the left.
No. XLV.--CHESS CAMEO
BY BLUMENTHAL AND KUND
BLACK
+---+---+---+---+---+---+---+---+
| |...| K |...| |.R.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| B |...| |...| |
+---+---+---+---+---+---+---+---+
| p |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.r.| n |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| k |...| p |...| |...| |.Q.|
+---+---+---+---+---+---+---+---+
|...| |...| N |...| |...| |
+---+---+---+---+---+---+---+---+
| b |.P.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
No. XLVI.--CHESS CAMEO
BY A. F. MACKENZIE
_A Prize Problem_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |.R.| |...|
+---+---+---+---+---+---+---+---+
|...| |.p.| |.B.| |...| Q |
+---+---+---+---+---+---+---+---+
| n |...| |.R.| |...| |.b.|
+---+---+---+---+---+---+---+---+
|.p.| |.k.| P |...| |...| |
+---+---+---+---+---+---+---+---+
| K |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.n.| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
A SMART SCHOOLBOY
The question, “How many times can 19 be subtracted from a million?” was
set by an examiner, who no doubt expected that the answer would be
obtained by dividing a million by 19. One bright youth, however, filled
a neatly-written page with repetitions of
1,000,000 1,000,000 1,000,000
19 19 19
--------- --------- ---------
999,981 999,981 999,981
and added at the foot of the page, “_N.B._--I can do this as often as
you like.”
There was a touch of unintended humour in this, for, after all, the boy
gave a correct answer to a badly worded question.
No. XLVII.--CHESS CAMEO
BY A. CYRIL PEARSON
BLACK
+---+---+---+---+---+---+---+---+
| |.N.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| r |.n.| |...| n |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |.R.| |...|
+---+---+---+---+---+---+---+---+
|...| |.P.| k |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| p |.P.| |...| |...|
+---+---+---+---+---+---+---+---+
|.Q.| |.P.| |.K.| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| P |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
No. XLVIII.--CHESS CAMEO
BY FRANK HEALEY
_Quite a Gem_
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |.b.|
+---+---+---+---+---+---+---+---+
|...| |...| n |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.K.| |...| |...| |.Q.| |
+---+---+---+---+---+---+---+---+
| |.P.| |.k.| b |...| P |...|
+---+---+---+---+---+---+---+---+
|.R.| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| B |...| |...| |.P.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
LEWIS CARROLL’S SHORT CUT
Here is a very smart and very simple method of dividing any multiple of
9 by 9, from the fertile brain of Lewis Carroll:--Place a cypher over
the final figure, subtract the final figure from this, place the result
above in the tens place, subtract the original tens figure from this,
and so on to the end. Then the top line, excluding the intruded cypher,
gives the result desired. Thus:--
36459 ÷ 9 = 4051,0
= 4051.
36459
No. XLIX.--CHESS CAMEO
BY A. BAYERSDORFER
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| K |...| |
+---+---+---+---+---+---+---+---+
| |...| |.k.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |.p.| B |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| Q |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
ANOTHER FREAK OF FIGURES
1 × 8 + 1 = 9
12 × 8 + 2 = 98
123 × 8 + 3 = 987
1234 × 8 + 4 = 9876
12345 × 8 + 5 = 98765
123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543
12345678 × 8 + 8 = 98765432
123456789 × 8 + 9 = 987654321
No. L.--CHESS CAMEO
BY J. DOBRUSKY
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.n.| |...| |...| B |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| q |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| k |...| |...| |
+---+---+---+---+---+---+---+---+
| |.R.| N |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| K |.R.| |...| |...| |
+---+---+---+---+---+---+---+---+
| Q |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.n.| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
DIVINATION BY NUMBERS
Here is one of the methods by which we can readily discover a number
that is thought of. The thought-reader gives these directions to his
subject: “Add 1 to three times the number you have thought of; multiply
the sum by 3; add to this the number thought of; subtract 3, and tell me
the remainder.” This is always ten times the number thought of. Thus, if
6 is thought of--6 × 3 + 1 = 19; 19 × 3 = 57; 57 + 6 - 3 = 60, and 60 ÷
10 = 6.
No. LI.--CHESS CAMEO
BY KONRAD BAYER
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| p |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.k.| |.K.| |...| |...| |
+---+---+---+---+---+---+---+---+
| b |.p.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |.P.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.R.| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
COINCIDENCES
Here is a curious rough rule for remembering distances and sizes:--
The diameter of the earth multiplied by 108 gives approximately the
sun’s diameter. The diameter of the sun multiplied by 108 gives the mean
distance of the earth from the sun. The diameter of the moon multiplied
by 108 gives the mean distance of the moon from the earth.
No. LII.--CHESS CAMEO
BY J. BERGER
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| B |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| p |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| k |...| |...|
+---+---+---+---+---+---+---+---+
|.B.| Q |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.p.| |.K.| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
PERSONAL ARITHMETIC
Says Giles, “My wife and I are two,
Yet faith I know not why, sir.”
Quoth Jack, “You’re ten, if I speak true,
She’s one, and you’re a cypher!”
No. LIII.--CHESS CAMEO
BY H. F. L. MEYER
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| R |...| |...|
+---+---+---+---+---+---+---+---+
|...| k |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| b |.p.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| p |...| P |...| |...| |
+---+---+---+---+---+---+---+---+
| |.K.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |.B.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| Q |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
DIVISION BY SUBTRACTION
Here is a curious and quite uncommon method of dividing any multiple of
11 by 11.
Set down the multiple of 11, place a cypher under its last figure, draw
a line, and subtract, placing the first remainder under the tens place.
Subtract this from the next number in order, and so on throughout,
adding in always any number that is carried. Thus:--
363 56408 375034
0 0 0
--- ----- ------
33 5128 34094
No. LIV.--CHESS CAMEO
BY FRANK HEALEY
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.B.| |...| |...| |...| p |
+---+---+---+---+---+---+---+---+
| |.r.| p |.p.| |...| b |...|
+---+---+---+---+---+---+---+---+
|...| |.k.| n |...| |.Q.| |
+---+---+---+---+---+---+---+---+
| P |...| |...| p |...| |...|
+---+---+---+---+---+---+---+---+
|.K.| |...| |.P.| |...| N |
+---+---+---+---+---+---+---+---+
| B |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
LUCK IN ODD NUMBERS
Perhaps the old saying, “there is luck in odd numbers,” may have some
connection with the curious fact that the sum of any quantity of
consecutive odd numbers, beginning always with 1, is the square of that
number. Thus:--
1 + 3 + 5 = 9 = 3 × 3.
1 + 3 + 5, etc., up to 17 = 81 = 9 × 9.
1 + 3 + 5, etc., up to 99 = 2500 = 50 × 50.
No. LV.--CHESS CAMEO
BY FRANK HEALEY
BLACK
+---+---+---+---+---+---+---+---+
| |.K.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|.n.| |...| |.p.| |...| |
+---+---+---+---+---+---+---+---+
| |.N.| |.k.| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |.N.| |...| |...| |
+---+---+---+---+---+---+---+---+
| |.P.| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |.n.| Q |.P.| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
THE VERSATILE NUMBER
In the number 142857, if the digits which belong to it are in succession
transposed from the first place to the end, the result is in each case a
multiple of the original number. Thus:--
285714 = 142857 × 2
428571 = 142857 × 3
571428 = 142857 × 4
714285 = 142857 × 5
857142 = 142857 × 6
No. LVI.--CHESS CAMEO
BY J. E. CAMPBELL
BLACK
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |.p.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| p |...| p |...| B |
+---+---+---+---+---+---+---+---+
| |...| |...| |.k.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| K |...| N |...| |
+---+---+---+---+---+---+---+---+
| |...| |...| |...| |.P.|
+---+---+---+---+---+---+---+---+
|...| |...| |...| |.R.| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in three moves.
A PARADOX
By the following simple method, a plausible attempt is made to prove
that 1 is equal to 2:--
Suppose that _a_ = _b_, then
_ab_ = _a_²
∴ _ab_ - _b_² = _a_² - _b_²
∴ _b_(_a_ - _b_) = (_a_ + _b_)(_a_ - _b_)
∴ _b_ = _a_ + _b_
∴ _b_ = 2_b_
∴ 1 = 2
This process only proves in reality that 0 × 1 = 0 × 2, which is true.
No. LVII.--CHESS CAMEO
_Double First Prize_
BY A. CYRIL PEARSON
BLACK
+---+---+---+---+---+---+---+---+
| |...| b |...| |...| |...|
+---+---+---+---+---+---+---+---+
|...| |...| p |.K.| |...| p |
+---+---+---+---+---+---+---+---+
| |...| p |...| |.p.| |...|
+---+---+---+---+---+---+---+---+
|...| |...| B |.k.| |...| |
+---+---+---+---+---+---+---+---+
| |.b.| |...| |...| P |...|
+---+---+---+---+---+---+---+---+
|.N.| |.N.| |.P.| |...| |
+---+---+---+---+---+---+---+---+
| |.R.| |.P.| |.R.| |...|
+---+---+---+---+---+---+---+---+
|.b.| q |...| |...| |...| |
+---+---+---+---+---+---+---+---+
WHITE
White to play, and mate in four moves.
QUICK CALCULATION
Few people know a very singular but simple method of calculating rapidly
how much any given number of pence a day amounts to in a year. The rule
is this:--Set down the given number of pence as pounds; under this place
its half, and under that the result of the number of original pence
multiplied always by five. Take, for example, 7d a day:--
£7 0 0
3 10 0
2 11
---------
£10 12 11
---------
The reason for this is evident as soon as we remember that the 365 days
of a year may be split up into 240, 120, and 5, and that 240 happens to
be the number of pence in a pound.
SCIENCE AT PLAY
No. LVIII.--THE GEARED WHEELS
A small wheel with ten teeth is geared into a large fixed wheel which
has forty teeth. This small wheel, with an arrow mark on its highest
cog, is revolved completely round the large wheel. How often during its
course is the arrow pointing directly upwards? Here is a diagram of the
starting position.
[Illustration]
No. LIX.--ADVANCING BACKWARDS
Here is a most curious and interesting question:--When an engine is
drawing a train at full speed from York to London, what part of the
train at any given moment is moving _towards York_?
At any time, when the engine is drawing a train at full speed from York
to London, that part of the flange of each wheel which is for the moment
at its lowest is actually _moving backwards towards York_.
[Illustration]
For any point, such as A, on the circumference of the tyre, describes in
running along a series of curves, as shown by _full_ lines in the
diagram; and any point, B, on the outer edge of the flange, follows a
path shown by the _dotted_ curves.
If these lines are followed round with a pencil in the direction of the
arrows, it will be found that the point on the flange actually moves
_backwards_ as it passes _below the track_, while the point A, as it
completes each curve, is _at rest_ for the instant on the track, just
before it starts afresh. The speed of the train does not affect these
very curious facts.
No. LX.--THE FIFTEEN BRIDGES
In the subjoined diagram A and B represent two islands, round which a
river runs as is indicated, with fifteen connecting bridges, that lead
from the islands to the river’s banks.
[Illustration]
Can you contrive to pass in turn over all these bridges without ever
passing over the same one twice?
ARRANGING THE DIGITS
In a school where two boys were taught to think out the bearings of
their work, a sharp pupil remarked that 100 is represented on paper by
the smallest digit and two cyphers, which are in themselves symbols of
nothing. The master, quick to catch any signs of mental activity, took
the opportunity to propound to his class the following ingenious
puzzle:--How can the sum of 100 be represented exactly in figures and
signs by making use of all the nine digits in their reverse order? This
is how it is done:--
9 × 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 100.
Another ingenious method of using the nine digits, so that by simple
addition they sum up to exactly 100, and each is used once only, is
this:--
15 + 36 + 47 = 98 + 2 = 100
Here is another arrangement by which the nine digits written in their
inverse order can be made to represent exactly 100:--
98 - 76 + 54 + 3 + 21 = 100.
Here is yet another way of arriving at 100 by using each of the digits,
this time with an 0:--
40¹⁄₂
59³⁸⁄₇₆
--------
100
No. LXI.--LOOPING THE LOOP
Here is quite a pretty scientific experiment, which any one of a handy
turn can construct and arrange:--
[Illustration]
The spiral track is formed of two wires bent, and connected by curved
cross-pieces. The upper twist is turned so that the ball starts on a
horizontal course.
During the accelerated descent the ball acquires momentum enough to keep
it on the vertical track, held outwardly against the wires by
centrifugal force.
Convenient proportions are: height of spiral two feet, diameter six
inches, and wire rails three-quarters of an inch apart.
No. LXII.--A MECHANICAL BIRD
A close approach to an ideal flying machine can be made with a little
ingenuity. Two Y-shaped standards, secured to the backbone rod, support
two wires which carry wings of thin silk, provided with light stays, and
connected at their inner corners with the backbone by threads.
[Illustration]
Rubber bands are attached to a loop on the inner end of the crank shaft,
and secured to a post at the rear. These are twisted by turning the
shaft with the cross wire, and when the tension is released the wings
beat the air and carry the bird forward. It is known as Penaud’s
mechanical bird, and has been sold as an attractive toy.
No. LXIII.--LINE OF SWIFTEST DESCENT
A simple apparatus constructed on the lines of this illustration will
give an interesting proof of the laws which govern falling bodies on an
inclined plane or on a curved path.
[Illustration]
In the case of the inclined plane the ball is governed by the usual law
which controls falling bodies. In that of the concave circular curve, as
it is accelerated rapidly at the start, it makes its longer journey in
quicker time. In the case of the cycloidal curve it acquires a high
velocity. This curve has therefore been called “the curve of swiftest
descent,” as a falling body passes over it in less time than upon any
path except the vertical.
No. LXIV.--A CENTRIFUGAL RAILWAY
Here is another very simple and pretty illustration of the natural
forces which come into play in “looping the loop.”
[Illustration]
This scientific toy on a small scale may be easily made, if care is
taken that the height of the higher end of the rails is to the height of
the circular part in a greater ratio than 5 to 4.
A ball started at the higher end follows the track throughout, and at
one point is held by centrifugal force against the under side of the
rails, against the force of gravity.
No. LXV.--A QUESTION OF GRAVITY
If a ball is fired point blank from a perfectly horizontal gun, and
travels half a mile over a level plain before it touches ground, and
another similar ball is at the same moment dropped from the same height
by some mechanical means, the two balls will touch ground
simultaneously. The flight, however long, of one through the air has no
influence upon the force of gravity, which draws it earthward at the
same resistless rate as it draws the other that is merely dropped.
[Illustration]
A SHORT CUT
A quick method of multiplying any number of figures by 5 is to divide
them by 2, annexing a cypher to the result when there is no remainder,
and if there is any remainder annexing a 5. Thus:--
464 × 5 = 2320; 464 ÷ 2 = 232, annex 0, = 2320.
753 × 5 = 3765; 753 ÷ 2 = 376, annex 5, = 3765.
No. LXVI.--A DUCK HUNT
A duck begins to swim round the edge of a circular pond, and at the same
moment a water spaniel starts from the middle of the pond in pursuit of
it.
[Illustration]
If both swim at the same pace, how must the dog steer his course so that
he is sure in any case to overtake the duck speedily?
THE MAGIC OF DATES
LOUIS NAPOLEON, EMPEROR 1852
1852 1852 1852
date 1 date 1 date 1
of 8 of 8 of 8
his 0 Empress’s 2 their 5
birth 8 birth 6 marriage 3
---- ---- ----
1869 1869 1869
Thus, by a most remarkable series of coincidences, the principal dates
of the Emperor and Empress of the French added, as is shown above, to
the year of the Emperor’s accession, express in each instance the year
before his fall.
No. LXVII.--GEOMETRY WITH DOMINOES
In this domino diagram we have a pretty and practical proof that the
squares of the sides containing the right angle in any right-angled
triangle are together equal to the square of the side opposite to the
right angle.
[Illustration]
Each stone forms two squares, and it is easily seen that the number of
squares which make up the whole square on the line opposite the right
angle are equal to the number of those which make up the two whole
squares on the lines which contain that angle.
A second point to be noticed is that the number of pips on the large
square are equal to the number on the other two squares combined, an
arrangement of the stones which forms quite a game of patience to
reproduce, if this pattern is not at hand.
No. LXVIII.--TO COLOUR MAPS
Four colours at most are needed to distinguish the surfaces of separate
districts on any plane map, so that no two with a common boundary are
tinted alike.
[Illustration]
On this diagram A, B, and C, are adjoining districts, on a plane
surface, and X borders, in one way or another, upon each.
It is clearly impossible to introduce a fifth area which shall so adjoin
these four districts as to need another tint.
A FREAK OF FIGURES
Here is another freak of figures:--
9 × 1 - 1 = 8
9 × 21 - 1 = 188
9 × 321 - 1 = 2888
9 × 4321 - 1 = 38888
9 × 54321 - 1 = 488888
9 × 654321 - 1 = 5888888
9 × 7654321 - 1 = 68888888
9 × 87654321 - 1 = 788888888
9 × 987654321 - 1 = 8888888888
No. LXIX.--THE TETHERED BIRD
A bird made fast to a pole six inches in diameter by a cord fifty feet
long, in its flight first uncoils the cord, _keeping it always taut_,
and then recoils it in the reverse direction, rewinding the coils close
together. If it starts with the cord fully coiled, and continues its
flight until it brings up against the pole, how far does it fly in its
double course?
[Illustration]
STRIKE IT OUT
Ask a person to write down in a line any number of figures, then to add
them all together as units, and to subtract the result from the sum set
down. Let him then strike out any one figure, and add the others
together as units, telling you the result.
If this has been correctly done, the figure struck out can always be
determined by deducting the final total from the multiple of 9 next
above it. If the total happens to be a multiple of 9, then a 9 was
struck out.
No. LXX.--THE MOVING DISC AND THE FLY
A fly, starting from the point A, just outside a revolving disc, and
always making straight for its mate at the point B, crosses the disc in
four minutes, while the disc is revolving twice. What effect has the
revolution of the disc on the path of the fly?
[Illustration]
A MAGIC SQUARE
This Magic Square is so arranged that the product of the continued
multiplication of the numbers in each row, column, or diagonal is 4096,
which is the cube of the central 16.
+---+---+---+
| 8|256| 2|
+---+---+---+
| 4| 16| 64|
+---+---+---+
|128| 1| 32|
+---+---+---+
No. LXXI.--A SHUNTING PUZZLE
The railway, D E F, has two sidings, D B A and F C A, connected at A.
The rails at A, common to both, are long enough to hold a single wagon
such as P or Q, but too short to admit the whole of the engine R, which,
if it runs up either siding, must return the same way.
[Illustration]
How can the engine R be used to interchange the wagons P and Q without
allowing any flying shunts?--From _Ball’s Mathematical Recreations_.
No. LXXII.--A CURIOUS FACT
It is a little known and very interesting fact that an equilateral
triangle can easily be drawn by rule of thumb in the following
way:--Take a triangle of any shape or size, and on each of its sides
erect an equilateral triangle. Find and join the centres of these, and a
fourth equilateral triangle is always thus formed, as shown by the
dotted lines.
[Illustration]
These centres are _centres of gravity_, and they are symmetrically
distributed around the centre of gravity of the original triangle.
The figure formed by joining them must therefore be symmetrical, and, as
in this case, it is a triangle, it _must be_ always equilateral.
No. LXXIII.--TRY THIS EXPERIMENT
There can be no better instance of how the eye may be deceived than is
so strikingly afforded in these very curious diagrams:--
[Illustration]
The square which obviously contains sixty-four small squares, is to be
cut into four parts, as is shown by the thicker lines. When these four
pieces are quite simply put together, as shown in the second figure,
there seem to be sixty-five squares instead of sixty-four.
This phenomena is due to the fact that the edges of the four pieces,
which lie along the diagonal A B, do not exactly coincide in direction.
In reality they _include a very narrow diamond_, not easily detected,
whose area is just equal to that of one of the sixty-four small squares.
FIGURES IN SWARMS
Very curious are the results when the nine digits in reverse order are
multiplied by 9 and its multiples up to 81. Thus:--
987654321 × 9 = 8888888889
× 18 = 17777777778
× 27 = 26666666997
× 36 = 35555555556
× 45 = 44444444445
× 54 = 53333333334
× 63 = 62222222223
× 72 = 71111111112
× 81 = 80000000001
It will be seen that the figures by which the reversed digits are
multiplied reappear at the beginning and end of each result except the
first, and that the figures repeated between them are to be found by
dividing the divisors by 9 and subtracting the result from 9. Thus, 54 ÷
9 = 6, and 9 - 6 = 3.
No. LXXIV.--A TRIANGLE OF TRIANGLES
[Illustration]
In this nest of triangles there are no less than six hundred and
fifty-three distinct triangles of various shapes and sizes.
No. LXXV.--PHARAOH’S SEAL
In a chamber of the Great Pyramid an ancient Egyptian jar was found,
marked with the device now known as Pharaoh’s seal.
[Illustration]
Can you count the number of triangles or pyramids, of many sizes, but
all of similar shape that are expressed on it? Solvers should draw the
figure on a larger scale.
MAKING CUBES
It is interesting to note that the repeated addition of odd numbers to
one another can be so arranged as to produce cube numbers in due
sequence. Thus:--
1 = 1 × 1 × 1
3 + 5 = 2 × 2 × 2
7 + 9 + 11 = 3 × 3 × 3
13 + 15 + 17 + 19 = 4 × 4 × 4
21 + 23 + 25 + 27 + 29 = 5 × 5 × 5
and so on, to any extent.
No. LXXVI.--ROUND THE GARDEN
In a large old-fashioned garden walks were arranged round a central
fountain in the shape of a Maltese cross.
[Illustration]
If four persons started at noon from the fountain, walking round the
four paths at two, three, four and five miles an hour respectively, at
what time would they meet for the third time at their starting-point, if
the distance on each track was one-third of a mile?
A NICE SHORT CUT
When the tens of two numbers are the same, and their units added
together make ten, multiply the units together, increase one of the tens
by unity, and multiply it by the other ten. The result is the product of
the two original numbers, if the first result follows the other. Thus:--
43 × 47 = 2021.
No. LXXVII.--A JOINER’S PUZZLE
Can you cut Fig. A into two parts, and so rearrange these that they form
either Fig. B or Fig. C?
+--------------+
| |
+--------------+ | +--+
| | | |
| | +-----------------+ | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | +--+ |
| | | | | |
+--------------+ +-----------------+ +--------------+
A B C
The two parts of A must not be _turned round_ to form B or C, but must
retain their original direction.
A CALCULATION
Coal may fail us, but we can never run short of material for “words that
burn.” It has been calculated that if a man could read 100,000 words in
an hour, and there were 4,650,000 men available, they could not
pronounce the possible variations which could be formed from the
alphabet in 70,000 years!
A PARADOX
It is possible, in a sense, by the following neat method, to take 45
from 45, and find that 45 remains:--
987654321 = 45.
123456789 = 45.
---------
864197532 = 45.
No. LXXVIII.--THE BROKEN OCTAGON
Cut out in stiff cardboard four pieces shaped as Fig. 1, four as Fig. 2,
and four as Fig. 3, taking care that they are all exactly true to
pattern in shape and proportion to one another.
[Illustration]
Now see whether you can put the twelve pieces together so as to form a
perfect octagon.
PROPERTIES OF SEVEN
Here is a proof that 7, if it cannot rival the mystic 9, has quaint
properties of its own:--
15873 × 7 = 111111
31746 × 7 = 222222
47619 × 7 = 333333
63492 × 7 = 444444
79365 × 7 = 555555
95238 × 7 = 666666
111111 × 7 = 777777
126984 × 7 = 888888
142857 × 7 = 999999
A SWARM OF EIGHTS
Here is an arithmetical curiosity:--
9 × 9 + 7 = 88
9 × 98 + 6 = 888
9 × 987 + 5 = 8888
9 × 9876 + 4 = 88888
9 × 98765 + 3 = 888888
9 × 987654 + 2 = 8888888
9 × 9876543 + 1 = 88888888
9 × 98765432 + 0 = 888888888
No. LXXIX.--AT A DUCK POND
A farmer’s wife kept a pure strain of Aylesbury ducks for market on a
square pond, with a duck-house at each corner. As trade grew brisk she
found that she must enlarge her pond. An ingenious neighbour undertook
to arrange this without altering the shape of the pond, and without
disturbing the duck-houses. What was his plan?
○-------------○
| |
| |
| |
| |
| |
| |
○-------------○
STRANGE SUBTRACTION
It would seem impossible to subtract 69 from 55, but it can be arranged
thus, with six as a remainder:--
SIX IX XL
IX X L
-------------
S I X
=============
No. LXXX.--ALL ON THE SQUARE
Cut out in cardboard twenty triangular pieces exactly the size and shape
of this one, and try to place them together so that they form a perfect
square.
[Illustration]
ANOTHER MYSTIC NUMBER
The decimal equivalent of ¹⁄₁₃ is .076923. This (omitting the point),
multiplied by 1, 3, 4, 9, 10, or 12, yields results in which the same
figures appear in varied order, but similar sequence, and multiplied by
2, 5, 6, 7, 8, or 11, it yields a different series, with similar
characteristics. Thus:--
76923 × 1 = 76923
× 3 = 230769
× 4 = 307692
× 9 = 692307
× 10 = 769230
× 12 = 923076
76923 × 2 = 153846
× 5 = 384615
× 6 = 461538
× 7 = 538461
× 8 = 615384
× 11 = 846153
DON’T BUY IT TO TRY IT
A kaleidoscope cylinder contains twenty small pieces of coloured glass.
As we turn it round, or shake it, so as to make ten changes of pattern
every minute, it will take the inconceivable space of time of
462,880,899,576 years and 360 days to exhaust all the possible
symmetrical variations. (The 360 days is good!)
No. LXXXI.--PINS AND DOTS
Here is an amusing little exercise for the ingenuity of our solvers.
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
Take six sharp pins, and puzzle out how to stick them into six of the
black dots, so that no two pins, are on the same line, in any direction,
vertical, horizontal, or diagonal.
No. LXXXII.--A TRICKY COURSE
The middle of a large playground was paved with sixty-four square
flagstones of equal size, which are numbered on this diagram from one to
sixty-four.
+----+----+----+----+----+----+----+----+
| _1_| _9_|_17_|_25_|_33_|_41_|_49_|_57_|
+----+----+----+----+----+----+----+----+
| _2_|_10_|_18_|_26_|_34_|_42_|_50_|_58_|
+----+----+----+----+----+----+----+----+
| _3_|_11_|_19_|_27_|_35_|_43_|_51_|_59_|
+----+----+----+----+----+----+----+----+
| _4_|_12_|_20_|_28_|_36_|_44_|_52_|_60_|
+----+----+----+----+----+----+----+----+
| _5_|_13_|_21_|_29_|_37_|_45_|_53_|_61_|
+----+----+----+----+----+----+----+----+
| _6_|_14_|_22_|_30_|_38_|_46_|_54_|_62_|
+----+----+----+----+----+----+----+----+
| _7_|_15_|_23_|_31_|_39_|_47_|_55_|_63_|
+----+----+----+----+----+----+----+----+
| _8_|_16_|_24_|_32_|_40_|_48_|_56_|_64_|
+----+----+----+----+----+----+----+----+
One of the schoolmasters, who had a head for puzzles, took his stand
upon the square here numbered 19, and offered a prize to any boy who,
starting from the square numbered 46, could make his way to him, passing
through every square once, and only once. It was after many vain
attempts that the course was at last discovered. Can you work it out?
No. LXXXIII.--FOR THE CHILDREN
Place twelve draughtsmen, or buttons, in a square, so that you count
four along each side of it, thus:--
● ● ● ●
● ●
● ●
● ● ● ●
Now take the same men or buttons, and arrange them so that they form
another square, and you can count five along each side of it.
A GAME OF NINES
Here is a good specimen of the eccentricities and powers of numbers:--
153846 × 13 = 1999998
230769 × 13 = 2999997
307692 × 13 = 3999996
384615 × 13 = 4999995
461538 × 13 = 5999994
538461 × 13 = 6999993
615384 × 13 = 7999992
692307 × 13 = 8999991
No. LXXXIV.--TELL-TALE TABLES
She was quite an old maid, and her age was a most absolute secret.
Determined to discover it, her scapegrace nephew, on Christmas Eve,
produced these tables, and asked her with well simulated innocence on
which of them she could see the number of her age.
+--+--+--+ +--+--+--+ +--+--+--+
| 1|23|45| | 2|23|46| |16|27|54|
+--+--+--+ +--+--+--+ +--+--+--+
| 3|25|47| | 3|26|47| |17|28|55|
+--+--+--+ +--+--+--+ +--+--+--+
| 5|27|49| | 6|27|50| |18|29|56|
+--+--+--+ +--+--+--+ +--+--+--+
| 7|29|51| | 7|30|51| |19|30|57|
+--+--+--+ +--+--+--+ +--+--+--+
| 9|31|53| |10|31|54| |20|31|58|
+--+--+--+ +--+--+--+ +--+--+--+
|11|33|55| |11|34|55| |21|48|59|
+--+--+--+ +--+--+--+ +--+--+--+
|13|35|57| |14|35|58| |22|49|60|
+--+--+--+ +--+--+--+ +--+--+--+
|15|37|59| |15|38|59| |23|50|61|
+--+--+--+ +--+--+--+ +--+--+--+
|17|39|61| |18|39|62| |24|51|62|
+--+--+--+ +--+--+--+ +--+--+--+
|19|41| | |19|42| | |25|52| |
+--+--+ A| +--+--+ B| +--+--+ C|
|21 43| | |22 43| | |26|53| |
+--+--+--+ +--+--+--+ +--+--+--+
+--+--+--+ +--+--+--+ +--+--+--+
| 8|27|46| | 4|23|46| |32|43|54|
+--+--+--+ +--+--+--+ +--+--+--+
| 9|28|47| | 5|28|47| |33|44|55|
+--+--+--+ +--+--+--+ +--+--+--+
|10|29|56| | 6|29|52| |34|45|56|
+--+--+--+ +--+--+--+ +--+--+--+
|11|30|57| | 7|30|53| |35|46|57|
+--+--+--+ +--+--+--+ +--+--+--+
|12|31|58| |12|31|54| |36|47|58|
+--+--+--+ +--+--+--+ +--+--+--+
|13|40|59| |13|36|55| |37|48|59|
+--+--+--+ +--+--+--+ +--+--+--+
|14|41|60| |14|37|60| |38|49|60|
+--+--+--+ +--+--+--+ +--+--+--+
|15|42|61| |15|38|61| |39|50|61|
+--+--+--+ +--+--+--+ +--+--+--+
|24|43|62| |20|39|62| |40|51|62|
+--+--+--+ +--+--+--+ +--+--+--+
|25|44| | |21|44| | |41|52| |
+--+--+ D| +--+--+ E| +--+--+ F|
|26|45| | |22|45| | |42|53| |
+--+--+--+ +--+--+--+ +--+--+--+
From her answer he was able to calculate that the old lady was
fifty-five.
The tell-tale tables disclosed her age thus:--As it appeared in tables
A, B, C, E, and F, he added together the numbers at the top left-hand
corners, and found the total to be fifty-five. This rule applies in all
cases.
No. LXXXV.--A PAPER PUZZLE
Of the many paper-cutting tricks which appeal to us none is more simple
and attractive than this:--
+---+
| |
| |
+-----+ +-----+
| |
+-----+ +-----+
/ \ | | / \
\ / | | \ /
+-+ | | +-+
| | | | | |
| | | | | |
| | | | | |
| | +---+-+-+---+ | |
+-+ | | | +-+
+---+ | +-+-+ | +---+
| +---+---+-+-+---+---+ |
| | |
+-------------+-------------+
Take a piece of paper, say 5 inches by 3 inches, but any oblong shape
and size will do, and after folding it four times cut it lengthways up
the centre. Unfold the pieces, and to your surprise you will find a
perfect cross and other pieces in pairs of the shapes shown above. The
puzzle is how to fold the paper.
+--------------+----------+
|b d¦ |
| ¦ |
| ¦ |
| e¦ |
| ¦ |
| ¦ |
|a c¦ |
+--------------+----------+
The paper must be folded first so that B comes upon C, then so that A
comes upon D, then from D to C, and lastly from E to C. If it is now cut
lengthways exactly along the centre the figures shown on the original
diagram will be formed, which resemble a cross and lighted candles on an
altar.
No. LXXXVI.--A HOME-MADE PUZZLE
Take a thin board, about eight inches square, and mark it out into
thirty-six equal parts; bore a hole in the centre of each part, and then
fit in a small wooden peg, leaving about a quarter inch above the
surface, as is shown in Fig. 1, the section below the diagram.
[Illustration]
Prepare thirty-six pieces of white or coloured cardboard of the length A
to B, and place them over the pegs in any direction in which they will
fit so as to form some such symmetrical pattern as is given on the
second diagram, putting two holes only on each peg. Chess-players will
see that this is the regular knight’s move.
[Illustration]
Quite a number of beautiful designs can be thus formed, and those who
have not the means at hand for making a complete set can enjoy the
puzzle by merely marking out thirty-six squares, and drawing lines from
centre to centre of the exact length from A to B, with black or coloured
pencils.
No. LXXXVII.--LOYD’S MITRE PROBLEM
[Illustration]
Divide this figure into four similar and equal parts.
A PRETTY PROBLEM
The solution of the pretty little problem: place three twos in three
different groups, so that twice the first group, or half the third group
equals the second group, is this:--
2 1 2 2 + 2
----- = - 2 - - = 1 ----- = 2
2 + 2 2 2 2
No. LXXXVIII.--CONTINUOUS LINES
The following figure, which represents part of a brick wall, cannot be
marked out along all the edges of the bricks in less than six continuous
lines without going more than once over the same line:--
[Illustration]
Here, in strong contrast to the simple figure given above, which could
not be traced without lifting the pen six times from the paper, is an
intricate design, the lines of which, on the upper or on the lower half,
can be traced without any break at all.
[Illustration]
The general rule that governs such cases is, that where an uneven number
of lines meet a fresh start has to be made. In the diagram now given the
only such points are at the extremities of the upper and lower halves of
the figure at A and X. At all other points two, or four, or six lines
converge, and there is no break of continuity in a tracing of the
figure.
No. LXXXIX.--CUT OFF THE CORNERS
Can you suggest quite a simple and practical way to fix the points on
the sides of a square which will be at the angles of an octagon formed
by cutting off equal corners of the square, as shown below?
A E F B
+------+--------+------+
| / \ |
| / \ |
|/ \|
M+ +G
| |
| |
| |
L+ +H
|\ /|
| \ / |
| \ / |
+------+--------+------+
C K I D
MYSTIC FIGURES
Very interesting and curious are the properties of the figures 142857,
used in varied order but always in similar sequence, in connection with
7 and 9:--
142857 × 7 = 999999 ÷ 9 = 111111
285714 × 7 = 1999998 ÷ 9 = 222222
428571 × 7 = 2999997 ÷ 9 = 333333
571428 × 7 = 3999996 ÷ 9 = 444444
714285 × 7 = 4999995 ÷ 9 = 555555
857142 × 7 = 5999994 ÷ 9 = 666666
No. XC.--THE FIVE TRIANGLES
The subjoined diagram shows how a square with sides that measure each 12
yards can be divided into five triangles, no two of which are of equal
area, and of which the sides and areas can be expressed in yards by
whole numbers:--
[Illustration]
The areas of these triangles are 6, 12, 24, 48, and 54 square yards
respectively, and the sum of these, 144 square yards, is the area of the
square.
CURIOUS COINCIDENCES
Our readers may remember the remarkable fact that the figures of the
sum, £12, 12s. 8d., when written thus, 12,128, exactly represent the
number of farthings it contains. Now this, so far as we know, is the
only instance of the peculiarity, but there are at least five other
cases which come curiously near to it. They are these:--
£ s. d.
9 9 6 = 9096 farthings
6 6 4 = 6064 „
3 3 2 = 3032 „
10 10 6¹⁄₂ = 10106 „
13 13 8¹⁄₂ = 13138 „
No. XCI.--PLACING A LADDER
If a ladder, with rungs 1 foot apart, rests against a wall, and its
thirteenth rung is 12 feet above the ground, the foot of the ladder is
25 feet from the wall.
[Illustration]
_Proof._--Drop a perpendicular from A to B. Then, as A B C is a right
angle, and the squares on A C, A B, are 169 feet and 144 feet, the
square on C B must be 25 feet, and the length of C B is 5 feet. We thus
move 5 feet towards the wall in going 13 feet up the ladder, and in
mounting 65 feet (five times as far) we must cover 25 feet.
No. XCII.--GRACEFUL CURVES
A prettily ingenious method of dividing the area of a circle into
quarters, each of them a perfect curve, with perimeter (or enclosing
line) equal to the circumference of the circle, and with which four
circles can be formed, is clearly shown by the subjoined diagrams:--
[Illustration]
NIGHTS AT A ROUND TABLE
The host of a large hotel at Cairo noticed that his Visitors’ Book
contained the names of an Austrian, a Brazilian, a Chinaman, a Dane, an
Englishman, a Frenchman, a German, and a Hungarian. Moved by this
curious alphabetical list, he offered them all free quarters and the
best of everything if they could arrange themselves at a round
dining-table so that not one of them should have the same two neighbours
on any two occasions for 21 successive days.
The following is one of many ways in which this arrangement can be made,
and it seems to be the simplest of them all.
Number the persons 1 to 8; and for our first day set them down in
numerical order _except that the two centre ones (4 and 5) change
places_:
(1st day)--1 2 3 5 4 6 7 8
Keep the 1 and the 7 unaltered but double each of the other numbers.
When the product is greater than 8, divide by 7, and only set down the
remainder. Thus we get:
(8th day)--1 4 6 3 8 5 7 2
(Here the fourth figure 3 is 5 × 2 ÷ 7, giving _remainder_ 3, and so
on.)
Repeat this operation once more:
(15th day)--1 8 5 6 2 3 7 4
To fill in the intermediate days we have only to keep 1 unchanged and
let the remaining numbers run downwards in _simple numerical order_,
following 8 with 2, 2 with 3, and so on. Thus:--
1st day--1 2 3 5 4 6 7 8
2nd day--1 3 4 6 5 7 8 2
3rd day--1 4 5 7 6 8 2 3
4th day--1 5 6 8 7 2 3 4
5th day--1 6 7 2 8 3 4 5
6th day--1 7 8 3 2 4 5 6
7th day--1 8 2 4 3 5 6 7
-------------------------
8th day--1 4 6 3 8 5 7 2
9th day--1 5 7 4 2 6 8 3
10th day--1 6 8 5 3 7 2 4
11th day--1 7 2 6 4 8 3 5
12th day--1 8 3 7 5 2 4 6
13th day--1 2 4 8 6 3 5 7
14th day--1 3 5 2 7 4 6 8
-------------------------
15th day--1 8 5 6 2 3 7 4
16th day--1 2 6 7 3 4 8 5
17th day--1 3 7 8 4 5 2 6
18th day--1 4 8 2 5 6 3 7
19th day--1 5 2 3 6 7 4 8
20th day--1 6 3 4 7 8 5 2
21st day--1 7 4 5 8 2 6 3
This completes the schedule. It will be found on examination that every
number is between every pair of the other numbers once, and once only.
In order to reduce our first-day ring to exact numerical order we have
only to interchange the numbers 4 and 5 throughout. The first three
lines for example would then become:
1 2 3 4 5 6 7 8
1 3 5 6 4 7 8 2
1 5 4 7 6 8 2 3, etc.
or, by putting letters for figures,
A B C D E F G H
A C E F D G H B
A E D G F H B C, etc.
An arrangement of the guests is thus arrived at for twenty-one
successive days, so that not one of them has the same two neighbours on
any two occasions.
No. XCIII.--MAKING MANY SQUARES
Can you apply the two oblongs drawn below to the two concentric squares,
so as to produce thirty-one perfect squares?
+------+ +------+
| | | |
| | | |
+----------------------------------+ +------+ +------+
| | | | | |
| | | | | |
| +--------------------+ | +------+ +------+
| | | | | | | |
| | | | | | | |
| | | | +------+ +------+
| | | | | | | |
| | | | | | | |
| | | | +------+ +------+
| | | | | | | |
| | | | | | | |
| +--------------------+ | +------+ +------+
| | | | | |
| | | | | |
+----------------------------------+ +------+ +------+
| | | |
| | | |
+------+ +------+
No. XCIV.--CUT ACROSS
Take a piece of cardboard in the form of a Greek cross with arms, as
shown here, and divide it by two straight cuts, so that the pieces when
reunited form a perfect square.
+------+
| |
| |
+------+ +------+
| |
| |
+------+ +------+
| |
| |
+------+
No. XCV.--A PRETTY PUZZLE
The diagrams which we give below show how a hollow square can be formed
of the pieces of three-quarters of another square from which a corner
has been cut away:--
+-------+ +-------+ +-------+-------+
| | | | | | |
| | | +---+ | +---+---+ |
| | | | | | | | |
| +-------+ +---+ +---+---+ +---+ +---+
| | | | | | | | | |
| | | +---+---+ | | +---+---+ |
| | | | | |
+---------------+ +---------------+ +---------------+
No. XCVI.--A FIVE-FOLD SQUARE
The subjoined diagram shows how a square of paper or cardboard may be
cut into nine pieces which, when suitably arranged, form five perfect
squares.
[Illustration]
THE SOCIABLE SCHOOLGIRLS
On how many days can fifteen schoolgirls go out for a walk so arranged
in rows of three, that no two are together more than once?
Fifteen schoolgirls can go out for a walk on seven days so arranged in
rows of three that no two are together more than once.
It is said, on high authority, that there are no less than
15,567,522,000 different solutions to this problem. Here is one of them,
given in _Ball’s Mathematical Recreations_, in which _k_ stands for one
of the girls, and _a_, _b_, _c_, _d_, _e_, _f_, _g_, in their
modifications, for her companions on the seven different days:--
+---------+---------+---------+---------+---------+---------+--------+
| Sunday | Monday | Tuesday |Wednesday| Thursday| Friday |Saturday|
+---------+---------+---------+---------+---------+---------+--------+
|_ka₁a₂_ |_kb₁b₂_ |_kc₁c₂_ |_kd₁d₂_ |_ke₁e₂_ |_kf₁f₂_ |_kg₁g₂_ |
|_b₁d₁f₁_ |_a₁d₂e₂_ |_a₁d₁e₁_ |_a₂b₂c₂_ |_a₂b₁c₁_ |_a₁b₂c₁_ |_a₁b₁c₂_|
|_b₂e₁g₁_ |_a₂f₂g₂_ |_a₂f₁g₁_ |_a₁f₂g₁_ |_a₁f₁g₂_ |_a₂d₂e₁_ |_a₂d₁e₂_|
|_c₁d₂g₂_ |_c₁d₁g₁_ |_b₁d₂f₂_ |_b₁e₁g₂_ |_b₂d₁f₂_ |_b₁e₂g₁_ |_b₂d₂f₁_|
|_c₂e₂f₂_ |_c₂e₁f₁_ |_b₂e₂g₂_ |_c₁e₂f₁_ |_c₂d₂g₁_ |_c₂d₁g₂_ |_c₁e₁f₂_|
+---------+---------+---------+---------+---------+---------+--------+
It is an excellent game of patience, for those who have time and
inclination, to place the figures 1 to 15 inclusive in seven such
columns, so as to fulfil the conditions.
No. XCVII.--THE THREE CROSSES
It is possible from a Greek cross to cut off four equal pieces which,
when put together, will form another Greek cross exactly half the size
of the original, and by this process to leave a third Greek cross
complete.
[Illustration]
This is how to do it:--
Bisect _C D_ at _N_, _F G_ at _O_, _K L_ at _P_, and _B I_ at _Q_.
Join _N H_, _O M_, _P A_, _Q E_, intersecting at _R_, _S_, _T_, _U_.
Bisect _A R_ at _V_, _E S_ at _W_, _T H_ at _X_, and _M U_ at _Y_.
Join _V Q_, _N Y_, _W P_, _O X_, _N W_, _V O_, _Q X_, _Y P_.
Carefully cut out from the original Greek cross the newly-formed Greek
cross, and the odd pieces from around it can be arranged to form another
Greek cross.
No. XCVIII.--THE HAMMOCK
The greatest number of plane figures that can be formed by the union of
ten straight lines is thirty-six.
[Illustration]
The two equal lines at right angles are first drawn, and each is divided
into eight equal parts. The other eight straight lines are then drawn
from _a_ to _a_, from _b_ to _b_, and so on, until the hammock-shaped
network of thirty-six plane figures is produced.
No. XCIX.--CUTTING A CRUMPET
It will be seen on the diagram below that seven straight vertical cuts
with a table-knife will divide a crumpet into twenty-eight parts.
[Illustration]
BALANCE THE SCALES
The nine digits can be so adjusted as to form an equation, or, if taken
as weight, to balance the scales. Thus:--
9, 6¹⁄₂ = 3, 5, 7⁴⁄₈
TRUE STRETCHES OF IMAGINATION
How large is the sea? This is a bold big question, and any possible
answer involves a considerable stretch of the imagination. Here is a
startling illustration of its vast volume:--
If the water of the sea could be gathered into a round column, reaching
the 93,000,000 miles which separate us from the sun, the diameter of
this column would be nearly two miles and a half!
It is perhaps even more difficult to realise that this mighty mass of
waters could be dissipated in a few moments, if the column we have
imagined could become ice, and if the entire heat of the sun could be
concentrated upon it. All would be melted in _one second of time_, and
converted into steam in eight seconds!
No. C.--TO MAKE AN ENVELOPE
Many of our readers may be glad to know an easy way to make an envelope
of any shape or size.
[Illustration]
This diagram speaks for itself. When the lines _A B_, _A C_, _D B_, _D
C_ have been drawn, the corners of the rectangle, _H E G F_, are folded
over, as shown by the dotted lines, after the corners have been rounded,
and the margins touched with gum.
No. CI.--SQUARING AN OBLONG
The diagrams below will show how a piece of paper, 15 inches long and 3
inches wide, can be cut into five parts, and rearranged to form a
perfect square.
[Illustration]
A PLAGUE OF BLOW-FLIES
The following astounding calculation is answer enough to a question put
by one of the authors of “Rejected Addresses:”--“Who filled the
butchers’ shops with big blue flies?”
A pair of blow-flies can produce ten thousand eggs, which mature in a
fortnight. If every egg hatches out, and there are equal numbers of
either sex, which forthwith increase and multiply at the same rapid
rate, and if their descendants do the like, so that all survive at the
end of six months, it has been calculated that, if thirty-two would fill
a cubic inch of space, the whole innumerable swarm would cover the
globe, land and sea, half a mile deep everywhere.
No. CII.--BY RULE OF THUMB
Here is quite a neat way to make an equilateral triangle without using
compasses:--
[Illustration]
Take a piece of paper exactly square, which we will call _A B C D_, fold
it across the middle, so as to form the crease _E F_; unfold it, and
fold it again so that the corner _D_ falls upon the crease _E F_ at _G_,
and the angle at _G_ is exactly divided. Again unfold the square, and
from _G_ draw the straight lines _G C_ and _G D_. Then _G C D_ is the
equilateral triangle required.
THE VALUE OF A FRENCHWOMAN
How can we be sure that the value of a Frenchwoman is just 1 franc 8
centimes?
We can be sure that the exact value of a Frenchwoman is 1 franc 8
centimes, for
Two Frenchwomen = Deux Françaises.
Deux Françaises = deux francs seize.
(2 francs 16).
Therefore, One Frenchwoman = 1 franc 8!
No. CIII.--CLEARING THE WALL
If a 52-feet ladder is set up so as just to clear a garden wall 12 feet
high and 15 feet from the building, it will touch the house 48 feet from
the ground.
[Illustration]
Our diagram shows this, and also, by a dotted line, the only other
possible position in which it could fulfil the conditions, if it were
then of any practical use.
A BURDEN OF PINS
If one pin could be dropped into a vessel this week, two the next, four
the next, and so on, doubling each time for a year, the accumulated
quantity would be 4,503,599,627,370,495, and their weight, if we reckon
200 pins to the ounce, would amount to 628,292,358 tons, a full load for
27,924 ships as large as the _Great Eastern_, whose capacity was 22,500
tons.
No. CIV.--MEMORIES OF EUCLID
When at the signpost which said “To _A_ 4 miles, to _B_ 9 miles” on one
arm, and on the other “To _C_ 3 miles, to _D_ ---- miles,” and the boy
whom I met could only tell me that the farm he worked at was equidistant
from _A_, _B_, _C_, and _D_, and nearer to them than to the signpost,
and that all the roads ran straight, I found, thanks to memories of
Euclid, that I was 12 miles from _D_.
[Illustration]
Since _B A_ and _D C_ intersect outside the circle at the signpost _E_,
therefore _A E_ × _E B_ = _C E_ × _E D_.
but _A E_ × _E B_ = 4 × 9 = 36,
therefore _C E_ × _E D_ = 36,
and _C E_ = 3, therefore _E D_ = 12.
_Q.E.D._
No. CV.--A TRANSFORMATION
This seems to be quite a poor attempt at a Maltese cross, but there is
method in the madness of its make.
[Illustration]
It is possible by two straight cuts to divide this uneven cross into
four pieces which can be arranged together again so that they form a
perfect square. Where must the cuts be made, and how are the four pieces
rearranged?
BREVITY IS THE SOUL OF WIT
We all remember that splendidly terse message of success sent home to
the authorities by Napier when he had conquered the armies of
Scinde--“Peccavi!” (I have sinned).
History had an excellent opportunity for repeating itself when Admiral
Dewey defeated the Spaniel fleet, for he might have conveyed the news of
his victory by the one burning word--“Cantharides”--“The Spanish fly!”
No. CVI--SHIFTING THE CELLS
In the diagram below a square is subdivided into twenty-five cells.
+-----------+-----------+-----------+-----------+-----------+
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
|/ \|/ \|/ \|/ \|/ \|
| | | | | |
| | | | | |
+-----------+-----------+-----------+-----------+-----------+
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
|/ \|/ \|/ \|/ \|/ \|
| | | | | |
| | | | | |
+-----------+-----------+-----------+-----------+-----------+
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
|/ \|/ \|/ \|/ \|/ \|
| | | | | |
| | | | | |
+-----------+-----------+-----------+-----------+-----------+
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
|/ \|/ \|/ \|/ \|/ \|
| | | | | |
| | | | | |
+-----------+-----------+-----------+-----------+-----------+
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
|/ \|/ \|/ \|/ \|/ \|
| | | | | |
| | | | | |
+-----------+-----------+-----------+-----------+-----------+
Can you, keeping always on the straight lines, cut this into four
pieces, and arrange these as two perfect squares, in which every
semicircle still occupies the upper half of its cell?
A HOME-MADE MICROSCOPE
The following very simple recipe for a home-made microscope has been
suggested by a Fellow of the Royal Microscopical Society:--
Take a piece of black card, make a small pinhole in it, put it close to
the eye, and look at some small object closely, such as the type of a
newspaper. A very decided magnifying power will be shown thus.
No. CVII.--IN A TANGLE
Where on this diagram must we place twenty-one pins or dots so that they
fall into symmetrical design and form thirty rows, with three in each
row?
[Illustration]
ON ALL FOURS
Those who are fond of figures will find it a most interesting exercise
to see how far they are able to represent every number, from one up to a
hundred, by the use of four fours. Any of the usual signs and symbols of
arithmetic may be brought into use. Here are a few instances of what may
thus be done:--
4 + 4 + 4 4
3 = ---------; 9 = 4 + 4 + -;
4 4
4
36 = 4(4 + 4) + 4; 45 = 44 + -;
4
52 = 44 + 4 + 4; 60 = 4 × 4 × 4 - 4.
No. CVIII.--STILL A SQUARE
This figure, which now forms a square, and the quarter of that square,
can be so divided by two straight lines that its parts, separated and
then reunited, form a perfect square. How is this done?
+------+------+------+
| | | |
| | | |
+------+------+------+
| | |
| | |
+------+------+
A MAGIC SQUARE
Here we have arranged five rows of five cards each, so that no two
similar cards are in the same lines. Counting the ace as eleven, each
row, column, and diagonal adds up to exactly twenty-six.
/-------\ /-------\ /-------\ /-------\ /-------\
| ♣ | | ♥ | | ♠ ♠ | | ♥ ♥ | | ♣ ♣ |
| | | | | | | ♥ | | ♣ ♣ |
| | | ♥ | | ♠ | | ♥ | | ♣ |
| | | | | | | ♥ | | ♣ ♣ |
| ♣ | | ♥ | | ♠ ♠ | | ♥ ♥ | | ♣ ♣ |
\-------/ \-------/ \-------/ \-------/ \-------/
/-------\ /-------\ /-------\ /-------\ /-------\
| ♦ ♦ | | ♠ ♠ | | ♦ ♦ | | | | ♦ |
| | | ♠ | | ♦ ♦ | | | | |
| ♦ | | ♠ | | ♦ ♦ | | ♠ | | ♦ |
| | | ♠ | | ♦ ♦ | | | | |
| ♦ ♦ | | ♠ ♠ | | ♦ ♦ | | | | ♦ |
\-------/ \-------/ \-------/ \-------/ \-------/
/-------\ /-------\ /-------\ /-------\ /-------\
| ♥ ♥ | | | | ♠ | | ♥ ♥ | | ♣ ♣ |
| ♥ ♥ | | | | | | | | ♣ |
| ♥ | | ♣ | | ♠ | | ♥ | | ♣ ♣ |
| ♥ ♥ | | | | | | | | ♣ |
| ♥ ♥ | | | | ♠ | | ♥ ♥ | | ♣ ♣ |
\-------/ \-------/ \-------/ \-------/ \-------/
/-------\ /-------\ /-------\ /-------\ /-------\
| ♣ | | ♥ ♥ | | ♣ ♣ | | ♦ ♦ | | |
| | | | | ♣ | | ♦ ♦ | | |
| ♣ | | ♥ ♥ | | ♣ | | ♦ | | ♥ |
| | | | | ♣ | | ♦ ♦ | | |
| ♣ | | ♥ ♥ | | ♣ ♣ | | ♦ ♦ | | |
\-------/ \-------/ \-------/ \-------/ \-------/
/-------\ /-------\ /-------\ /-------\ /-------\
| ♦ ♦ | | ♠ ♠ | | | | | | ♣ ♣ |
| ♦ | | ♠ ♠ | | | | ♠ ♠ | | |
| ♦ | | ♠ | | ♦ | | | | ♣ |
| ♦ | | ♠ ♠ | | | | ♠ ♠ | | |
| ♦ ♦ | | ♠ ♠ | | | | | | ♣ ♣ |
\-------/ \-------/ \-------/ \-------/ \-------/
After you have looked at this Magic Square, and set it out on the table,
shuffle the cards, and try to re-arrange them so as to give the same
results.
No. CIX.--A TRANSFORMATION
Cut a square of paper or cardboard into seven such pieces as are marked
in this diagram.
[Illustration]
Can you rearrange them so that they form the figure 8.
A SECRET REVEALED
There are several ways in which strange juggling with figures and
numbers is to be done, but none is more curious than this:--
Ask someone, whose age you do not know, to write down secretly the date
and month of his birth in figures, to multiply this by 2, to add 5, to
multiply by 50, to add his age last birthday and 365. He then hands you
_this total only_ from this you subtract 615. This reveals to you at a
glance his age and birthday.
Thus, if he was born April 7 and is 23, 74 (the day and the month) × 2 =
148; 148 + 5 = 153; 153 × 50 = 7650; 7650 + 23 (his age) = 7673; and
7673 + 365 = 8038. If from this you subtract 615, you have 7423, which
represents to you the _seventh day of the fourth month, 23 years age_!
This rule works out correctly in all cases.
No. CX.--TO MAKE AN OBLONG
Cut out in stiff paper or cardboard two pieces of the shape and size of
the small triangle, and four pieces of the shapes and sizes of the other
three patterns--fourteen pieces in all.
[Illustration]
The puzzle is to fit these pieces together so that they form a perfect
oblong.
SLEEPERS THAT SLIP AND SLEEP
Here is a string of sentences, which may be used as stimulating mental
gymnastics when we leave the “Land of Nod.”
A sleeper runs on sleepers, and in this sleeper on sleepers sleepers
sleep. As this sleeper carries its sleepers over the sleepers that are
under the sleeper, a slack sleeper slips. This jars the sleeper and its
sleepers, so that they slip and no longer sleep.
DAYS THAT ARE BARRED
Clever calculation has established a fact which we shall not be able to
verify by personal experience. Whatever else may happen, the first day
of a century can never fall on Sunday, Wednesday, or Friday.
No. CXI.--SQUARES ON THE CROSS
On this cross there are seventeen distinct and perfect squares marked
out at their corners by asterisks.
*-----------*
| |
| |
| |
| |
| |
*-----------*
/| \ / |\
/ | \ / | \
/ | * | \
/ | / \ | \
/ | / \ | \
*-----------*-----------*-----------*-----------*-----------*
| | \ / | \ / | \ / | |
| | \ / | \ / | \ / | |
| | * | * | * | |
| | / \ | / \ | / \ | |
| | / \ | / \ | / \ | |
*-----------*-----------*-----------*-----------*-----------*
\ | \ / | /
\ | \ / | /
\ | * | /
\ | / \ | /
\| / \ | /
*-----------*
| |
| |
| |
| |
| |
*-----------*
How few, and which, of these can you remove, so that not a single
perfect square remains?
STANDING ROOM FOR ALL
On a globe 2 feet in diameter the Dead Sea appears but as a small
coloured dot. If it were frozen over there would be standing room on its
surface for the whole human race, allowing 6 square feet for each
person; and if they were all suddenly engulfed, it would merely raise
the level of the lake about 4 inches.
No. CXII.--A CHINESE PUZZLE
Here is quite a good exercise for ingenious brains and fingers. Cut a
piece of stiff paper or cardboard into such a right-angled triangle as
is shown below.
+
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
+----------------------------+
+----+
| |
+--+ +--+
| |
+--+ +--+
| |
+--+ +--+
| |
+--+ +--+
| |
+--+ +--+
| |
+--+ +--+
| |
+----+
Can you divide this into only three pieces, which, when rearranged, will
form the design given as No. 2?
A DEAL IN ROSES
I sent an order for dwarf roses to a famous nursery-garden, asking for a
parcel of less than 100 plants, and stipulating that if I planted them 3
in a row there should be 1 over; if 4 in a row 2 over; if 5 in a row 3
over, and if 6 in a row 4 over, as a condition for payment.
The nurseryman was equal to the occasion, charged me for 58 trees, and
duly received his cheque.
No. CXIII.--FIRESIDE FUN
This puzzle is not so easy of solution as it may seem at first sight.
Take a counter, or a coin, and place it on one of the points; then push
it across to the opposite point, and leave it there. Do this with a
second counter or coin, starting on a vacant point, and continue this
process until every point is covered, as we place the eighth counter or
coin on the last point.
A+ +B
| \ / |
| \ / |
| + |
| / \ |
| / \ |
H+-----------+-----------+-----------+C
\ / | | \ /
\ / | | \ /
+ | | +
/ \ | | / \
/ \ | | / \
G+-----------+-----------+-----------+D
| \ / |
| \ / |
| + |
| / \ |
| / \ |
F+ +E
A NOVEL EXERCISE
“Write down,” said a schoolmaster, “the nine digits in such order that
the first three shall be one third of the last three, and the central
three the result of subtracting the first three from the last.”
The arrangement which satisfies these conditions is, 219, 438, 657.
CURIOUS CALCULATIONS
1. There is a sum of money of such sort that its pounds, shillings, and
pence, written down as one continuous number, represent exactly the
number of farthings which it contains. What is it?
THE SLIP CARRIAGE
2. If on a level track a train, running all the time at 30 miles an
hour, slips a carriage, which is uniformly retarded by the brakes, and
which comes to rest in 200 yards, how far has the train itself then
travelled?
3. A traveller said to the landlord of an inn, “Give me as much money as
I have in my hand, and I will spend sixpence with you.” This was done,
and the process was twice repeated, when the traveller had no money
left. How much had he at first?
4. How can we obtain eleven by adding one-third of twelve to four-fifths
of seven?
FILL IN THE GAPS
5. Can you replace the missing figures in this mutilated long division
sum?
215)*7*9*(1**
***
-----
*5*9
*5*5
-----
*4*
***
=====
6. I buy as many heads of asparagus in the market as can be contained by
a string 1 foot long. Next day I take a string 2 feet long, and buy as
many as it will gird, offering double the price that I have given
before. Was this a reasonable offer?
ALIKE FROM EITHER END
7. As “one good turn deserves another,” first reverse me, then reverse
my square, then my cube, then my fourth power. When all this is done no
change has been made. What am I?
THE SEALED BAGS
8. How can a thousand pounds be so conveniently stored in ten sealed
bags that any sum in pounds from £1 to £1000 can be paid without
breaking any of the seals?
9. This is at once a problem and a puzzle:--
Though you twist and turn me over,
Yet no change can you discover.
Take me thrice, and cut in twain,
You will find but one remain.
10. Three gamblers, when they sit down to play, agree that the loser
shall always double the sum of money that the other two have before
them. After each of them has lost once, it is found that each has eight
sovereigns on the table. How much money had each at starting?
FIND THE MULTIPLIER
11. When Tom’s back was turned, the boy sitting next to him rubbed out
almost all his sum. Tom could not remember the multiplier, and only
this remained on his slate--
345
..
-----
....
....
-----
..76.
Can you reconstruct the sum?
JUGGLING WITH THE DIGITS
12. The sum of the nine digits is 45. Can you hit upon other
arrangements of 1, 2, 3, 4, 5, 6, 7, 8, 9, writing each of them once
only, which will produce the same total. Of course fractions may be
used.
A BRAIN TWISTER
13. The combined ages of Mary and Ann are forty-four years. Mary is
twice as old as Ann was when Mary was half as old as Ann will be when
Ann is three times as old as Mary was when Mary was three times as old
as Ann. How old, then, is Mary?
14. Mr Oldboy was playing backgammon with his wife on the eve of his
golden wedding, and could not make up his mind whether he should leave a
blot where it could be taken up by an ace, or one which a tré would hit.
His grandson, at home from Cambridge for the Christmas vacation, solved
the question for him easily. What was his decision?
“ASK WHERE’S THE NORTH?”--_Pope._
15. I am aboard a steamer, anchored in a bay where the needle points due
north, and exactly 1200 miles from the North Pole. If the course is
perfectly clear, and I steam continuously at the rate of 20 miles an
hour, always steering north by the compass needle, how long will it take
me to reach the North Pole?
16. Three persons, _A_, _B_, and _C_, share twenty-one wine casks of
equal capacity, of which seven are full, seven are half full, and seven
are empty. How can these be so apportioned that each person shall have
an equal number of casks, and an equal quantity of wine, without
transferring any of it from cask to cask?
17. A hungry mouse, in search of provender, came upon a box containing
ears of corn. He could carry three ears home at a time, and only had
opportunity to make fourteen journeys to and fro. How many ears could he
add to his store?
18. Take exactly equal quantities of lard and butter; mix a small piece
of the butter intimately with all the lard. From this blend take a piece
just as large as the fragment removed from the butter, and mix this
thoroughly with the butter. Is there now more lard in the butter or more
butter in the lard?
WHERE IS THE FALLACY?
19. Here is an apparent proof that 2 = 3:--
4 - 10 = 9 - 15
4 - 10 + ²⁵⁄₄ = 9 - 15 + ²⁵⁄₄
and the square roots of these:--
2 - ⁵⁄₂ = 3 - ⁵⁄₂
therefore
2 = 3.
PARCEL POST LIMITATIONS
20. Our Parcel Post regulations limit the length of a parcel to 3 feet 6
inches, and the length and girth combined to 6 feet. What is the largest
parcel of any size that can be sent through the post under these
conditions?
21. How can we show, or seem to show, that either four, five, or six
nines amount to one hundred?
TEST YOUR SKILL
22. Can you arrange nine numbers in the nine cells of a square, the
largest number 100, and the least 1, so that the product by
multiplication of each row, column and diagonal is 1000?
CATCHING CRABS
23. Seven London boys were at the seaside for a week’s holiday, and
during the six week-days they caught four fine crabs in pools under the
rocks, when the tide was out at Beachy Head.
Hearing of this, the twenty-one boys of a school in the neighbourhood
determined to explore the pools; but with the same rate of success they
only caught one large crab. For how long were they busy searching under
the seaweed?
SETTING A WATCH
24. On how many nights could a watch be set of a different trio from a
company of fifteen soldiers, and how often on these terms could one of
them, John Pipeclay, be included?
“IMPERIAL CÆSAR”
25. If Augustus Cæsar was born on September 23rd, B.C. 63, on what day
and in what year did he celebrate his sixty-third birthday, and by what
five-letter symbol can we express the date?
26. _A_ was born in 1847, _B_ in 1874. In what years have the same two
digits served to express the ages of both, if they are still living?
THIS SHOULD “AMUSE”
27. A hundred and one by fifty divide,
To this let a cypher be duly applied;
And when the result you can rightly divine,
You find that its value is just one in nine.
OVER THE FERRY
28. A man started one Monday morning with money in his purse to buy
goods in a neighbouring town. He paid a penny to cross the ferry, spent
half of the money he then had, and paid another penny at the ferry on
his return home.
He did exactly the same for the next five days, and on Saturday evening
reached home with just one penny in his pocket. How much had he in his
pocket on Monday before he reached the ferry?
THE MEN, THE MONKEY, AND THE MANGOES
29. Three men gathered mangoes, and agreed that next day they would give
one to their monkey and divide the rest equally. The first who arrived
gave one to the monkey, and then took his proper share; the second came
later and did likewise, and the third later still, neither knowing that
any one had preceded him. Finally they met, and, as there were still
mangoes, gave one to the monkey, and shared the rest equally. How many
mangoes at least must there have been if all the divisions were
accurate?
30. I look at my watch between four and five, and again between seven
and eight. The hands have, I find, exactly changed places, so that the
hour-hand is where the minute-hand was, and the minute-hand takes the
place of the hour-hand. At what time did I first look at my watch?
A LARGE ORDER
31. There is a number consisting of twenty-two figures, of which the
last is 7. If this is moved to the first place, the number is increased
exactly sevenfold. Can you discover this lengthy number?
32. A farmer borrowed from a miller a sack of wheat, 4 feet long and 6
feet in circumference. He sent in repayment two sacks, each 4 feet long
and 3 feet in circumference. Was the miller satisfied?
THE FIVE GAMBLERS
33. Five gamblers, whom we will call _A_, _B_, _C_, _D_, and _E_, play
together, on the condition that after each hazard he who loses shall
give to all the others as much as they then have in hand.
Each loses in turn, beginning with _A_, and when they leave the table
each has the same sum in hand, thirty-two pounds. How much had each at
first?
34. Knowing that the square of 87 is 7569, how can we rapidly, without
multiplication, determine in succession the squares of 88, 89, and 90?
NOT WHOLE NUMBERS
35. Two numbers seek which make eleven,
Divide the larger by the less,
The quotient is exactly seven,
As all who solve it will confess.
AN AMPLE CHOICE
36. If there are twenty sorts of things from which
^99999999999999999999^ different selections can be made, how many of
each sort are there?
37. Three women, with no money, went to market. The first had
thirty-three apples, the second twenty-nine, the third twenty-seven.
Each woman sold the same number of apples for a penny. They all sold
out, and yet each received an equal amount of money. How was this?
SIMPLE SUBTRACTION
38. Take five from five, oh, that is mean!
Take five from seven, and this is seen.
39. If a bun and a half cost three halfpence, how many do you buy for
sixpence?
40. How many times in a day would the hands of a watch meet each other,
if the minute-hand moved backward and the hour-hand forward?
41. How can half-a-crown be equally divided between two fathers and two
sons so that a penny is the coin of smallest value given to them?
SIZE AND SPEED
42. If the number of the revolutions of the wheel of a bicycle in six
seconds is equal to the number of miles an hour at which it is running,
what is the circumference of the wheel?
43. Hearing a clock strike, and being uncertain of the hour, I asked a
policeman. He had a turn for figures, and replied: “Take half, a third,
and a fourth of the hour that has just struck, and the total will be one
larger than that hour.” What o’clock was it?
AFTER LONG YEARS
44. If cash is lent at five per cent.
To those who choose to borrow,
How soon shall I be worth a pound
If I lend a crown to-morrow?
ON THE JUMP
45. If I jump off a table with a 20-lb. dumb-bell in my hand, what is
the pressure upon me of its weight while I am in the air?
AT A BAZAAR
46. In charitable mood I went recently to a bazaar where there were four
tents arranged to tempt a purchaser. At the door of each tent I paid a
shilling, and in each tent I spent half of the money remaining in my
purse, giving the door-keepers each another shilling as I came out.
It took my last shilling to pay the fourth door-keeper. How much money
had I at first, and what did I spend in each tent?
OUT IN THE RAIN
47. Rain is falling vertically, at a speed of 5 miles an hour. I am
walking through it at 4 miles an hour. At what angle to the vertical
must I hold my umbrella, so that the raindrops strike its top at right
angles?
A MONKEY PUZZLER
48. The following interesting problem, translated from the original
Sanscrit, is given by Longfellow in his “Kavanagh”:--
“A tree, 100 cubits high, is distant from a well 200 cubits. From the
top of this tree one monkey descends, and goes to the well. Another
monkey leaps straight upwards from the top, and then descends to the
well by the hypotenuse. Both pass over an equal space. How high does the
second monkey leap?”
49. A steamboat 105 miles east of Tynemouth Lighthouse springs a leak.
She puts back at once, and in the first hour goes at the rate of 10
miles an hour.
More and more water-logged, she decreases her speed each succeeding hour
at the rate of one-tenth of what it has been during the previous hour.
When will she reach the lighthouse?
50. If a hen and a half lays an egg and a half in a day and a half, how
many eggs will twenty-one hens lay in a week?
51. If the population of Bristol exceeds by two hundred and thirty-seven
the number of hairs on the head of any one of its inhabitants, how many
of them at least, if none are bald, must have the same number of hairs
on their heads?
52. A benevolent uncle has in his pocket a sovereign, a half-sovereign,
a crown, a half-crown, a florin, a shilling, and a threepenny piece. In
how many different ways can he tip his nephew, using only these coins,
and how is this most easily determined?
53. Here is a prime problem, in more senses than one, which will tax the
ingenuity of our solvers:--I am a prime number of three figures.
Increased by one-third, ignoring fractions, I become a square number.
Transpose my first two figures and increase me by one-third, and again
I am a square number. Put my first figure last, and increase me by
one-third, and I am another square number. Reverse my three figures, and
increase as before by one-third, and for a fourth time I become a square
number. What are my original figures?
54. In how many different ways can six different things be divided
between two boys?
55. What is quite the highest number that can be scored at six card
cribbage by the dealer, if he has the power to select all the cards, and
to determine the order in which every card shall be played?
COVERING THE WALLS
56. A fanciful collector, who bought pictures with more regard to
quantity than quality, gave instructions that the area of each frame
should exactly equal that of the picture it contained, and that the
frames should be of the same width all round.
At an auction he picked up a so-called “old master,” unframed, which
measured 18 inches by 12 inches. What width of frame will fulfil his
conditions?
A FAMILY REGISTER
57. Our family consists of my mother, a brother, a sister, and myself.
Our average age is thirty-nine. My mother was twenty when I was born; my
sister is two years my junior, and my brother is four years younger than
she is. What are our respective ages?
58. A spider in a dockyard unwittingly attached her web to a mechanical
capstan 1 foot in diameter, at the moment when it began to revolve. To
hold her ground she paid out 73 feet of thread, when the capstan
stopped, and she found herself drained of silk.
To make the best of a bad job she determined to unwind her thread,
walking round and round the capstan at the end of the stretched thread.
When she had gone a mile in her spiral path she stopped, tired and in
despair. How far was she then from the end of her task?
59. A mountebank at a fair had six dice, each marked only on one face 1,
2, 3, 4, 5, or 6, respectively. He offered to return a hundredfold any
stake to a player who should turn up all the six marked faces once in
twenty throws. How far was this from being a fair offer?
CATS’-MEAT FOR DOGS
60. If ninety groats for twenty cats
Will furnish three weeks’ fare,
How many hounds for forty pounds,
Less one, may winter there?
Just ninety days and one assume
The winter’s space to be;
And note that what five cats consume
Will serve for dogs but three.
(A groat = 4d.)
61. Two wineglasses of equal size are respectively half and one-third
full of wine. They are filled up with water, and their contents are then
mixed. Half of this mixture is finally poured back into one of the
wineglasses. What part of this will be wine and what part will be
water?
62. A legend goes that on a stout ship on which St Peter was carried
with twenty-nine others, of whom fourteen were Christians and fifteen
Jews, he so arranged their places, that when a storm arose, and it was
decided to throw half of the passengers overboard, all the Christians
were saved. The order was that every ninth man should be cast into the
sea. How did he place the Christians and the Jews?
A PROLIFIC COW
63. Farmer Southdown was the proud possessor of a prize cow, which had a
fine calf every year for sixteen years. Each of these calves when two
years old, and their calves also in their turn, followed this excellent
example. How many head did they thus muster in sixteen years?
64. A shepherd was asked how many sheep he had in his flock. He replied
that he could not say, but he knew that if he counted them by twos, by
threes, by fours, by fives, or by sixes, there was always one over, but
if he counted them by sevens, there was no remainder. What is the
smallest number that will answer these conditions?
READY RECKONING
65. If a number of round bullets of equal size are arranged in rows one
above another evenly graduated till a single bullet crowns the flat
pyramid, how can their number be readily reckoned, however long the base
line may be?
THE TITHE OF WAR
66. Old General Host
A battle lost,
And reckoned on a hissing,
When he saw plain
What men were slain,
And prisoners, and missing.
To his dismay
He learned next day
What havoc war had wrought;
He had, at most,
But half his host
Plus ten times three, six, ought.
One-eighth were lain
On beds of pain,
With hundreds six beside;
One-fifth were dead,
Captives, or fled,
Lost in grim warfare’s tide.
Now, if you can,
Tell me, my man,
What troops the general numbered,
When on that night
Before the fight
The deadly cannon slumbered?
67. A farmer sends five pieces of chain, of three links each, to be made
into one continuous length. He agrees to pay a penny for each link cut,
and a penny for each link joined. What was the blacksmith entitled to
charge if he worked in the best interest of the _farmer_?
68. In a parcel of old silver and copper coins each silver piece is
worth as many pence as there are copper coins, and each copper coin is
worth as many pence as there are silver coins, and the whole is worth
eighteen shillings. How many are there of each?
A FEAT WITH FIGURES
69. Take the natural numbers 1 to 11, inclusive, and arrange them in
five groups, not using any of them more than once, so that these groups
are equal. Any necessary signs or indices may be used.
HOW OLD WAS JOHN?
70. John Bull passed one-sixth of his life in childhood and one-twelfth
as a youth. When one-seventh of his life had elapsed he had a son who
died at half his father’s age, and John himself lived on four years
more. How old was he at the last?
FIGURE IT OUT
71. There are two numbers under two thousand, such that if unity is
added to each of them, or to the half of each, the result is in every
case a square number. Can you find them?
72. A cheese in one scale of a balance with arms of unequal length seems
to weigh 16 lbs. In the other scale it weighs but 9 lbs. What is its
true weight?
“DIVISION IS AS BAD!”
73. Can you divide 100 into two such parts that if the larger is divided
by the lesser the quotient is also 100?
74. I have marbles in my two side pockets. If I add one to those in the
right-hand pocket, and multiply its increased contents by the number it
held at first, and then deal in a similar way with those in the other
pocket, the difference between the two results is 90. If, however, I
multiply the sum of the two original quantities by the square of their
difference, the result is 176. How many marbles had I at first in each
pocket?
A SURFEIT OF BRIDGE
75. A friendly circle of twenty-one persons agreed to meet each week,
five at a time, for an afternoon of bridge, so long as they could do so
without forming exactly the same party on any two occasions.
As a central room had to be hired, it was important to have some idea as
to the length of time for which they would require it. How long could
they keep up their weekly meetings?
76. A herring and a half costs a penny and a half; what is the price of
a dozen?
77. What sum of money is in any sense seen to be the double of itself?
COMIC ARITHMETIC
78. At the close of his lecture upon unknown quantities, Dr Bulbous
Roots, in playful mood, wrote this puzzle on his blackboard:--
Divide my fifth by my first and you have my fourth; subtract my first
from my fifth and you have my second; multiply my first by my fourth
followed by my second, and you have my third; place my second after my
first and you have my third multiplied by my fourth. What am I?
DROPPED THROUGH THE GLOBE
79. If we can imagine the earth at a standstill for the purpose of our
experiment, and if a perfectly straight tunnel could be bored through
its centre from side to side, what would be the course of a cannon ball
dropped into it from one end, under the action of gravity?
LOVE LETTERS
80. A lady to her lover cried,
“How many notes have you of mine?”
“Six more I’ve sent,” the youth replied,
“Than I have had of thine.”
“But if from one pound ten you take
The pennies we on stamps have spent,
One eighth their cost you thus will make.”
How many had they had and sent?
81. A man, on the day of his marriage, made his will, leaving his money
thus:--If a son should be born, two-thirds of the estate to that son and
one-third to the widow. If a daughter should be born, two-thirds to the
widow and one-third to that daughter. In the course of time twins were
born, a boy and a girl. The man fell sick and died without making a
fresh will. How ought his estate to be divided in justice to the widow,
son, and daughter?
82. My carpet is 22 feet across. My stride, either backwards or
forwards, is always 2 feet, and I make a stride every second. If I take
three strides forwards and two backwards continuously until I cross the
carpet, how long does it take me to reach the end of it?
NO TIME TO BE LOST
83. A merchant at Lisbon has an urgent business call to New York. Taking
these places to be, as they appear on a map of the world, on the same
parallel of latitude, and at a distance measured along the parallel, of
some 3600 miles, if the captain of a vessel chartered to go there sails
along this parallel, will he be doing the best that he can for the
impatient merchant?
ROUND THE ANGLES
84. Two schoolboys, John and Harry, start from the right angle of a
triangular field, and run along its sides. John’s speed is to Harry’s as
13 is to 11.
They meet first in the middle of the opposite side, and again 32 yards
from their starting point. How far was it round the field?
AN ECHO FROM THE PAST
85. The following question is given and spelt exactly as it was
contributed to a puzzle column by “John Hill, Gent.,” in 1760:--
“A vintner has 2 sorts of wine, viz. A and B, which if mixed in equal
parts a flagon of mixed will cost 15 pence; but if they be mixed in a
_sesqui-alter_ proportion, as you should take two flagons of A as often
as you take three of B, a flagon will cost 14 pence. Required the price
of each wine singly.”
PROMISCUOUS CHARITY
86. A man met a beggar and gave him half the money he had in his pocket,
and a shilling besides. Meeting another he gave him half of what was
left and two shillings, and to a third, he gave half of the remainder
and three shillings. This left a shilling in his pocket. How much had he
at first?
87. A young clerk wishes to start work at an office in the City on
January 1st. He has two promising offers, one from _A_ of £100 a year,
with a yearly rise of £20, the other from _B_ of £100 a year with a
half-yearly rise of £5. Which should he accept, and why?
HOW CAN I PAY MY BILL?
88. I have an abundance of florins and half-crowns, but no other coins.
In how many different ways can I pay my tailor £11, 10s. without
receiving change?
89. A monkey climbing up a greased pole ascends 3 feet and slips down 2
feet in alternate seconds till he reaches the top. If the pole is 60
feet high, how long does it take him to arrive there?
“SAFE BIND, SAFE FIND”
90. Old Adze, the village carpenter, who kept his tools in an open
chest, found that his neighbours sometimes borrowed and forgot to return
them.
To guard against this, he secured the lid of the chest with a letter
lock, which carried six revolving rings, each engraved with twelve
different letters. What are the chances against any one discovering the
secret word formed by a letter on each ring, which will open the lock,
and be the only key to the puzzle?
91. Five merry married couples happened to meet at a Swiss hotel, and
one of the husbands laughingly proposed that they should dine together
at a round table, with the ladies always in the same places so long as
the men could seat themselves each between two ladies, but never next to
his own wife. How long would their nights at the round table be
continued under these conditions?
SOUNDING THE DEPTH
92. In calm water the tip of a stiff rush is 9 inches above the surface
of a lake. As a steady wind rises it is gradually blown aslant, until at
the distance of a yard it is submerged. Can you decide from these data
the depth of the water in which the rush grows?
AMINTA’S AGE
93.
If to Aminta’s age exact
Its square you add, and eighteen more,
And from her age its third subtract,
And to the difference add three score,
The latter to the former then
Will just the same proportion bear
As eighteen does to nine times ten.
Can you Aminta’s age declare?
ONE FOR THE PARROT
94. A bag of nuts was to be divided thus among four boys:--Dick took a
quarter, and finding that there was one over when he made the division,
gave it to the parrot. Tom dealt in exactly the same way with the
remainder, as did Jack and Harry in their turns, each finding one nut
from the reduced shares to spare for the parrot. The final remainder
was equally divided among the boys, and again there was one for the
bird. How many nuts, at the lowest estimate, did the bag contain?
95. Here is an easy one:--
If five times four are thirty-three,
What will the fourth of twenty be?
96. What fraction of a pound, added to the same fraction of a shilling,
and the same fraction of a penny, will make up exactly one pound?
MENTAL ARITHMETIC
97. “Now, boys!” said Dr Tripos, “I think of a number, add 3, divide by
2, add 8, multiply by 2, subtract 2, and thus arrive at twice the number
I thought of.” What was it?
98. Two club friends, _A_ and _B_, deposit similar stakes with _C_, and
agree that whoever first wins three games at billiards shall take the
whole of them. _A_ wins two games and _B_ wins one. Upon this they
determine to divide the stakes in proper shares. How must this division
be arranged?
99. Not so simple as it sounds is the following compact little
problem:--If I run by motor from London to Brighton at 10 miles an hour,
and return over the same course at 15 miles an hour, what is my average
speed?
100. “I can divide my sheep,” says Farmer Hodge, who from his schooldays
had a turn for figures, “into two unequal parts, so that the larger part
added to the square of the smaller part shall be equal to the smaller
part added to the square of the larger part.”
How many sheep had the farmer?
A HELPFUL BURDEN
101. The following question was proposed in an old book of Mathematical
Curiosities published more than a hundred years ago:--
“It often happens that if we take two horses, in every respect alike,
yet, if both are put to the draught, that horse which is most loaded
shall be capable of performing most work; so that the horse which
carries the heavier weight can draw the larger load. How is this?”
102. In the king’s treasury were six chests. Two held sovereigns, two
shillings, and two pence, in equal numbers of these coins. “Pay my
guard,” said the king, “giving an equal share to each man, and three
shares to the captain; give change if necessary.” “It may not be
possible,” replied the treasurer, “and the captain may claim four
shares.” “Tut, tut,” said the king, “it can be done whatever the amount
of the treasure, and whether the captain has three shares or four.”
Was the king right? If so, how many men were there in the guard?
NUTS TO CRACK
103. I bought a parcel of nuts at forty-nine for twopence. I divided it
into two equal parts, one of which I sold at twenty-four, the other at
twenty-five for a penny. I spent and received an integral number of
pence, but bought the least possible number of nuts. How many did I buy?
What did they cost? What did I gain?
MONEY MATTERS
104. My purse contained sovereigns and shillings. After I had spent half
of its contents there were as many pounds left as I had shillings at
first. With what sum did I start?
A DELICATE QUESTION
105. A lady was asked her age in a letter, and she replied by postcard
thus:--
If first my age is multiplied by three,
And then of that two-sevenths tripled be,
The square root of two-ninths of this is four,
Now tell my age, or never see me more!
What was her age?
106. If cars run at uniform speed on the twopenny tube, from Shepherd’s
Bush to the Bank at intervals of two minutes, how many shall I meet in
half an hour if I am travelling from the Bank to Shepherd’s Bush?
PAYMENT BY RESULTS
107. What would it cost me to keep my word if I were to offer my
greengrocer a farthing for every different group of ten apples he could
select from a basket of a hundred apples?
108. If the minute-hand of a clock moves round _in the opposite
direction_ to the hour-hand, what will be the real time between three
and four, when the hands are exactly together?
109. Two monkeys have stolen some filberts and some walnuts. As they
begin their feast they see the owner of the garden coming with a stick.
It will take him two and a half minutes to reach them. There are twice
as many filberts as walnuts, and one monkey finishes the walnuts at the
rate of fifteen a minute in four-fifths of the time and bolts. The other
manages to finish the filberts just in time.
If the walnut monkey had stopped to help him till all was finished, when
would they have got away if they ate filberts at equal rates?
110. A cashier, in payment for a cheque, gives by mistake pounds for
shillings and shillings for pounds. The receiver spends half-a-crown,
and then finds that he has twice as much as the cheque was worth. What
was its value?
111. What five uneven figures can be added together so as to make up 14?
112. Three posts which vary in value are vacant in an office. In how
many ways can the manager fill these up from seven clerks who apply for
the appointments?
113. “It is now ⁵⁄₁₁ of the time to midnight,” said the fasting man, who
began his task at noon. What time was it?
A STRIKING TIME
114. If a clock takes six seconds to strike six how long will it take to
strike eleven?
WHAT ARE THE ODDS?
115. How would you arrange twenty horses in three stalls so as to have
an odd number of horses in each stall?
116. Here is a pretty little problem, which has at any rate an Algebraic
form, and is exceedingly ingenious:--
Given _a_, _b_, _c_, to find _q_.
WHEN WAS HE BORN?
117. Tom Evergreen was asked his age by some men at his club on his
birthday in 1875. “The number of months,” he said, “that I have lived
are exactly half as many as the number which denotes the year in which I
was born.” How old was he?
118. Draw three circles of any size, and in any position, so long as
they do not intersect, or lie one within another. How many different
circles can be drawn touching all the three?
119. We have seen that the nine digits can be so dealt with, using each
once, as to add up to 100. How can 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 be
arranged so that they form a sum which is equal to 1?
120. How is it possible, by quite a simple method, to find the sum of
the first fifty numbers without actually adding them together?
121. Two tram-cars, _A_ and _B_, start at the same time. _A_ runs into a
“lie by” in four minutes, and waits there five minutes, when _B_ meets
and passes it. Both complete the whole course at the same moment. In
what time can _A_ complete it without a rest?
A CURIOUS DEDUCTION
122. Take 10, double it, deduct 10, and tell me what remains.
123. The average weight of the Oxford crew is increased by 2 lbs., when
one of them, who weighs 12 stone, is replaced by a fresh man. What is
the fresh man’s weight?
ASK ANY MOTORIST
124. A motor car is twice as old as its tyres were when it was as old as
its tyres are. When these tyres are as old as the car is now, the
united ages of car and tyres will be two years and a quarter. What are
their respective ages now?
125. _A_ and _B_ on the edge of a desert can each carry provisions for
himself for twelve days. How far into the desert can an advance be made,
so that neither of them misses a day’s food?
126. A bottle of medicine and its cork cost half-a-crown, but the bottle
and the medicine cost two shillings and a penny more than the cork. What
did the cork cost?
IN A FIX
127. A boat’s crew are afloat far from land with no sail or oars. How
can they, without making any use of wind or stream, and without any
outside help, regain the shore by means of a coil of rope which happens
to be at hand.
128. What is the largest sum in silver that I can have in my pockets
without being able to give change for a half-sovereign.
129. I have apples in a basket. Without cutting an apple I give half of
the number and half an apple to one person; half of what then remains
and half an apple to another, and half of what are still left and half
an apple to a third. One apple now remains in the basket. How many were
there at first?
A QUEER DIVISION
130. A third of twelve divide
By just a fifth of seven;
And you will soon decide
That this must give eleven.
131. A motor goes 9 miles an hour uphill, 18 miles an hour downhill, and
12 miles an hour on the level. How long will it take to run 50 miles and
return at once over the same course?
132. In firing at a mark _A_ hits it in two out of three shots, _B_ in
three out of four, and _C_ in four out of five. The mark was hit 931
times. If each fired the same number of shots, how many hits did each
make, and how many shots were fired?
133. If a cat and a dog, evenly matched in speed, run a race out and
back over a course 75 yards in all, and the dog always takes 5 feet at a
bound and the cat 3 feet, which will win?
IN A FOG
134. In a fog a man caught up a wagon going in the same direction at 3
miles an hour. If the wagon was just visible to him at a distance of 55
yards, and he could see it for five minutes, at how many miles an hour
was he walking?
135. Three horses start in a race. In how many different ways can they
be placed by the judge?
NEW ZEALAND FOOTBALL
136. The New Zealanders, winning a match against Oxbridge, scored 34
points, from tries and tries converted into goals.
If every try had been converted they would have made four-fifths of the
maximum which a score of 34 points from tries and goals can yield.
What is this maximum, and what was their actual score?
137. What is the smallest number, of which the alternate figures are
cyphers, that is divisible by 9 and by 11?
138. Here is an interesting little problem:--_A_, with 8d. in his hand,
meets _B_ and _C_, who have five and three loaves respectively. In
hungry mood they all agree to share the loaves equally, and to divide
the money fairly between _B_ and _C_. How much does each receive?
THE MONEY-BOXES
139. When four money-boxes, containing pennies only, were opened and
counted, it was found that the number in the first with half those in
all the others, in the second with a third of all the others, in the
third with a fourth of all the others, and in the fourth with a fifth of
all the others, amounted in each case to 740. How much money did the
boxes contain, and how was it divided?
140. Two steamers start together to make a trip to a far-off buoy and
back. Steamer _A_ runs all the time at 10 miles an hour. Steamer _B_
does the passage out at 8 miles an hour, and the return at 12 miles.
Will they regain port together?
141. A golf player has two clubs mended in London. One has a new head,
the other a new leather face. The head costs four times as much as the
face. At St Andrews it costs five times as much, and the leather face at
St Andrews is half the London price. Including a shilling for a ball he
pays twice the St Andrews charges for these repairs. What is the London
charge for each?
FROM TWO WRONGS TO MAKE A RIGHT
142. Two children were asked to give the total number of animals in a
pasture, where sheep and cattle were grazing. They were told the numbers
of sheep and of cattle, but one subtracted, and gave 100 as the answer,
and the other arrived at 11,900 by multiplication. What was the correct
total?
THE STONE CARRIER
143. Fifty-two stones are placed at intervals along a straight road. The
distance between the first and the second is 1 yard, between the second
and the third it is 3 yards, between the next two 5 yards, and so on,
the intervals increasing each time by 2 yards.
How far would a tramp have to travel to earn five shillings promised to
him when he had brought them one by one to a basket placed at the first
stone?
144. On a division in the House of Commons, if the Ayes had been
increased by fifty from the Noes, the motion would have been carried by
five to three. If the Noes had received sixty votes from the Ayes, it
would have been lost by four to three. Did the motion succeed? How many
voted?
A WATCH PUZZLE
145. How many positions are there on the face of a watch in which the
places of the hour and minute-hands can be interchanged so as still to
indicate a possible time?
CRICKET SCORES
146. In a cricket match the scores in each successive innings are a
quarter less than in the preceding innings. The match was played out,
and the side that went in first won by fifty runs. What was the complete
score?
HOW HIGH CAN YOU THROW?
147. A boy throws a cricket ball vertically upwards, and catches it as
it falls just five seconds later. How high from his hands does the ball
go?
MEASURE THE CARPET
148. It may be said of a section of the gigantic carpet at Olympia that
had it been 5 feet broader and 4 feet longer it would have contained 116
more feet; but if 4 feet broader and 5 longer the increase would have
been but 113 feet. What were its actual breadth and length?
149. In estimating the cost of a hundred similar articles, the mistake
was made of reading pounds for shillings and shillings for pence in each
case, and under these conditions the estimated cost was £212 18s. 4d. in
excess of the real cost. What was the true cost of the articles?
SQUARES IN STREETS
150. The square of the number of my house is equal to the difference of
the squares of the numbers of my next door neighbour’s houses on either
side.
My brother, who lives in the next street, can say the same of the number
of his house, though his number is not the same as mine. How are our
houses numbered?
151. Two men of unequal strength are set to move a block of marble which
weighs 270 lbs., using for the purpose a light plank 6 feet long. The
stronger man can carry 180 lbs. How must the block be placed so as to
allow him just that share of the weight?
152. A man has twenty coins, of which some are shillings and the rest
half-crowns. If he were to change the half-crowns for sixpences and the
shillings for pence he would have 156 coins. How many shillings has he?
COUNT THE COINS
153. Some coins are placed at equal distances apart on a table, so that
they form the sides of an equilateral triangle.
From the middle of each side as many are then taken as equal the square
root of the number on that side, and placed on the opposite corner coin.
The number of coins on each side is then to the original number as 5 is
to 4. How many coins are there in all?
PUTTING IN THE POSTS
154. A gardener, wishing to fence round a piece of ground with some
light posts, found that if he set them a foot apart there would be 150
too few, but if placed a yard apart there would be 70 to spare. How many
posts had he?
155. _A_ gives _B_ £100 to buy 100 animals, which must be cows at £5
each, sheep at £1, and geese at 1s. How many of each sort can he buy?
156. John is twice as old as Mary was when he was as old as Mary is.
John is now twenty-one. How old is Mary?
157. In a cricket match _A_ made 35 runs; _C_ and _D_ made respectively
half and one-third as many as _B_, and _B_’s score was as much below
_A_’s as _C_’s was above _D_’s. What did _B_, _C_, and _D_ each score?
SETTLED BY REMAINDERS
158. What is the least number which, divided by 2, 3, 4, 5, 6, 7, 8, 9,
or 10, leaves respectively as remainders 1, 2, 3, 4, 5, 6, 7, 8, and 9?
TABLE TURNING
159. A square table stands on four legs, which are set at the middle
point of its sides. What is the greatest weight that this table can
uphold upon one of its corners?
BRIBING THE BOYS
160. Well pleased with the inspector’s report, the rector of a country
parish came into his school with 99 new pennies in his pocket, and said
that he would give them to the five boys in Standard VII. if they could,
within an hour, show him how to divide them so that the first share
should exceed the second by 3, be less than the third by 10, be greater
than the fourth by 9, and less than the fifth by 16. What was the answer
which would satisfy these conditions?
SHEEP-STEALING
161. Some Indian raiders carried off a third of a flock of sheep, and a
third of a sheep. Another party took a fourth of what remained, and a
fourth of a sheep. Others took a fifth of the rest and three-fifths of a
sheep. What was the number of the full flock, if there were then 409
left?
162. Three boys begin to fill a cistern. _A_ brings a pint at the end of
every three minutes, _B_ a quart every five minutes, and _C_ a gallon
every seven minutes. If the cistern holds fifty-three gallons, in what
time will it be filled, and who will pour in the last contribution?
ESTIMATE OF AGE
163. A man late in the last century said that his age was the square
root of the year in which he was born. In what year did he say this?
A DEAL IN CHINA
164. A dealer in Eastern curios sold a Satzuma vase for £119, and on
calculation found that the number which expressed his profit per cent.
expressed also the cost price in pounds of the vase. What was this
number?
165. What is the chance of throwing at least one ace in a single throw
with a pair of dice?
166. A thief starts running from a country house as fast as he can. Four
minutes later a policeman starts in pursuit. If both run straight along
the road, and the policeman gets over the ground one-third faster than
the thief, how soon will he catch him?
167. Twenty-seven articles are exposed for sale on one of the stalls of
a bazaar. What choice has a purchaser?
VERY PERSONAL
168. “How old are _you_, dad?” said Nellie on her birthday, as her
father gave her as many shillings as she was years old. His answer was
quite a puzzle for a time, but with the help of her schoolfellows Nellie
worked it out.
This is what he said:--
“I was twice as old as you are
The day that you were born.
You will be just what I was then
When fourteen years are gone.”
How old was Nellie, and how old was her dad?
WORD AND LETTER PUZZLES
A MAGIC COCOON
This Magic Cocoon is so cleverly spun that the word can be traced and
read in many ways.
N
N O N
N O O O N
N O O C O O N
N O O C O C O O N
N O O C O C O C O O N
N O O C O C O O N
N O O C O O N
N O O O N
N O N
N
How many readings can you discover starting from one or other of the Cs,
and passing up and down or sideways, but not diagonally, and never over
the same letter twice in a reading? There are 756!
THE CHRONOGRAM
The Chronogram, severely classed by Addison as “a species of false wit”
is a sentence in which the salient letters represent in Roman numerals
some particular year. A good English specimen is this: “My Day Closed Is
In Immortality.” The capital letters in these words give MDCIII., or
1603, the year in which Queen Elizabeth died.
A FRENCH CHRONOGRAM
The battle-cry at Montlhéry in 1465 was:--“à CheVaL, à CheVaL,
gendarMes, à CheVaL!” Taking the letters printed in capitals--
M = 1000
CCC = 300
LLL = 150
VVV = 15
----
we have the date of the battle 1465
A NOTABLE CHRONOGRAM
QVI CHRISTI IAVDES CANTANT
SANCTÆ PASSIONIS SVÆ VIRTVTE
IN IPSO ET PATRE VNVM SINT.
This curious inscription is placed over the organ at Ober Ammergau. Add
together its Roman numerals and they give the date at which the organ
was dedicated. The English of it is:--
May those who sing the praises of Christ be by virtue of His Sacred
Passion one in The Father and in Himself.
A PERFECT CHRONOGRAM
On a damaged inscription to Bishop Berkeley in Winchester Cathedral are
the words--VIXI, LVXI--I have lived, I have shone. Added together in
their values as Roman numerals the letters of these two words give his
age exactly at his death--eighty-three.
A PRIZE MOTTO
On the return of the C.I.V. from the Boer War a prize was offered by
_Truth_ for the best motto appropriate to them. This was to consist of
three words of which the first must begin with C the second with I and
the third with V.
The prize was taken by the following Latin motto which is singularly
happy both in construction and in meaning:--
CIVI IVI VICI
_I roused_ _I went_ _I won._
The sequence of events is perfect; no letters but C.I.V. are used and
the motto is a palindrome if read by syllables.
THE MUSICAL SCALE
As in olden days some of the Psalms and other writings were constructed
in acrostic form, so in the Middle Ages even serious writers would
juggle with letters, as though they felt that such tricky methods were
an aid to memory.
It was in this spirit that Guido Aretino, a Benedictine monk of Tuscany
in 1204, gave names to the notes used in the musical scale from the
first syllables of the lines of a Latin hymn. “Ut” is still used in
France, though we and the Italians have substituted “do.”
UT queant laxis REsonare fibris,
MIra gestorum FAmuli tuorum,
SOLve polutis LAbii reatis
O Pater alme!
ALL THE ALPHABET!
Many of us know that there is a long verse in the Book of Ezra in which
all the letters of the alphabet are used, taking “j” as “i” (_Ezra_
vii., v. 21).
This very curious coincidence also occurs in a comparatively short
sentence in “The Beth Book,” by Sarah Grand:--“It was an exquisitely
deep blue just then, with filmy white clouds drawn up over it like
gauze;” and here “j” is itself in evidence.
APT ALLITERATION
Schopenhauer, the famous German philosopher, who was a confirmed
bachelor and misogynist, was compelled while living at Frankfort to
support an old lady who had been crippled by his violence. When her
death came as a welcome relief to him, he composed the following clever
epitaph:--
Obit anus,
Abit onus.
which by the interchange of two letters pictured the position. It may be
freely rendered:--
Old lady dies,
My burden flies.
A DOUBLE SEQUENCE
The following clever composition, which appeared in the pages of
_Truth_, contains a _double_ sequence of words, which increase a letter
at a time, the same letters appearing in varied order until at last “o”
culminates in _thornless_, and “a” in _restrainest_. It is quite a
remarkable _tour-de-force_.
O lack-_a_-day! _at_ eve we _sat_,
One _star_ had lit its lamps _on_ high.
We did _not note_ the circling bat,
_Start_ from the _stone_ when flitting nigh.
For the _strait_ gate of _honest_ doubt
Shut off the _thrones_ of Love and Gain;
We dreamed not, as we mourned without,
That Time’s swift _transit shortens_ pain.
O Thou, Who _trainest_ souls to shine,
Though once we craved a _thornless_ lot,
This gracious truth we now divine:
The bruised reed Thou _strainest_ not;
But by _restraints_, that gently tame;
_Restrainest_ Passion’s kindling flame.
THE REIGN OF TERROR
During the Reign of Terror, France and her people and position were thus
alphabetically described:--
Le peuple Français A B C. (abaissé).
La gloire nationale F A C. (effacée).
Les places fortes O Q P. (occupées).
Quarante trois députés C D. (cédés).
L’armée D P C. (dépaysée).
Les ministres A J. (agés).
La liberté O T. (ôtée).
La charte L U D. (éludée).
SEE-SAW
This elaborate method of piling up no less than seven consecutive
“thats,” so that they make tolerable sense, was told to his boys during
school-time by Dr Moberly, then headmaster of Winchester, and afterwards
Bishop of Salisbury, just fifty years ago:--
I saw that C saw.
C saw that that I saw.
I saw that that that C saw was so.
C saw that, that that that I saw was so.
I saw that, that _that_ that that C saw was so.
C saw _that_ that, that _that_ that that I saw was so.
I saw _that_ that, that _that_ that that _that_ C saw was so.
FOR A ROMAN HOLIDAY
If the Roman ladies and children, at their equivalent for Christmas,
amused themselves by acting verbal charades, an excellent word was at
their disposal, “sustineamus”--“let us endure,” which can be broken up
exactly into _sus_, _tinea_, _mus_--_a sow_, _a moth_, _a mouse_.
A WORD SQUARE
1. Can you complete this word square, so that its four words read alike
from top to bottom and from left to right?
* E * *
E * * *
* * * E
* * E *
ANOTHER WORD SQUARE
2. Can you fill in this word square?
C * * C * E
* N U * E S
* U * E S *
C * E * S *
* E S * * E
E * T E * *
DUPLICATE LETTERS
3. In this sentence, when complete,
So****AG****LATI****X****ITH
each group of four missing letters contains two pairs of letters which
are alike. Can you on these lines complete the sentence?
Here is a similar sentence by way of illustration:
T****M****TERTAIN****MUND,
which becomes when filled in--
T_wo_ _wo_m_en_ _en_tertain_ed_ _Ed_mund.
ANOTHER WORD SQUARE
4. Can you complete this word square by substituting letters for the
dots?
W * * * E
* * T * *
* T O N *
* * N * *
E * * * T
WORD BUILDING
5. What word can be made with these?
L S D U D O D U D.
6. A lovelorn youth consulted a married lady on his condition, and was
asked by her on a slip of paper:--
“Loruve?”
When he had deciphered this, and had answered in the affirmative, she
handed to him another slip, on which this advice was written:--
L
“Prove A F and ensure success.”
D
What did it all mean?
A DOUBLE ACROSTIC
7. _Saint of Spain, whose daily word
Twenty years hath London heard!_
Sweet days, elastic metal, motion sharp.
My halls once echoed to an Irish harp.
The “son of sorrow,” honourable of yore.
Dread goddess, loosing the loud dogs of war.
Time’s atom--total of eternities.
This name an insect bears, a patriot bore.
“So do, yet hear me,” said Themistocles.
ANOTHER WORD SQUARE
8. Can you complete this word square?
* M * N * S
M * N * O *
* N * B * E
N * B * L *
* O * L * R
S * E * R *
A FRENCH ORACLE
9. A spruce young Frenchman at a _fête_ consulted a modern oracle as to
how he could best please the ladies. This was the mystic response:--
MEC DO BIC.
Can you interpret it?
A QUAINT EQUATION
10. In our young days we have often wrestled with vulgar fractions, but
apart from Algebra we have had no serious concern with any in which
letters take the place of figures. A specimen of this sort, not known to
science, is the following curiosity:--
m
--
ot
-- = mo.
y
11. The puzzle in _Truth_ was recently founded upon “ourang-outang,”
which had been cleverly buried. We will give a few of the best results.
This is one:--
Poor wretch! a moisture filled his eye,
“Do not rebuff a lonely boy,”
Said he, “If ere I sink and die
Your smile--O! pardon will be joy!”
Another is:--
Though I jump, and row, and run,
Cap or cup I never won.
What animals are buried in these lines?
LIKE A PEACOCK’S TAIL
12. Fourteen letters here we fix,
Vowels only two are spoken;
All together these we mix
Into what can not be broken.
A WEIRD WORD
13. There is an English word of thirteen letters in which the same vowel
occurs four times, the same consonant six times, another consonant
twice, and another once. Can you hit upon it?
A CONDENSED PROVERB
14. Though brevity is said to be the soul of wit, we are too often
flooded nowadays with a superabundance of words.
Here is an attempt at modest condensation. A familiar English proverb is
quite clearly expressed to the solver’s seeing eyes in this brief
phrase:--
WE IS DO
What is the proverb?
ANOTHER WORD SQUARE
15. Can you complete this word square?
W * * * * S
* R * * R *
* * O R * *
* * R M * *
* R * * N *
S * * * * M
CAN YOU DECIPHER IT?
16. The following puzzle lines are attributed to Dr Whewell:--
O O N O O.
-----------
U O A O O I O U
O N O O O O M E T O O.
U O A O I D O S O
I O N O O I O U T O O!
A BROKEN DIAMOND
17. Can you fill in the vacancies in this diamond?
P
F O *
C * R * *
F * * C * * *
P O R C E L A I N
R * * L * * *
S * A * *
S I *
N
Its words must read alike from left to right and from top to bottom.
WHAT IS THIS?
18. Tan HE Edsa VEN in
It N Gja SmeTs AsgN
aD Az Rett De.
A PHONETIC JOURNEY
19. I can travel first-class on the Great Eastern Railway from 2 2 2 2 2
2 2 2 4 4 4 4 4 5 0 0. What is the cost of my journey, and its length in
time?
A CURIOUS OLD INSCRIPTION
20. Seogeh sreve ereh wcisume vahl
Lah sehs se otreh nos llebdnas
Regni freh nos gnires rohyer
Ganoed iryd ale nifae esots sorcy
Rub nabot es rohk co caed ir.
Can you decipher it?
IRISH STEW AT SIMPSON’S
21. I wrote the following note recently:--
Dear Jack,--Meet me at Simpson’s to-morrow at 1.30. We will sample
their excellent Irish stew. Here are some catchwords that will remind
you of the invitation:--
Join me at and
i
s
Why should they remind him of it?
ENGLISH AS SHE IS SPELT!
22. This was the exact text of a letter sent to the master of an English
village school by a labourer as an excuse for his boy’s absence:--
“Cepatomtogoatatrin”
Can you decipher it?
A DOUBLE ACROSTIC
23. This double Acrostic will afford an easy exercise in mental
gymnastics for those to whom such pastime appeals:--
Now we are fain
To rack your brain.
1. More fit for babes and sucklings than for you.
2. Robbed of externals this is very true.
3. Diminutive in measure and in weight.
4. Pen-name of one a true pen potentate.
5. A palindrome quite plain is here in sight.
6. Sans head and tail it also yields this light.
7. Here is in short what anyone may write.
FIND THE PROVERB
24. c e f h i m n o r s t v y
3 2 2 2 7 1 1 2 6 5 8 3 9
4 4 1 2 1 6 1
3 1 5 8 2 3
5 7 9 6
4
The letters with ones under them are the first letters of words, those
with twos under them are second letters of words, and so on.
A PUZZLE WILL
25. Having occasion to make a few slight additions to my will, I called
in my lawyer to arrange the matter. How far forward did the instructions
contained in the following lines carry him in his work?
Set down a hundred in my will,
Add nothing to the text;
Five hundred now a space may fill,
And one be added next.
Another hundred write as well,
And yet another one;
Then fifty more, and try to tell
The deed that now is done.
ANOTHER WORD SQUARE
26. Can you complete this word square?
* D * * O *
D * * I * E
* S * A * D
T * A * A *
* R * A * E
R * D * E *
MUSICAL EPITAPHS
27. Over the grave of a French musician, who was choked by a fish bone,
the following epitaph was inscribed in notes of music:--A. G. A. E. A.
Over the porch of the house of Gustave Doré these musical notes were
placed on a tablet:--C. E. B. A. C. D.
What do these inscriptions signify?
QUITE TOO TOO
28. “Where can we meet to-morrow?” said Jack Spooner to his best girl.
“We will go,” she replied, “at 222222222222 LEY STREET.”
When and where did they meet?
A BROKEN WORD
29. What does this spell?
C
-------------------
T T T T T T T T T T
CONTRADICTORY TERMS
30. What English word is it which may be so treated as to affirm or
disallow the use of its own initial or final letter?
PRINTERS’ PIE
31. Can you arrange these letters
E I O O O U
B C N N R R S S
so that they form the title of a book well-known to boys?
FILL IN THE GAPS
32. Keeping these letters in their present order make a sensible
sentence by inserting among them as often as is necessary another
letter, which must be in every case the same.
A DEN I I CAN DOCK.
DISTORTED SHAKESPEARE
33. Here is a well-known quotation from Shakespeare, which seems to need
some straightening out:--
OXXU8 MAAULGIHCTE
NOR
A PHONETIC NIGHTMARE
34. Here, as an awful warning to those who are ready to accept the
definition of English spelling given by a former headmaster of
Winchester--“Consonants are interchangeable, and vowels do not
count”--is a common English word of twelve letters, in “linked sweetness
long drawn out.”
Iewkngheaurrhphthewempeighghtips.
Can you decipher it?
ANOTHER WORD SQUARE
35. Can you, by filling in letters, complete this word square so that it
shall read alike across and from top to bottom?
* A * *
A * * A
* E * *
* A * E
A QUAINT INSCRIPTION
36. The following curious inscription may be seen on a card hanging up
in the bar of an old riverside inn in Norfolk:--
THEM * ILL * ERSLEA * VET * HEMI
LLT * HEW * HER * RYMEN * LOW
ERTH * EIRS * AILTH * EMA
LTS * TER * SLE * AVET * HE * KI
LN * FORAD * ROPO * FTH
EWHI * TESW * AN * SALE.
Can you decipher it?
A POET’S PI
37. TONDEBNIOTOCHUMFOARYHUR
OTDIRECTTHAWHOTERSOFKLSYA;
TIKATESTUBALIGHTSTILLETRUFLYR
OTBOWLALLNEFESLEAVARFWYAA.
In this printer’s pie the words are in their proper sequence, but the
letters are tangled.
BURIED PLACES
38. In the following short sentences five names of places are
buried--that is to say, the letters which spell them in proper order
form parts of more words than one. Thus, for example “Paris” might be
buried in the words “go u_p a ris_e:”
“The men could ride all on donkeys, the skipper, though, came to a bad
end.”
When you have discovered these places, try to find out what very
unexpected word of more than four letters is buried in the sentence, “On
Christmas Eve you rang out angel peals.”
TREASON CONDONED
39. According to an old poet, Sir John Harrington (1561-1612):--
“Treason doth never flourish; what’s the reason?
For if it prosper none dare call it treason!”
The classic lines may possibly have been the germ of the flippant modern
riddle, “Why is it no offence to conspire in the evening?”
A BIT OF BOTANY
40. Inscribe an _m_ above a line
And write an _e_ below,
This woodland flower is hung so fine
It bends when zephyrs flow.
A PIED PROVERB
41. The following letters, if they are properly rearranged, will fall
into the words which form a popular proverb:--
AAEEGGHILLMNNNOOOORRSSSSTT
Can you place them in position?
A DROP LETTER PUZZLE
42. Can you fill in the gaps of this proverb?
E**t* *e*s**s *a*e *h* *o** **i*e.
MULTUM IN PARVO
43. There is an English word of five syllables which has only eight
letters, five of them vowels--an a, an e, twice i, and y. What are its
consonants?
DOUBLETS
44. Can you turn TORMENT to RAPTURE, using four links, changing only one
letter each time, and varying the order of the letters?
A PIED PROVERB
45. Can you arrange these letters so that they form a sentence of five
words?
aaceeeffhhiiiiimnnoooprrssttttt.
The result is a well-known English proverb.
WHAT CAN IT BE?
46. Add one letter, and make this into a sensible English sentence:--
GDLDPRTFRRTHDXXFRDDNS
OUT OF PROPORTION
47. One vowel in an English word is found,
Which by eight consonants is hedged around.
48. Can you form an English word with these letters?
AAAAABBNNIIRSSTT.
49. What is this? It is found in Shakespeare:--
K I N I.
ALPHA BETA
50. There are two English words which contain each of them ten letters,
and six of these are a, b, c, d, e, f, the first six letters of the
alphabet. Can you build up either or both of them without looking at the
solution?
SHIFTING NUMBERS
51. Of a band of true kinsmen I stand at the head,
Who, to keep themselves warm, cluster three in a bed.
Put four into gaol and their number has risen,
So that six can be counted together in prison.
Take the six and recount them, they dwindle to three;
Count again, and a change into five you will see.
With no number from one to one hundred I mix,
Yet with five of my mates I am seen to make six.
AN IMPUDENT PRODIGAL
52. The prodigal son of a wealthy colonial farmer received a letter from
his father, to suggest that a considerable part of his inheritance
should be safeguarded before he squandered it. His reply ran
thus:--“Dear dad, keep 1000050.” As such a sum, even in dollars, was out
of the question, the father was completely puzzled.
What did the prodigal mean?
BURIED POETS
53. The names of eight famous British poets are buried in these lines,
that is to say, the letters that spell the names form in their proper
order parts of different words:--
The sun is darting rays of gold
Upon the moor, enchanting spot,
Whose purpled heights, by Ronald loved,
Up open to his Shepherd cot.
And sundry denizens of air
Are flying, aye, each to his nest;
And eager make at such an hour
All haste to reach the mansions-blest.
Can you dig them up?
A FATEFUL LETTER
54. When _A. B._ gave up the reins of government, and _C. B._ took
office in his place, it was found that their political positions could
be exactly described by two quite common English verbs, which differ
only in this, that the one is longer by one letter than the other, while
the rest of the letters are the same, and in the same order. What are
these two verbs?
A PRIZE REBUS
55. The following is a prize Rebus:--
done |
mutt | a glutt
and |
i | T. c. d.
you make me
A LETTER TANGLE
56. First a _c_ and _a_ _t_, last _a_ _c_ and a _t_,
With a couple of letters between,
Form a sight that our eyes are delighted to see,
Unless in their sight it is seen.
A TRANSPOSITION
57. Cut off my tail and set it at my head,
What was an island is a little bear instead.
A REBUS
T S.
58. What English word do these two letters indicate? There are two
possible solutions of equal merit.
A PHONETIC PHRASE
59. How can we read this?
I N X I N X I N.
A GOOD END
60.
[Illustration: I F S]
SOLUTIONS
CHESS CAMEOS
No. XXVI
Black has made the false move Kt from Q sq to Kt 3. When this is
replaced, and the king is moved as the proper penalty, White mates at
once with one or other of the Knights.
No. XXVII
Replace the White Kt at B 7, and a Black Pawn at K 4; then P takes P _en
pas_. Mate.
ANALYSIS AND PROOF
It can be proved that Black’s last move _must have been_ P from K 2 to K
4, so that White may take the P _en pas_.
The Black King cannot have moved from any _occupied_ square.
(The White Kt now occupies B 7.)
Nor from Kt 3 or 4, as both are now _doubly_ guarded, so that he cannot
have moved _out of a check_.
(The White Kt now helps to guard Kt 5.)
Nor can he have moved from K 2, as the White P on Q 6 cannot have moved
_to give check_.
No other P can have moved.
The K P cannot have moved from K 3, became of the position of the White
King.
Therefore Black’s last move _must have been_ P from K 2 to K 4, which
White can take _en pas_ giving Mate.
No. XXVIII
B--Q 2 B--R 5 P--Kt 4
-------- ---------------- ------- White has no move.
P--R 7 P--R 7 becomes Q any
The way in which the B runs to earth and is shut in is most ingenious.
Black with the new Q cannot anyhow give White a move.
No. XXIX
R--Kt 7, ch. R--Kt 5 R--B 5, ch.
------------ ----------- -----------------
K moves P becomes Q Q × R, stalemate.
No. XXX
B--Kt 8.
No. XXXI
B--R 4.
No. XXXII
B--R sq.
No. XXXIII
B--Q 4.
No. XXXIV
B--B sq.
No. XXXV
K--R 4.
No. XXXVI
Kt--Kt’s 6.
No. XXXVII
R--Kt 5 Kt--B 6 Kt × Kt mate.
------- ----------- -------------
Kt × R Kt--B 6 ch.
No. XXXVIII
Kt--R 7 Q--KB 8 Q--R 8 mate.
------- --------- ------------
B moves B returns
Any other move of the Kt would impede the movements of the Q.
No. XXXIX
R--R sq. Q--Kt sq. Q to Kt sq. mate.
-------- ---------- -----------------
B moves. B returns.
No. XL
This beautiful problem is solved by:--
Q--Kt 6 K--B 2 mates accordingly.
------- ------ ------------------
P × Q any
or
R--B 3 mates accordingly.
------- ------ ------------------
Kt--K 3 any
No. XLI
R--R 2. Q--R sq. Q mates.
------- -------- --------
B × Kt any
if
Kt--QB 8, Q or Kt mates.
-------- --------- --------------
B--Q sq. any
if
Kt--QB 6, Q or Kt mates.
----------- --------- --------------
B elsewhere any
No. XLII
Kt--Kt 4, dis. ch. Q--KR 2, ch. Kt--B 2, mate.
------------------ ------------ --------------
K--R 8. P × Q.
There are other variations.
No. XLIII
B--Kt sq. Q--QR 7, Q mates.
--------- -------- --------
P × Kt, K × Kt.
If K × Kt, Q × P, and mates next move.
No. XLIV
K--Q 7, R--Q 5, Q mates.
------- ------- --------
K moves K × R
No. XLV
R--Q 8 Q × P, ch. B mates.
------- ---------- --------
K moves K × Q
if
Q--K 7 Q mates.
------- ------ --------
B moves any
No. XLVI
B--B 6 Q--Q 7, ch. R mates.
------ ----------- --------
K × R K × Q
if
R--B 6, ch. Q mates.
----- ----------- --------
B × R K × P
There are other variations.
No. XLVII
Q--R 8 Kt--B 6 mates accordingly.
------ ------- ------------------
Kt × Q any
No. XLVIII
B--Kt 8 Q × B, ch. Q--QR 7, mate.
--------- ---------- --------------
B--K Kt 2 Kt--K 4
if
Q--Q 2, ch. P mates.
------ ----------- --------
B--B 3 K moves
No. XLIX
B-Kt 2 Q--K 3 ch. mates.
------ ---------- ------
K--K 4 any
There are other variations.
No. L
Q--KR 2 Q--Q 6, ch. Kt--K 5. double ch. mate.
------------- ----------- -------------------------
K--B 3 or B 4 Q × Q
There are other variations.
No. LI
R--QR sq. R--R 2 P mates.
--------- ------ --------
P moves P × R
No. LII
Q--B sq. Q × BP ch. Q mates.
-------- ---------- --------
P--K 7 K--Q 3
if
Q × BP ch. Q mates.
------ ---------- --------
K--Q 2 K--B 3
There are other variations.
No. LIII
B--R 8 Q--QR sq. Q--QKt. 7, mate.
------ --------- ----------------
K--R 2 K moves
No. LIV
Q--R 5 Kt--Kt 5 Kt mates.
--------------- -------- ---------
B × Q or B--B 2 any
No. LV
K--Kt 7 Q--Q 5, ch. Kt. mates.
------- ----------- ----------
Kt--B 3 Kt × Q
if
Q--B 8, ch. Q mates.
------- ------- --------
P--K 3 K moves
No. LVI
R--Kt 6 B--Kt 4 R × P mate.
------- ------- -----------
P moves P × B
No. LVII
Kt from R 3--Kt 5 B--B 4 P--Q 4 ch. R--B 5 mate.
----------------- ------ -------------- ------------
P × Kt P × B P × P _en pas_
if
R--Kt 5 ch. mates accordingly.
----- ----------- ------------------
R × B any
and if
Kt--Q 6 R--B 5 ch. Kt--B 7 mate.
------ ------- ---------- -------------
Q--K 6 Q--Kt 3 Q × R
SCIENCE AT PLAY
No. LVIII.--THE GEARED WHEELS
The arrow head at the top of a small wheel with ten teeth, which is
geared into and revolved round a large fixed wheel with forty teeth,
will point directly upwards five times in its course round the large
wheel. Four of these turnings are due to the rotation of the small wheel
on its own axis, and one of them results from its revolution round the
large wheel.
No. LX.--THE FIFTEEN BRIDGES
It is possible to pass over all the bridges which connect the islands
_A_ and _B_ and the banks of the surrounding river without going over
any of them twice.
The course can be shown thus, using capital letters for the different
regions of land, and italics for the bridges:--E_a_ F_b_ B_c_ F_d_ A_e_
F_f_ C_g_ A_h_ C_i_ D_k_ A_m_ E_n_ A_p_ B_q_ E_l_D.
This order of the bridges can, of course, be reversed.
No. LXVI.--A DUCK HUNT
In order that a spaniel starting from the middle of a circular pond, and
going at the same pace as a duck that is swimming round its edge, shall
be sure to catch it speedily, the dog must always keep in the straight
line between the duck and the centre of the pond.
The duck can never gain an advantage by turning back, and if it swims on
continuously in a circle it will be overtaken when it has passed through
a quarter of the circumference, for the dog will in the same time have
described a semi-circle whose diameter is the radius of the pond, ending
at the point where the duck is caught.
No. LXIX.--THE TETHERED BIRD
When a bird tethered by a cord 50 feet long to a post 6 inches in
diameter uncoils the full length of the cord, and recoils it in the
opposite direction, keeping it always taut, it flies 10,157 feet, or
very nearly 2 miles, in its double course.
To avoid possible misunderstanding, we point out that, in order to pass
from the uncoiling to the recoiling position, the bird must fly through
a semicircle at the end of the fully extended cord.
No. LXX.--THE MOVING DISC AND THE FLY
[Illustration]
When a fly, starting from the point _A_, just outside the revolving
disc, and always making straight for its mate at the point _B_, crosses
the disc in four minutes, during which time the disc is turning twice,
the revolution of the disc has a most curious and interesting effect on
the path of the fly.
The fly is a quarter of a minute in passing from the outside circle to
the next, during which the disc has made an eighth of a revolution, and
the fly has reached the point marked 1. The succeeding points up to 16
show the position of the fly at each quarter of a minute, until, by a
prettily repeated curve, _B_ is reached.
No. LXXI.--A SHUNTING PUZZLE
The following method enables the engine _R_ to interchange the positions
of the wagons, _P_ and _Q_, for either of which there is room on the
straight rails at _A_, while there is not room there for the engine,
which, if it runs up either siding, must return the same way:--
1. _R_ pushes _P_ into _A_. 2. _R_ returns, pushes _Q_ up to _P_ in _A_,
couples _Q_ to _P_, draws them both out to _F_, and then pushes them to
_E_. 3. _P_ is now uncoupled, _R_ takes _Q_ back to _A_, and leaves it
there. 4. _R_ returns to _P_, pulls _P_ back to _C_, and leaves it
there. 5. _R_, running successively through _F_, _D_, _B_, comes to _A_,
draws _Q_ out, and leaves it at _B._
No. LXXV.--PHARAOH’S SEAL
It is quite puzzling to decide how many similar triangles or pyramids
are expressed on the seal of Pharaoh. There are in fact 96.
No. LXXVI.--ROUND THE GARDEN
The four persons who started at noon from the central fountain, and
walked round the four paths at the rates of two, three, four, and five
miles an hour would meet for the third time at their starting point at
one o’clock, if the distance on each track was one-third of a mile.
No. LXXVII.--A JOINER’S PUZZLE
This diagram shows how to divide Fig. _A_ into two parts, and so
rearrange these that they form either Fig. _B_ or Fig. _C_, without
turning either of the pieces.
+--------------+
| |
+--------------+ | +--+
| | | |
| +--+ +--------------+--+ | +--+
| | | | | | | | |
| +--+ | | +--+ | | +--+ |
| | | | | | | | |
| +--+ | | +--+ | | +--+ |
| | | | | | | | |
| +--+ | | +--+ | +--+ |
| | | | | | | |
+--+ | | +--+ | +--+ |
| | | | | | |
+--------------+ +--+--------------+ +--------------+
A B C
Cut the five steps, and shift the two pieces as is shown.
No. LXXVIII.--THE BROKEN OCTAGON
The Broken Octagon is repaired and made perfect if its pieces are put
together thus:--
[Illustration]
No. LXXIX.--AT A DUCK POND
The pond was doubled in size without disturbing the duck-houses, thus:--
+-----------○-----------+
| / \ |
| / \ |
| / \ |
| / \ |
| / \ |
○ ○
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
+-----------○-----------+
No. LXXX.--ALL ON THE SQUARE
This is a perfect arrangement:--
[Illustration]
No. LXXXI.--PINS AND DOTS
The pins may be placed thus:--
On the third dot in the top line; on the sixth dot in the second line;
on the second dot in the third line; on the fifth dot in the fourth
line; on the first dot in the fifth line; on the fourth dot in the sixth
line.
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
No. LXXXII.--A TRICKY COURSE
To trace this course draw lines upon the diagram from square 46 to
squares 38, 52, 55, 23, 58, 64, 8, 57, 1, 7, 42, 10, 13, 27, and 19.
This gives fifteen lines which pass through every square only once.
No. LXXXIII.--FOR THE CHILDREN
Make a square with three on every side, and place the remaining four one
on each of the corner men or buttons.
No. LXXXVII.--LOYD’S MITRE PROBLEM
The figure given is thus divided into four equal and similar parts:--
[Illustration]
No. LXXXIX.--CUT OFF THE CORNERS
A E F B
+------+--------+------+
| / \ |
| / \ |
|/ \|
M+ +G
| |
| |
| |
L+ +H
|\ /|
| \ / |
| \ / |
+------+--------+------+
C K I D
A very simple rule of thumb method for striking the points in the sides
of a square, which will be at the angles of an octagon formed by
cutting off equal corners of the square, is to place another square of
equal size upon the original one, so that the centre is common to both,
and the diagonal of the new square lies upon a diameter of the other
parallel to its side.
No. XCIII.--MAKING MANY SQUARES
The subjoined diagram shows how the two oblongs, applied to the two
concentric squares, produce 31 perfect squares, namely, 17 small ones,
one equal to 25 of these, 5 equal to 9, and 8 equal to 4.
+------+
| |
| |
+-------------+------+-------------+
| | | |
| | | |
| +------+------+------+ |
| | | | | |
| | | | | |
+-----+------+------+------+------+------+------+
| | | | | | | |
| | | | | | | |
+-----+------+------+------+------+------+------+
| | | | | |
| | | | | |
| +------+------+------+ |
| | | |
| | | |
+-------------+------+-------------+
| |
| |
+------+
No. XCIV.--CUT ACROSS
The Greek Cross can be divided by two straight cuts, so that the
resulting pieces will form a perfect square when re-set, as is shown in
these figures:--
[Illustration]
No. CV.--A TRANSFORMATION
The diagram which is given below shows how the irregular Maltese Cross
can be divided by two straight cuts into four pieces, which form when
properly rearranged, a perfect square.
[Illustration]
No. CVI.--SHIFTING THE CELLS
The following diagram shows by its dark lines how the whole square can
be cut into four pieces, and these arranged as two perfect squares in
which every semicircle still occupies the upper half of its cell.
One piece forms a square of nine cells, and it is easy to arrange the
other three pieces in a square of sixteen cells by lifting the three
cells and dropping the two.
+-----------+-----------+-----------+-----------+-----------+
| / \ | / \ | / \ | / \ ∥ / \ |
| / \ | / \ | / \ | / \ ∥ / \ |
|/ \|/ \|/ \|/ \∥/ \|
| | | | ∥ |
| | | | ∥ |
+-----------+-----------+-----------+-----------+-----------+
| / \ | / \ | / \ | / \ ∥ / \ |
| / \ | / \ | / \ | / \ ∥ / \ |
|/ \|/ \|/ \|/ \∥/ \|
| | | | ∥ |
| | | | ∥ |
+-----------+-----------+===========+===========+===========+
| / \ | / \ ∥ / \ | / \ | / \ |
| / \ | / \ ∥ / \ | / \ | / \ |
|/ \|/ \∥/ \|/ \|/ \|
| | ∥ | | |
| | ∥ | | |
+-----------+===========+-----------+-----------+-----------+
| / \ ∥ / \ ∥ / \ | / \ | / \ |
| / \ ∥ / \ ∥ / \ | / \ | / \ |
|/ \∥/ \∥/ \|/ \|/ \|
| ∥ ∥ | | |
| ∥ ∥ | | |
+===========+-----------+-----------+-----------+-----------+
| / \ | / \ ∥ / \ | / \ | / \ |
| / \ | / \ ∥ / \ | / \ | / \ |
|/ \|/ \∥/ \|/ \|/ \|
| | ∥ | | |
| | ∥ | | |
+-----------+-----------+-----------+-----------+-----------+
No. CVII.--IN A TANGLE
[Illustration]
It will be seen, on the subjoined diagram, how twenty-one counters or
coins can be placed on the figure so that they fall into symmetrical
design, and form thirty rows, with three in each row.
No. CVIII.--STILL A SQUARE
A
+------+------+------+
| | | |
| | | |
+------+------+------+ C
| | |
| | |
+------+------+
B
In order that a square and an additional quarter may be divided by two
straight lines so that their parts, separated and then reunited, form a
perfect square, lines must be drawn from the point _A_ to the corners
_B_ and _C_. Draw the figure on paper, cut through these lines, and you
will find that the pieces can be so reunited that they form a perfect
square.
No. CIX.--A TRANSFORMATION
The diagram below shows how the seven parts of the square can be
rearranged so that they form the figure 8.
[Illustration]
No. CX.--TO MAKE AN OBLONG
Here is an oblong formed by piecing together two of the smaller
triangles, and four of each of the other patterns--
[Illustration]
Here is another:--
[Illustration]
No. CXI.--SQUARES ON THE CROSS
This diagram shows how every indication of the seventeen squares is
broken up by the removal of seven of the asterisks which mark their
corners.
[Illustration]
Those surrounded by circles are to be removed.
No. CXII.--A CHINESE PUZZLE
|\
| \
| \
| \
| \
| \
| +--\
| | \
| +--+--+ \
| | | \
| +--+ +--+\
| | | \
+--+ +--+\
| | \
+-----------------+--+
The dotted lines on the triangular figure show how a piece of cardboard
cut to the shape of Fig. 1 can be divided into three pieces, and
rearranged so that these form a star shaped as in Fig. 2.
No. CXIII.--FIRESIDE FUN
To solve this puzzle slip the first coin or counter from _A_ to _D_,
then the others in turn from _F_ to _A_, from _C_ to _F_, from _H_ to
_C_, from _E_ to _H_, from _B_ to _E_, from _G_ to _B_, and place the
last on _G_. It can only be done by a sequence of this sort, in which
each starting point is the finish of the next move.
[Illustration]
AMUSING PROBLEMS
1. THE CARPENTER’S PUZZLE
The carpenter cleverly contrived to mend a hole 2 feet wide and 12 feet
long, by cutting the board which was 3 feet wide and 8 feet long, as is
shown in Fig. 1, and putting the two pieces together as is shown in Fig.
2.
Fig. 1.
+----------------+
| ________|
|________| |
| |
+----------------+
Fig. 2.
+------------------------+
| ________¦ |
| ¦ |
+------------------------+
2. GOLDEN PIPPINS
Here is another solution:--
1| 3| 5| 7| 9|11|13|15|17|19
39|37|35|33|31|29|27|25|23|21
2| 4| 6| 8|10|12|14|16|18|20
40|38|36|34|32|30|28|26|24|22
--+--+--+--+--+--+--+--+--+--
82|82|82|82|82|82|82|82|82|82
3. AN AWKWARD FIX
I was able to find my way in a strange district, when the sign-post lay
uprooted in the ditch, without any difficulty. I simply replaced the
post in its hole, so that the proper arm, with its lettering, _pointed
the way that I had come_, and then, of necessity, the directions of the
other arms were correct.
4. LINKED SWEETNESS LONG DRAWN OUT
The train was whistling for 5 minutes. Sound travels about a mile in 5
seconds, so the first I heard of it was 5 seconds after it began. Its
last sound reached me 7¹⁄₂ seconds after it ceased, so I heard the
whistle for 5 minutes, 2¹⁄₂ seconds.
5. These quarters were not so elastic as they are made to appear. In
good truth, considering that the second man who was placed in _A_ was
afterwards removed to _I_, no real _second_ man was provided for at
all.
6. The first day of a new century can never be Sunday, Wednesday, or
Friday. The cycle of the Gregorian calendar is completed in 400 years,
after which all dates repeat themselves.
As in this cycle there are only four first days of a century, it is
clear that three of the seven days of the week must be excluded. Any
perpetual calendar shows that the four which do occur are Monday,
Tuesday, Thursday, and Saturday, so that Sunday, Wednesday, and Friday
are shut out.
A neat corollary to this proof is that Monday is the only day which may
be the first, or which may be the last, day of a century.
7. A cricket bat with spliced handle has such good driving power,
because the elasticity of the handle allows the ball to be in contact
with the blade of the bat for a longer time than would otherwise be
possible.
With similar effect the “follow through” of the club head at golf
maintains contact with the ball, when it is already travelling fast.
8. When two volumes stand in proper order on my bookshelf, each 2 inches
thick over all, with covers ¹⁄₈ of an inch in thickness, a bookworm
would only have to bore ¹⁄₄ of an inch, to penetrate from the first page
of Vol. I, to the last page of Vol. II, for these pages would be in
actual contact if there was no binding. This very pretty and puzzling
question combines in its solution all the best qualities of a clever
catch with solid and simple facts.
9. A man would have to fall from a height of nearly 15 miles to reach
earth before the sound of his cry as he started. The velocity of sound
is constant, while that of a falling body is continually accelerated. At
first the cry far outstrips the falling man, but he _overtakes and
passes through his own scream_ in about 14¹⁄₂ miles, for his body falls
through the 15 miles in 70 seconds, and sound travels as far in 72
seconds. Air resistance, and the fact that sound cannot pass from a rare
to a dense atmosphere, are disregarded in this curious calculation.
10. A man on a perfectly smooth table in a vacuum, and where there was
no friction, though no contortions of his body would avail to get away
from this position, could escape from the predicament by throwing from
him something which he could detach from his person, such as his watch
or coat. He would himself instantly slide off in the opposite direction!
11. The monkey clinging to one end of a rope that passes over a single
fixed pulley, while an equal weight hangs on the other end, cannot climb
up the rope, or rise any higher from the ground.
If he continues to try to climb up, he will gradually pull the balancing
weight on the other end of the rope upwards, and the slack of the rope
will drop below him, while he remains in the same place.
If, after some efforts, he rests, he will sink lower and lower, until
the weight reaches the pulley, because of the extra weight of rope on
his side, if friction is disregarded.
12. Though the tension on a pair of traces tends as much to pull the
horse backward as it does to pull the carriage forward, it is the
initial pull from slack to taut which sets the traces in motion; and
this, once started, must continue indefinitely until checked by a
counter pull.
13. Some say that a rubber tyre leaves a double rut in dust and a
single one in mud, because the air, rushing from each side into the wake
of the wheel, piles up the loose dust. Others hold that the central
ridge is caused by the continuous contraction of the tyre as it passes
its point of contact with the road.
A correspondent, writing some years ago to “Knowledge,” said:--“It is
our old friend the sucker. The tyre being round, the weight on centre of
track only is great enough to enable the tyre to draw up a ridge of dust
after it.”
14. If two cats on a sloping roof are on the point of slipping off, one
might think that whichever had the longest paws (pause) would hold on
best. Todhunter, in playful mood, saw deeper into it than that, and
pronounced for the cat that had the _highest mew_, for to his
mathematical mind the Greek letter _mu_ was the coefficient of friction!
15. If a penny held between finger and thumb, and released by
withdrawing the finger, starts “heads” and makes half a turn in falling
through the first foot, it will be “heads” again on reaching the floor,
if it is held four feet above it at first.
16. HE DID IT!
Funnyboy had secretly prepared himself for the occasion by rubbing the
chemical coating from the side of the box on to his boot.
17. THE CYCLE SURPRISE
If a bicycle is stationary, with one pedal at its lowest point, and that
pedal is pulled backwards, while the bicycle is lightly supported, the
bicycle will move backwards, and the pedal relatively to the bicycle,
will move forwards. This would be quite unexpected by most people, and
it is well worth trying.
18. The rough stones, by which any number of pounds, from 1 to 364, can
be weighed, are respectively 1 ℔., 3 ℔s., 9 ℔s., 27 ℔s., 81 ℔s., and 243
℔s. in weight.
19. If we disregard the resistance of the air, a small clot of mud
thrown from the hindermost part of a wheel would describe a parabola,
which would, in its descending limb, bring it back into kissing contact
with the wheel which had rejected it.
20. THE CARELESS CARPENTER
When the carpenter cut the door _too little_, he did not in fact _cut it
enough_, and he had to cut it again, so that it might fit.
21. If from the North Pole you start sailing in a south-westerly
direction, and keep a straight course for twenty miles, you must steer
due north to get back as quickly as possible to the Pole, if, indeed, it
has been possible to start from it in any direction other than due
south.
22. DICK IN A SWING
Dick’s feet will travel in round numbers nearly 16 feet further than his
head, or to be exact, 15·707,960 feet.
23. A POSER
The initial letters of Turkey, Holland, England, France, Italy, Norway,
Austria, Lapland, and Spain spell, and in this sense are the same as,
“the finals.”
CURIOUS CALCULATIONS
1. The only sum of money which satisfies the condition that its pounds,
shillings, and pence written down as a continuous number, exactly give
the number of farthings which it represents, is £12, 12s., 8d., for this
sum contains 12,128 farthings.
2. If, when a train, on a level track, and running all the time at 30
miles an hour, slips a carriage which is uniformly retarded by brakes,
and this comes to rest in 200 yards, the train itself will then have
travelled 400 yards.
The slip carriage, uniformly retarded from 30 miles an hour to no miles
an hour, has an average speed of 15 miles an hour, while the train
itself, running on at 30 miles an hour all the time, has just double
that speed, and so covers just twice the distance.
3. The traveller had fivepence farthing when he said to the landlord,
“Give me as much as I have in my hand, and I will spend sixpence with
you.” After repeating this process twice he had no money left.
4. This is the way to obtain eleven by adding one-third of twelve to
four-fifths of seven--
TW(EL)VE + S(EVEN) = ELEVEN
5. Here is the completed sum:--
215)*7*9*(1** 215)37195(173
*** 215
---- ----
*5*9 1569
*5*5 1505
---- ----
*4* 645
*** 645
=== ===
The clue is that no figure but 3, when multiplied into 215, produces 4
in the tens place.
6. If I attempt to buy as many heads of asparagus as can be encircled by
a string 2 feet long for double the price paid for as many as half that
length will encompass, I shall not succeed. A circle double of another
in circumference is also double in diameter, and its area is four times
that of the other.
7. If, when you reverse me, and my square, and my cube, and my fourth
power, you find that no changes have been made, I am 11, my square is
121, my cube 1331, and my fourth power 14641.
8. A thousand pounds can be stored in ten sealed bags, so that any sum
in pounds up to £1,000 can be paid without breaking any of the seals, by
placing in the bags 1, 2, 4, 8, 16, 32, 64, 128, 256, and 489
sovereigns.
9. It is the fraction ⁶⁄₉ which is unchanged when turned over, and
which, when taken thrice, and then divided by two becomes 1.
10. When the three gamblers agreed that the loser should always double
the sum of money that the other two had before them, and they each lost
once, and fulfilled the conditions, remaining each with eight sovereigns
in hand, they had started with £13, £7, and £4 as the following table
shows:--
A B C
£ £ £
At starts 13 7 4
When A loses 2 14 8
When B loses 4 4 16
When C loses 8 8 8
11. Tom’s sum, which his mischievous neighbour rubbed almost out, is
reconstructed thus:--
345 345
** 37
----- -----
**** 2415
**** 1035
----- -----
**76* 12765
12. Here are two other arrangements of the nine digits which produce 45,
their sum; each is used once only:--
5 × 8 × 9 × (7 + 2)
------------------- = 45
1 × 3 × 4 × 6
7² - 5 × 8 × 9
-------------- + 1 = 45
3 × 4 × 6
13. If, when the combined ages of Mary and Ann are 44, Mary is twice as
old as Ann was when Mary was half as old as Ann will be when Ann is
three times as old as Mary was when Mary was three times as old as Ann,
Mary is 27¹⁄₂ years old, and Ann is 16¹⁄₂.
For, tracing the question backwards, when Ann was 5¹⁄₂ Mary was 16¹⁄₂.
When Ann is three times that age she will be 49¹⁄₂. The half of this is
24³⁄₄, and when Mary was at that age Ann was 13³⁄₄. Mary’s age, by the
question, was twice this, or 27¹⁄₂.
14. It is safer at backgammon to leave a blot in the tables which can be
taken by an ace than one which a three would hit. In either the case of
an actual ace or a three the chance is one in eleven; but there are two
chances of throwing deuce-ace, the equivalent of three.
15. If I start from a bay, where the needle points due north, 1200 miles
from the North Pole, and the course is perfectly clear, I can never
reach it if I steam continuously 20 miles an hour, steering always north
by the compass needle. After about 200 miles I come upon the Magnetic
Pole, which so affects the needle that it no longer leads me northward,
and I may have to steer south by it to reach the geographical Pole.
16. The 21 casks, 7 full, 7 half full, and 7 empty, were shared equally
by A, B, and C, as follows:--
Full cask. Half full. Empty.
A 2 3 2
B 2 3 2
C 3 1 3
or--
A 3 1 3
B 3 1 3
C 1 5 1
Thus each had 7 casks, and the equivalent of 3¹⁄₂ caskfuls of wine.
17. The foraging mouse, able to carry home three ears at a time from a
box full of ears of corn, could not add more than fourteen ears of corn
to its store in fourteen journeys, for it had each time to carry along
two ears of its own.
18. If, with equal quantities of butter and lard, a small piece of
butter is taken and mixed into all the lard, and if then a piece of this
blend of similar size is put back into the butter, there will be in the
end exactly as much lard in the butter as there is butter in the lard.
19. The fallacy of the equation--
4 - 10 = 9 - 15
4 - 10 + ²⁵⁄₄ = 9 - 15 + ²⁵⁄₄
and the square roots of these--
2 - ⁵⁄₂ = 3 - ⁵⁄₂
therefore 2 = 3
is explained thus:--The fallacy lies in ignoring the fact that the
square roots are _plus or minus_. In the working we have taken both
roots as _plus_. If we take one root plus, and the other minus, and add
⁵⁄₂, we have either 2 = 2, or 3 = 3.
20. The largest possible parcel which can be sent through the post under
the official limits of 3 feet 6 inches in length, and 6 feet in length
and girth combined, is a cylinder 2 feet long and 4 feet in
circumference, the cubic contents of which are 2⁶⁄₁₁ cubic feet.
21. We can show, or seem to show, that either four, five, or six nines
amount to 100, thus:--
IX
IX
99⁹⁄₉ = 100 IX 9 × 9 + 9 + 9⁹⁄₉ = 100
IX
IX
---
100
22. This is the magic square arrangement, so contrived that the
products of the rows, columns, and diagonals are all 1,000.
+---+---+---+
| 50| 1| 20|
+---+---+---+
| 4| 10| 25|
+---+---+---+
| 5|100| 2|
+---+---+---+
23. If seven boys caught four crabs in the rock-pools at Beachy Head in
six days, the twenty-one boys who searched under the seaweed and only
caught one crab with the same rate of success were only at work for
_half a day_.
24. A watch could be set of a different trio from a company of fifteen
soldiers for 455 nights, and one of them, John Pipeclay, could be
included ninety-one times.
25. If Augustus Cæsar was born September 23, B.C. 63, he celebrated his
sixty-third birthday on September 23, B.C. 0; or, writing it otherwise,
September 23, A.D. 0; or again, if we wish to include both symbols, B.C.
0 A.D. It is clear that his sixty-second birthday fell on September 23,
B.C. 1, and his sixty-fourth on September 23, A.D. 1, so that the
intervening year may be written as above.
26. The difference of the ages of _A_ and _B_ who were born in 1847 and
1874, is 27, or 30 - 03. Hence, when _A_ was 30 _B_ was 03. And _A_ was
30 in 1877. Eleven years later _A_ was 41 and _B_ 14, and eleven years
after that _A_ was 52 and _B_ 25. Thus the same two digits served to
express the ages of both in 1877, 1888, and 1899. This can only happen
in the cases of those whose ages differ by some multiple of nine.
27 A hundred and one by fifty divide,
To this let a cypher be duly applied;
And when the result you can rightly divine,
You find that its value is just one in nine--
is solved by CLIO, one of the nine Muses.
28. The man who paid a penny on Monday morning to cross the ferry, spent
half of what money he then had left in the town, and paid another penny
to recross the ferry, and who repeated this course on each succeeding
day, reaching home on Saturday evening with one penny in his pocket,
started on Monday with £1 1s. 1d. in hand.
29. When the three men agreed to share their mangoes equally after
giving one to the monkey, and when each helped himself to a third after
giving one to the monkey, without knowing that anyone had been before
him, and they finally met together, gave one to the monkey, and divided
what still remained, there must have been at least seventy-nine mangoes
for division at the first.
30. If, after having looked at my watch between 4 and 5, I look again
between 7 and 8, and find that the hour and minute-hands have then
exactly changed places, it was 36 12-13 minutes past 4 when I first
looked. At that time the hour-hand would be pointing to 23 1-13 minutes
on the dial, and at 23 1-13 minutes past 7 the hour hand would be
pointing to 36 12-13 minutes.
31. The number consisting of 22 figures, of which the last is 7, which
is increased exactly sevenfold if this 7 is moved to the first place, is
1,014,492,753,623,188,405,797.
32. The two sacks of wheat, each 4 feet long and 3 feet in
circumference, which the farmer sent to the miller in repayment for one
sack 4 feet long and 6 feet in circumference, far from being a
satisfactory equivalent, contained but half the quantity of the larger
sack, for the area of a circle the diameter of which is double that of
another is equal to four times the area of that other.
33. The five gamblers, who made the condition that each on losing should
pay to the others as much as they then had in hand, and who each lost in
turn, and had each £32 in hand at the finish, started with £81, £41,
£21, £11, and £6 respectively.
34. If we know the square of any number, we can rapidly determine the
square of the next number, without multiplication, by adding the two
numbers to the known square. Thus if we know that the square of 87 is
7569,
then the square of 88 = 7569 + 87 + 88 = 7744;
so too the square of 89 = 7744 + 88 + 89 = 7921;
and the square of 90 = 7921 + 89 + 90 = 8100.
35. The two numbers which solve the problem--
Two numbers seek which make eleven,
Divide the larger by the less,
The quotient is exactly seven,
As all who find them will confess--
are 1³⁄₈ and 9⁵⁄₈, for 1³⁄₈ + 9⁵⁄₈ = 11, and ⁷⁷⁄₈ ÷ ¹¹⁄₈ = 7.
36. There must be nine things of each sort, in order that
^99999999999999999999^ different selections may be made from twenty
sorts of things.
37. The women who had respectively 33, 29, and 27 apples, and sold the
same number for a penny, receiving an equal amount of money, began by
selling at the rate of three a penny. The first sold ten pennyworth, the
second eight pennyworth, and the third seven pennyworth.
The first had then left three apples, the second five, and the third
six. These they sold at one penny each, so that they received on the
whole--
The first 10d. + 3d. = 13d.
The second 8d. + 5d. = 13d.
The third 7d. + 6d. = 13d.
38. The puzzle--
Take five from five, oh, that is mean!
Take five from seven, and this is seen--
is solved by _fie_, _seen_.
39. If a bun and a half cost three halfpence, it is plain that each bun
costs a penny, but, by general custom, you buy seven for sixpence.
40. The hands of a watch would meet each other twenty-five times in a
day, if the minute-hand moved backwards and the hour-hand forwards. They
are, of course, together at starting.
41. The only way in which half-a-crown can be equally divided between
two fathers and two sons, so that a penny is the smallest coin made use
of, is to give tenpence each to a grandfather, his son, and his
grandson.
42. If the number of the revolutions of a bicycle wheel in six seconds
is equal to the number of miles an hour at which it is running, the
circumference of the wheel is 8⁴⁄₅ feet.
43. The hour that struck was twelve o’clock.
44. Sixty years.
45. If I jump off a table with a 20lb dumb-bell in my hand there is no
pressure upon me from its weight while I am in the air.
46. If at a bazaar I paid a shilling on entering each of four tents, and
another shilling on leaving it, and spent in each tent half of what was
in my pocket, and if my fourth payment on leaving took my last shilling,
I started with 45s., spending 22s. in tent 1, 10s. in tent 2, 4s. in
tent 3, and 1s. in tent 4, having also paid to the doorkeepers 8s.
47. When rain is falling vertically at 5 miles an hour, and I am walking
through it at 4 miles an hour, the rain drops will strike the top of my
umbrella at right angles if I hold it at an angle of nearly 39 degrees.
As I walk along, meeting the rain, the effect is the same as it would be
if I was standing still, and the wind was blowing the rain towards me at
the rate of 4 miles an hour.
48. When one monkey descends from the top of a tree 100 cubits high, and
makes its way to a well 200 yards distant, while another monkey, leaping
upwards from the top, descends by the hypotenuse to the well, both
passing over an equal space, the second monkey springs 50 cubits into
the air.
49. The steamboat which springs a leak 105 miles east of Tynemouth
Lighthouse, and, putting back, goes at the rate of 10 miles an hour the
first hour, but loses ground to the extent in each succeeding hour of
one-tenth of her speed in the previous hour, never reaches the
lighthouse, but goes down 5 miles short of it.
50. Twenty-one hens will lay ninety-eight eggs in a week, if a hen and
a-half lays an egg and a-half in a day and a-half. Evidently one egg is
laid in a day by a hen and a-half, that is to say three hens lay two
eggs in a day. Therefore, twenty-one hens lay fourteen eggs, in a day,
or ninety-eight in a week.
Q. E. D. (Quite easily done!)
51. If the population of Bristol exceeds by 237 the number of hairs on
the head of anyone of its inhabitants that are not bald, at least 474 of
them must have the same number of hairs on their heads.
52. In tipping his nephew from seven different coins, the uncle may give
or retain each, thus disposing of it in two ways, or of all in 2 × 2 × 2
× 2 × 2 × 2 × 2 ways. But as one of these ways would be to retain them
all, there are not 128, but only 127 possible variations of the tip.
53. The prime number which fulfils the various conditions of the
question is 127. Increased by one-third, excluding fractions, it becomes
169, the square of 13. If its first two figures are transposed, and it
is increased by one-third, it becomes 289, the square of 17. If its
first figure is put last, and it is increased by one-third, it becomes
361, the square of 19. If, finally, its three figures are transposed,
and then increased by one-third, it becomes 961, the square of 31.
54. Six things can be divided between two boys in 62 ways. They could be
_carried_ by two boys in 64 ways (2 × 2 × 2 × 2 × 2 × 2), but they are
not _divided_ between two boys if all are given to one, so that two of
the 64 ways must be rejected.
55. The highest possible score that the dealer can make at six cribbage,
if he is allowed to select the cards, and to determine the order of
play, is 78. The dealer and his opponent must each hold 3, 3, 4, 4, the
turn-up must be a 5, and crib must have the knave of the suit turned up,
and 5, 5, 5. It will amuse many of our readers to test this with the
cards.
56. The picture frame must be 3 inches in width all round, if it is
exactly to equal in area the picture it contains, which measures 18
inches by 12 inches.
57. If my mother was 20 when I was born, my sister is two years my
junior, and my brother is four years younger still, our ages are 56, 36,
34, and 30.
58. The spider in the dockyard, whose thread was drawn from her by a
revolving capstan 1 foot in diameter, until 73 feet of it were paid out,
after walking for a mile round and round the capstan at the end of the
stretched thread in an effort to unwind it all, had, when she stopped in
her spiral course, 49 more feet to walk to complete her task.
59. The mountebank at a fair, who offered to return any stake a
hundredfold to anyone who could turn up all the sequence in twenty
throws of dice marked each on one face only with 1, 2, 3, 4, 5, or 6,
should in fairness have engaged to return 2332 times the money; for of
the 46,656 possible combinations of the faces of the dice, only one can
give the six marked faces uppermost. Thus the chance of throwing them
all at one throw is expressed by ¹⁄₄₆₆₅₆, and in twenty throws by about
¹⁄₂₃₃₂.
60. If 90 groats (each = 4d.) feed twenty cats for three weeks, and five
cats consume as much as three dogs, seventy-two hounds can be fed for
£39 in a period of ninety-one days.
61. When equal wine-glasses, a half and a third full of wine, are filled
up with water, and their contents are mixed, and one wine-glass is
filled with the mixture, it contains ⁵⁄₁₂ wine and ⁷⁄₁₂ water.
62. The arrangement by which St Peter is said to have secured safety for
the fifteen Christians, when half of the vessel’s passengers were thrown
overboard in a storm, is as follows:--
XXXXIIIIIXXIXXXIXIIXXIIIXIIXXI
Each Christian is represented by an X, and if every ninth man is taken
until fifteen have been selected, no X becomes a victim.
63. If Farmer Southdown’s cow had a fine calf every year, and each of
these, and their calves in their turn, at two years old followed this
example, the result would be no less than 2584 head in sixteen years.
64. The number of the flock was 301. This is found by first taking the
least common multiple of 2, 3, 4, 5, 6, which is 60, and then finding
the lowest multiple of this, which with 1 added is divisible by 7. This
301 is exactly divisible by 7, but by the smaller numbers there is 1 as
remainder.
65. The rule for determining easily the number of round bullets in a
flat pyramid, with a base line of any length, is this:--
Add a half to half the number on the base line, and multiply the result
by the number on that line. Thus, if there are twelve bullets as a
foundation--
12 + ¹⁄₂ = ¹³⁄₂; and ¹³⁄₂ × ¹²⁄₁ = 78.
The same result is reached by multiplying the number on the base line by
a number larger by one, and then halving the result. Thus--
12 × 13 = 156, 156 ÷ 2 = 78.
66. We can gather from the lines--
Old General Host
A battle lost,
And reckoned on a hissing,
When he saw plain
What men were slain,
And prisoners, and missing.
To his dismay
He learned next day
What havoc war had wrought;
He had, at most,
But half his host
Plus ten times three, six, ought.
One-eighth were lain
On beds of pain,
With hundreds six beside;
One-fifth were dead,
Captives, or fled,
Lost in grim warfare’s tide.
Now, if you can,
Tell me, my man,
What troops the general numbered,
When on that night
Before the fight
The deadly cannon slumbered?
that old General Host had an army 24,000 strong.
67. When the farmer sent five pieces of chain of 3 links each, to be
made into one continuous length, agreeing to pay a penny for each link
cut, and a penny for each link joined, the blacksmith, if he worked in
the best interest of the farmer, could only charge sixpence: for he
could cut asunder one set of 3 links, and use these three single links
between the other four sets.
68. If, in a parcel of old silver and copper coins, each silver piece is
worth as many pence as there are copper coins, and each copper coin is
worth as many pence as there are silver coins, there are eighteen silver
and six copper coins, when the whole parcel is worth eighteen shillings.
69. These are five groups that can be arranged with the numbers 1 to 11
inclusive, so that they are all equal:--
(8² - 5² + 1) = (11² - 9²) = (7² - 3²) = (6² + 2²) = 4(10).
70. John Bull, under the conditions given, lived to the age of
eighty-four years.
71. The two numbers to each of which, or to the halves of which, unity
is added, forming in every case a square number, are 48 and 1680.
72. The true weight of a cheese that seemed to weigh 16 ℔s. in one scale
of a balance with arms of unequal length, and only 9℔s. in the other, is
12℔. This is found by multiplying the 16 by the 9, and finding the
square root of the result.
73. The two parts into which 100 can be divided, so that if one of them
is divided by the other the quotient is again exactly 100 are 99¹⁄₁₀₁
and ¹⁰⁰⁄₁₀₁.
74. If, with marbles in two pockets, I add one to those in that on the
right, and then multiply its contents by the number it held at first,
and after dealing in a similar way with those on the left, find the
difference between the two results to be 90; while if I multiply the sum
of the two original quantities by the square of their difference the
result is 176, I started with twenty-three in the right-hand pocket and
twenty-one in the other.
75. The circle of twenty-one friends who arranged to meet each week five
at a time for Bridge so long as exactly the same party did not meet more
than once, and who wished to hire a central room for this purpose, would
need it for no less than 20,349 weeks, or more than 390 years, to carry
out their plan.
76. If a herring and a half costs (not cost) a penny and a half, the
price of a dozen such quantities is eighteenpence.
77. The sum of money which in a sense appears to be the double of itself
is 1s. 10d., for we may write it _one_ and _ten_ pence or _two_ and
_twenty_ pence.
78. The “comic arithmetic” question set by Dr Bulbous Roots--
Divide my fifth by my first, and you have my fourth; subtract my first
from my fifth, and you have my second; multiply my first by my fourth
followed by my second, and you have my third; place my second after my
first, and you have my third multiplied by my fourth--is solved by
COMIC.
79. If the earth could stand still, and a straight tunnel could be bored
through it, a cannon ball dropped into it, if there is no air or other
source of friction, would oscillate continually from end to end.
Taking air into account, the ball would fall short of the opposite end
at its first lap, and in succeeding laps its path would become shorter
and shorter, until its initial energy was exhausted, when it would come
to rest at the centre.
80. He sent 163. She sent 157.
81. When twins were born the estate was properly divided thus:--
Taking the daughter’s share as 1
The widow’s share would be 2
And the son’s share 4
-
Total 7 shares.
So the son takes four-sevenths, the widow two-sevenths, and the daughter
one-seventh of the estate.
82. If each of my strides forwards or backwards across a 22 feet carpet
is 2 feet, and I make a stride every second; and if I take three strides
forwards and two backwards until I cross the carpet, I reach the end of
it in forty-three seconds. In three steps I advance 6 feet. Then in two
steps I retrace 4 feet, thus gaining only 2 feet in five steps, _i.e._,
in five seconds. I therefore advance 16 feet in forty seconds, and three
more strides cover the remaining 6 feet.
83. If the captain of a vessel chartered to sail from Lisbon to New
York, which appear on a map of the world to be on the same parallel of
latitude, and which are, along the parallel, about 3600 miles apart,
takes his ship along this parallel, he will not be doing his best for
the impatient merchant who has had an urgent business call to New York.
The shortest course between the two points is traced by a segment of a
“great circle,” having its centre at the centre of the earth, and
touching the two points. This segment lies wholly north of the parallel,
and is the shortest possible course.
84. When John and Harry, starting from the right angle of a triangular
field, run along its sides, and meet first in the middle of the opposite
side, and again 32 yards from their starting point, if John’s speed is
to Harry’s as 13 to 11, the sides of the field measure 384 yards.
85. If two sorts of wine when mixed in a flagon in equal parts cost
15d., but when mixed so that there are two parts of _A_ to three of _B_
cost 14d., a flagon of _A_ would cost 20d., and a flagon of _B_ 10d.
86. If, when a man met a beggar, he gave him half of his loose cash and
a shilling, and meeting another gave him half what was left and two
shillings, and to a third half the remainder and three shillings, he had
two guineas at first.
87. The clerk who has two offers of work from January 1, one from _A_ of
£100 a year, with an annual rise of £20, and the other from _B_ of £100
a year, with a half-yearly rise of £5, should accept _B_’s offer.
The half-yearly payments from _A_ (allowing for the rise), would be 50,
50, 60, 60, 70, 70, etc., etc.; and from _B_ they would be 50, 55, 60,
65, 70, 75, etc., etc., so that _B_’s offer is worth £5 a year more than
_A_’s always.
88. If I have a number of florins and half-crowns, but no other coins, I
can pay my tailor £11, 10s. in 224 different ways.
This can be found thus by rule of thumb: Start with 0 half-crowns and
115 florins. Then 4 half-crowns and 110 florins. Add 4 half-crowns and
deduct 5 florins each time till 92 half-crowns and 0 florins is reached.
89. The monkey climbing a greased pole, 60 feet high, who ascended 3
feet, and slipped back 2 feet in alternate seconds, reached the top in 1
minute, 55 seconds, for he did not slip back from the top.
90. When Adze, the carpenter, secured his tool-chest with a puzzle lock
of six revolving rings, each engraved with twelve different letters, the
chances against any one discovering the secret word formed by a letter
on each ring was 2,985,983 to 1; for the seventy-two letters may be
placed in 2,985,984 different arrangements, only one of which is the
key.
91. The five married couples who arranged to dine together in
Switzerland at a round table, with the ladies always in the same places,
so long as the men could seat themselves each between two ladies, but
never next to his own wife, were able under these conditions to enjoy
thirteen of these nights at the round table.
92. If in a calm the tip of a rush is 9 inches above the surface of a
lake, and as the wind rises it is gradually blown aslant, until at the
distance of a yard it is submerged, it is growing in water that is 5
feet 7¹⁄₂ inches deep.
93. Aminta was eighteen.
94. When Dick took a quarter of the bag of nuts, and gave the one over
to the parrot, and Tom and Jack and Harry dealt in the same way with the
remainders in their turns, each finding a nut over from the reduced
shares for the bird, and one was again over when they divided the final
remainder equally, there were, at the lowest estimate, 1021 nuts in the
bag.
95. Eight and a quarter is the answer to the nonsense question--
If five times four are thirty-three,
What will the fourth of twenty be?
96. The similar fraction of a pound, a shilling, and a penny which make
up exactly a pound are as follows:--
s. d.
²⁴⁰⁄₂₅₃ of £1 = 18 11¹⁶⁹⁄₂₅₃
²⁴⁰⁄₂₅₃ of 1s. = 11⁹⁷⁄₂₅₃
²⁴⁰⁄₂₅₃ of 1d. = ²⁴⁰⁄₂₅₃
---------------
£1 0 0
========
97. When Dr Tripos thought of a number, added 3, divided by 2, added 8,
multiplied by 2, subtracted 2, and thus arrived at double the number, he
started with 17.
98. When _A_ and _B_ deposited equal stakes with _C_, and agreed that
the one who should first win three games of billiards should take all,
but consented to a division in proper shares when _A_ had won two games
and _B_ one, it was evident that if _A_ won the next game all would go
to him, while if he lost he would be entitled to one half. One case was
as probable as the other, therefore he was entitled to _half of these
sums taken together_; that is, to three quarters of the stakes, and _B_
to a quarter only.
99. The average speed of a motor which runs over any course at 10 miles
an hour, and returns over the same course at 15 miles an hour, is 12
miles an hour, and not 12¹⁄₂, as might be imagined. Thus a run of 60
miles out takes, under the conditions, six hours, and the return takes
four hours; so that the double journey of 120 miles is done in ten
hours, at an average speed of 12 miles an hour.
100. Farmer Hodge, who proposed to divide his sheep into two unequal
parts, so that the larger part added to the square of the smaller part
should equal the smaller part added to the square of the larger part,
had but one sheep.
Faithful to his word, he divided this sheep into two unequal parts, ²⁄₃
and ¹⁄₃, and was able to show that ²⁄₃ + ¹⁄₉ = ⁷⁄₉, and that ¹⁄₃ + ⁴⁄₉ =
⁷⁄₉. He was heard to declare further, and he was absolutely right, that
_no number larger than_ 1 can be so divided as to satisfy the conditions
which he had laid down.
The fact that _sheep_ is both singular and plural, adds much to the
perplexing points of this attractive problem.
Here is a very simple proof that the number _must be_ 1:--
Let a + b = no. of sheep
then a² + b = b² + a
a² - b² = a - b
or (a + b)(a - b) = a - b
therefore a + b = 1.
101. A horse that carries a load can draw a greater weight _up the shaft
of a mine_ than a horse that bears no burden. The load holds him more
firmly to the ground, and thus gives him greater power over the weight
he is raising from below.
102. In the six chests, of which two contained pence, two shillings, and
two pounds, there must have been at least the value of 506 pence. This
can be divided into 22 (or 19 + 3) shares of 23d. each, or 23 (19 + 4)
shares of 22d. each. Evidently then the treasure can be divided so that
19 men have equal shares, while their captain has either 3 shares or 4
shares.
103. If I bought a parcel of nuts at 49 for 2d., and divided it into two
equal parts, one of which I sold at 24, the other at 25 a penny; and if
I spent and received an integral number of pence, but bought the least
possible number of nuts, I bought 58,800 nuts, at a cost of £10, and I
gained a penny.
104. When, with a purse containing sovereigns and shillings, after
spending half of its contents, I found as many pounds left as I had
shillings at first, I started with £13, 6s.
105. When the lady replied to a question as to her age--
If first my age is multiplied by three,
And then of that two-sevenths tripled be,
The square root of two-ninths of this is four;
Now tell my age, or never see me more--
she was 28 years old.
106. If cars run, at uniform speed, from Shepherd’s Bush to the Bank, at
intervals of two minutes, and I am travelling at the same rate in the
opposite direction, I shall meet 30 in half-an-hour, for there are
already 15 on the track approaching me, and 15 are started from the
other end during my half hour’s course.
107. If it was possible to carry out my offer of a farthing for every
different group of apples which my greengrocer could select from a
basket of 100 apples, he would be entitled to the stupendous sum of
£18,031,572,350 19s. 2d.
108. If the minute-hand of a clock moves round between 3 and 4 in the
opposite direction to the hour-hand, the hands will be exactly together
when it is really 41⁷⁄₁₃ minutes past 3.
109. If the walnut monkey had stopped to help the other, and they had
eaten filberts at equal rates, they would have escaped in 2¹⁄₄ minutes.
110. The value of the cheque, for which the cashier paid by mistake
pounds for shillings, was £5, 11s. 6d. The receiver to whom £11, 5s. 6d.
was handed, spent half-a-crown, and then found that he had left £11,
3s., just twice the amount of the original cheque.
111. The number 14 can be made up by adding together five uneven figures
thus:--11 + 1 + 1 + 1. It will be seen that although only four _numbers_
are used, 11 is made up of _two figures_.
Here is another, and quite a curious solution, 1 + 1 + 1 + 1 = 4, and
with another 1 we can make up 14!
112. A business manager can fill up three vacant posts of varying value
from seven applicants in 210 different ways. For the first post there
would be a choice among 7, for the second among 6, and for the third
among 5, so that the possible variations would amount to 7 × 6 × 5 =
210.
113. If the fasting man, who began his task at noon, said it is now ⁵⁄₁₁
of the time to midnight, he spoke at 3.45 p.m., meaning that ⁵⁄₁₁ of the
remaining time till midnight had elapsed since noon.
114. If a clock takes six seconds to strike 6, it will take 12 seconds
to strike 11, for there must be ten intervals of 1¹⁄₁₅ seconds each.
115. Twenty horses can be arranged in three stalls, so that there is an
odd number in each, by placing one in the first stall, three in the
second, and sixteen (an odd number to put into any stall!) in the third.
116. The little problem, “Given _a_, _b_, _c_, to find _q_,” is solved,
without recourse to algebra, thus: _a_, _b_, _c_, = _c_, _a_, _b_; take
a cab and go over Kew Bridge, and you find a phonetic _Q_!
117. Tom Evergreen was 75 years old when he was asked his age by some
men at his club in 1875, and said--“The number of months that I have
lived are exactly half as many as the number which denotes the year in
which I was born.”
118. Eight different circles can be drawn. A circle can have one of the
three inside and two outside in three ways, or one outside and three
inside in three ways (each of the three being inside or outside in
turn), or all three may be inside, or all three may be outside, the
touching circle.
119. The way to arrange 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, so that used once
each they form a sum which is equal to 1 is this:--
35 148
-- + --- = 1.
70 296
120. The sum of the first fifty numbers may be found without any
addition thus:--The first fifty numbers form twenty-five pairs of
fifty-one each (1 + 50, 2 + 49, etc., etc.), and 51 × 25 is practically
51 × 100 ÷ 4 = 1275.
121. The tramcar _A_, which started at the same time as _B_, but ran
into a “lie by” in four minutes, and waited there five minutes till _B_
came along, when they completed their courses at the same moment in
opposite directions, could have run the whole distance in ten minutes.
122. What remains will be 8 if we take 10 and double it by writing one
10 over another so as to form 18, and then deduct 10.
123. If the average weight of the Oxford crew is increased by 2℔s., when
one of them who weighs 12 stone, is replaced by a fresh man, the weight
of that substitute is 13 stone 2℔s.
124. If a motor-car is twice as old as its tyres were when it was old as
its tyres are, and if, when these tyres are as old as the car itself is
now, their united ages will be 2¹⁄₄ years, the car is now 12 months old,
and the tyres have had 9 months’ wear.
125. _A_ and _B_, who could each carry provisions for himself for twelve
days, started to penetrate as far as possible into a desert, on the
understanding that neither of them should miss a day’s food. After an
advance of four days, each had provisions still for eight days. One gave
four portions of his store to his companion, which did not overload him,
and returned with the other four. His comrade was then able to advance
another four days’ journey, and still have rations for the eight days’
return. Thus the furthest possible penetration into the desert under the
conditions was an eight days’ march.
126. If, when a bottle of medicine and its cork cost half-a-crown, the
bottle and the medicine cost two and a penny more than the cork, the
cork cost twopence half-penny.
127. A boat’s crew far from land, with no sail or oars, and with no
assistance from wind or stream, or outside help of any kind, can regain
the shore by means of a coil of rope. Motion is given to the boat by
tying one end of the rope to the after thwart, and giving the other end
a series of violent jerks in a direction parallel to the keel. This
curious illustration of mechanical principles is from “Ball’s Mechanical
Recreations.” (_Macmillan._)
128. It will be found that after a crown and as many four-shilling
pieces as possible have been crammed into our pockets, there would still
be room for one sixpence and one threepenny-piece in some corner or
cranny. We can, therefore, have one crown, one sixpence, one
threepenny-piece, and as many four-shilling pieces as our pockets will
hold, and yet be unable to give change for a half-sovereign.
129. There were fifteen apples in the basket. Half of these and half an
apple, _i.e._, eight were first given, then half the remainder and half
an apple, _i.e._, four, then on similar lines two, leaving one in the
basket.
130. The Queer Division--
A third of twelve divide
By just a fifth of seven;
And you will soon decide
That this must give eleven--
is solved by LV ÷ V, or 55 ÷ 5 = 11.
131. A motor that goes 9 miles an hour uphill, 18 miles an hour
downhill, and 12 miles an hour on the level, will take 8 hours and 20
minutes to run 50 miles out and return at once over the same course.
132. The number of shots fired at a mark was 420 each by _A_, _B_, and
_C_. _A_ made 280 hits, _B_ 315, and _C_ 336.
133. If a dog and a cat, evenly matched in speed, run a race out and
back over a course of 75 yards in all, and the dog always takes 5 feet
at a bound, and the cat 3 feet, the cat will win, because at the turning
point the dog overleaps the half distance more than the cat does, and so
has a longer run in.
134. When a man caught up a wagon going at 3 miles an hour, which was
just visible to him in a fog at a distance of 55 yards, and which he saw
for five minutes before reaching it, he was walking at the rate of 3³⁄₈
miles an hour.
135. Three horses, _A B C_, can be placed after a race in thirteen
different ways, thus:--_A B C_, _A C B_, _B A C_, _B C A_, _C A B_, _C B
A_, or _A B C_ as a dead heat; or _A B_, _A C_, or _B C_ equal for the
first place; or _A_ first with _B C_ equal seconds; or _B_ first with _A
C_ equal seconds; or _C_ first with _A B_ equal seconds.
136. The 34 points scored against Oxbridge by the New Zealanders can be
made up in two ways, either by 8 tries and 2 converted tries, or by 3
tries and 5 converted tries.
The highest possible score on these lines is 10 tries converted,
equalling 50 points, and as the New Zealanders’ score, if all tries are
converted, becomes four-fifths of this, their actual score was 3 tries
and 5 converted into goals.
137. The smallest number, of which the alternate figures are cyphers,
which is divisible by 9 and by 11 is 909090909090909090909!
138. Our problem in which it is stated that _A_ with 8d. met _B_ and _C_
with five and three loaves, and asked how the cash should be divided
between _B_ and _C_, if all agreed to share the loaves. Now each eats
two loaves and two-thirds of a loaf, and _B_ gives seven-thirds of a
loaf to _A_, while _C_ gives him one-third of a loaf. So _B_ receives
7d. and _C_ 1d.
139. When, on opening four money-boxes containing pennies only, it was
found that those in the first with half of all the rest, those in the
second with a third of the others, those in the third with a fourth, and
those in the fourth with a fifth of all the rest, amounted in each case
to 740, the four boxes held £6. 1s. 8d., and the numbers of pennies were
20, 380, 500, and 560.
140. If two steamers, _A_ and _B_, start together for a trip to a
distant buoy and back, and _A_ steams all the time at ten knots an hour,
while _B_ goes outward at eight knots and returns at twelve knots an
hour, _B_ will regain port later than _A_, because its loss on the
outward course will not have been recovered on the run home.
141. If in London a new head to a golf club costs four times as much as
a new leather face, while at St Andrews it costs five times as much, and
if the leather face costs twice as much in London as in St Andrews, and
if, including a shilling paid for a ball, the charges in London were
twice as much as they would have been at St Andrews, the London cost of
a new head is four shillings, and of a leather face a shilling.
142. When two children were asked to give the total number of sheep and
cattle in a pasture, from the number of each sort, and one by
subtraction answered 10, while the other arrived at 11,900 by
multiplication, the true numbers were 170 sheep, 70 cattle, 240 in all.
143. If a man picks up one by one fifty-two stones, placed at such
intervals on a straight road that the second is a yard from the first,
the third 3 yards from the second, and so on with intervals increasing
each time by 2 yards, and bring them all to a basket placed at the first
stone, he has to travel about 52 miles, or, to be quite exact, 51 miles,
1292 yards.
144. When, in the House of Commons, if the Ayes had been increased by 50
from the Noes, the motion would have been carried by 5 to 3; and if the
Noes had taken 60 votes from the Ayes it would have been lost by 4 to 3,
the motion succeeded; 300 voted “Aye,” and 260 “No.”
145. There are 143 positions on the face of a watch in which the places
of the hour and minute-hands can be interchanged, and still indicate a
possible time. There would be 144 such positions but for the fact that
at twelve o’clock the hands occupy the same place.
146. If in a cricket match the scores in each successive innings are a
quarter less than in the preceding innings, and the side which goes in
first wins by 50 runs, the complete scores of the winners are 128 and
72, and of the losers 96 and 54.
147. When a ball is thrown vertically upwards, and caught five seconds
later, it has risen 100 feet. It takes the same time to rise as to fall,
and when a body falls from rest, it travels a number of feet represented
by sixteen times the square of the time in seconds.
Hence comes the rule that the height in feet of a vertical throw is
found by squaring the time in seconds of its flight, and multiplying by
four.
148. The carpet which, had it been 5 feet broader and 4 feet longer,
would have contained 116 more feet, and if 4 feet broader and 5 longer
113 more, was 12 feet long and 9 feet broad.
149. When, in estimating the cost of a hundred similar articles,
shillings were read as pounds, and pence as shillings, and the estimated
cost was in consequence £212, 18s. 4d. in excess of the real cost, the
true cost of each article was 2s. 5d.
150. If the square of the number of my house is equal to the difference
of the squares of the numbers of my next door neighbours’ houses, and if
my brother in the next street can say the same of his house, though its
number is not the same as that of mine, our houses are numbered 8 and 4.
In my street the even numbers are all on one side, in my brother’s
street they, run odd and even consecutively, and so 8² = 10² - 6², and
4² = 5² - 3².
151. When two men of unequal strength have to move a block which weighs
270 ℔s., on a light plank 6 feet long, if the stronger man can carry 180
℔s., the block must be placed 2 feet from him, so that he may have that
share of the load.
152. If a man who had twenty coins, some shillings, and the rest
half-crowns, were to change the half-crowns for sixpences, and the
shillings for pence, and then found that he had 156 coins, he must have
had eight shillings at first.
153. If, when coins are placed on a table at equal distances apart, so
as to form sides of an equilateral triangle, and when as many are taken
from the middle of each side as equal the square root of the number on
that side, and placed on the opposite corner, the number on each side is
then to the original number as five is to four, there are forty-five
coins in all.
154. When the gardener found that he would have 150 too few if he set
his posts a foot apart, and seventy to spare if he set them at every
yard, he had 180 posts.
155. In order to buy with £100 a hundred animals, cows at £5, sheep at
£1, and geese at 1s. each, the purchaser must secure nineteen cows, one
sheep, and eighty geese.
156. If John, who is 21, is twice as old as Mary was when he was as old
as Mary is, Mary’s age now is 15³⁄₄ years.
157. If in a cricket match _A_ makes 35 runs, and _C_ and _D_ make
respectively half and a third of _B_’s score, and if _B_ scores as many
less than _A_ as _C_ scores more than _D_, _B_ made 30, _C_ 15, and _D_
10 runs.
158. The least number which, divided by 2, 3, 4, 5, 6, 7, 8, 9, or 10,
leaves remainders 1, 2, 3, 4, 5, 6, 7, 8, 9, is 2519, their least common
multiple less 1.
159. A square table standing on four legs, which are set at the middle
points of its sides, can at most uphold its own weight upon one of its
corners.
160. The division of ninety-nine pennies, so that share 1 exceeds share
2 by 3, is less than share 3 by 10, exceeds share 4 by 9, and is less
than share 5 by 16, is 17, 14, 27, 8, and 33.
161. If Indians carried off a third of a flock and a third of a sheep,
and others took a fourth of the remainder and a fourth of a sheep, and
others a fifth of the rest and three-fifths of a sheep, and there were
then 409 left, the full flock was 1025 sheep.
162. When a cistern which held fifty-three gallons was filled by three
boys, _A_ bringing a pint every three minutes, _B_ a quart every five
minutes, and _C_ a gallon every seven minutes, it took 230 minutes to
fill it, and _B_ poured in the final quart, _A_ and _C_ _coming up one
minute too late_ to contribute at the last.
163. A man who said, late in the last century, that his age then was the
square root of the year in which he was born, was speaking in the year
1892.
164. If when a dealer in curios sold a vase for £119, his profit per
cent., and the cost price of the vase, were expressed by the same
number, it had cost him £70.
165. The chance of throwing at least one ace in a single throw with a
pair of dice is ¹¹⁄₃₆, for there are five ways in which each dice can be
thrown so as not to give an ace, so that twenty-five possible throws
exclude aces. Hence the chance of _not_ throwing an ace is ²⁵⁄₃₆, which
leaves ¹¹⁄₃₆ in favour of it.
166. The policeman who ran after a thief starting four minutes later,
and running one-third faster, if they both ran straight along the road,
caught him in twelve minutes.
167. At a bazaar stall, where twenty-seven articles are exposed for
sale, a purchaser may buy one thing or more, and the number of choices
open to him is one less than the continued product of twenty-seven twos,
or 134217727.
VERY PERSONAL
168. When Nellie’s father said:--
I was twice as old as you are
The day that you were born.
You will be just what I was then
When fourteen years are gone--
he was 42, and she was 14.
WORD AND LETTER PUZZLES
1. The word square is completed thus:--
MEAD
EDGE
AGUE
DEED
2. The word square filled in is:--
CIRCLE
INURES
RUDEST
CREASE
LESSEE
ESTEEM
_Notice the curious diagonal of E’s._
3. In the incomplete sentence,
SO****AG****LATI****X****ITH
the duplicate letters are filled in thus:--
SOME MEAGRE RELATIVE VEXED EDITH
The two last letters of each word are repeated as the two first of the
word that follows.
4. The word square is completed thus:--
WASTE
ACTOR
STONE
TONIC
ERECT
5. By twice building up two Ds into a B we make BULBOUS.
6. The question put on paper to the love-lorn youth, “Loruve?” is, when
interpreted, “Are you in love?” and the advice given to him on another
slip, “Prove
L
A F
D
and ensure success,” reads into, “Prove a fond lover, and ensure
success” (a f _on_ d l _over_).
7. DOUBLE ACROSTIC ST. JAMES’ GAZETTE
S . . . prin . . . G
T . . . ar . . . A
J . . . abe . . . Z
A . . . t . . . E
M . . . omen . . . T
E . . . mme . . . T
S . . . trik . . . E
8. The completed word square is--
AMENDS
MINION
ENABLE
NIBBLE
DOLLAR
SNEERS
9. The oracular response to a young Frenchman at a _fête_, who inquired
how he could best please the ladies--
MEC DO BIC
conceals this sage advice--
Aimez, cédez, obéissez!
Love, yield, obey!
10. The solution to our Letter Fraction Problem is of a verbal
character. The original statement
15844
m
--
ot = mo
--
y
is dealt with thus:--
m _on_ ot _on_ y = mo _not on_ y, and so the word monotony solves the
equation.
11. The buried beasts are _chamois_, _buffalo_, _heifer_, and _leopard_;
and when the Oxford athlete cries--
“Though I jump and row and run,
Cap or cup I never won”
he introduces us to a _porcupine_.
12. The lines--
Fourteen letters here we fix,
Vowels only two are spoken;
All together these we mix
Into what can not be broken--
is solved by _indivisibility_, which has many an _i_, like a peacock’s
tail.
13. The English word of thirteen letters in which the same vowel occurs
four times, the same consonant six times, another twice, and another
once, is _Senselessness_.
14. The condensed proverb “WE IS DO” reads at its full length as “Well
begun is half done.”
15. This is the completed word square:--
WASHES
ARTERY
STORMS
HERMIT
ERMINE
SYSTEM
16. Dr Whewell’s puzzle lines--
O O N O O.
----------
U O A O O I O U,
O N O O O O M E T O O.
U O A O I D O S O
I O N O O I O U T O O!
read thus:--
OH SIGH FOR NO CIPHER
You sigh for a cipher, O, I sigh for you,
Sigh for no cipher, O sigh for me too.
You sigh for a cipher, I decipher so,
I sigh for no cipher, I sigh for you too!
17. This is the completed diamond:--
P
POR
CORES
FORCEPS
PORCELAIN
REFLECT
SPACE
SIT
N
18. The medley--
Tan HE Edsa VEN in
It N Gja SmeTs AsgN
aD Az Rett De
is read by taking first the capitals in their order, and then the small
type. It comes put out as “The Evening Standard and Saint James’s
Gazette.”
19. The statement, I can travel first-class on the G.E.R. from
2222222244444500, reads into--from 22 to 2 to 22 to 4 for 44 4d; or, in
plain terms, from 1.38 to 3.38 for 14s. 8d. This works out at about 3d.
a mile, the usual allowance for first-class, for two hours, at about 29
miles an hour.
20. A CURIOUS OLD INSCRIPTION
Read the inscription backwards, and it resolves itself into the lines
familiar to us in our childhood:--
Ride a cock horse to Banbury Cross
To see a fine lady ride on a grey horse.
Rings on her fingers and bells on her toes,
She shall have music wherever she goes!
21. The reason why the invitation to Jack to sample the Irish stew at
Simpson’s was to be kept in mind by the catch words--
Join me at and
i
s,
is because if you join _me_ and _at_, and note that _and_ is _on i_,
which is _on s_, you arrive at the suggestive sentence--_meat and
onions_.
22. The labourer’s quaint letter, which ran “Cepatomtogoatatrin,” was,
in plainer English, “Kept at home to go a tatering.”
23. Our double acrostic comes out thus:--
PROBLEM--PUZZLES
P ........a....... P
(T) R ................ U (E)
O ................ Z
B ........o....... Z
L .......eve...... L
E ........v....... E
M ................ S
24. The Hidden Proverb is--
“Necessity is the mother of invention.”
25. The “deed done” in our Will puzzle is the making in Roman numerals
of “Codicil.” The lawyer was to set down, a hundred, to add nothing, to
set down five hundred, then one, then another hundred, and then one
more, and, finally, fifty, and accordingly he wrote upon the parchment
the one word CODICIL.
26. The word square is--
EDITOR
DESIRE
ISLAND
TIARAS
ORNATE
REDSEA
27. The notes of music A. G. A. E. A. over the grave of a French
musician, who was choked by a fish bone, are in the French notation, “La
sol la mi la,” which reads into “La sole l’a mis 1à.”
Similarly the inscription over the porch of Gustave Doré’s house C. E.
B. A. C. D. is equivalent to “Do, mi, si, la, do, re,” which may be
taken to represent “Domicile à Doré.”
28. When his best girl said to Jack Spooner, “We can go to-morrow at
222222222222 LEY STREET,” he understood her to mean, “We can go
to-morrow, at two minutes to two, to two twenty-two, to 222 Tooley
Street.”
29
C
---------- spells _contents_ (c on ten ts!).
TTTTTTTTTT
30. We can treat the word _disused_ so as to affirm or to disallow the
use of its initial or final d, for we can write it _d is used_, or
_disuse d_!
31. The title of the book shaken up into
EIOOOU
BCNNRRSS
is “Robinson Crusoe.”
32. If the letter M only is inserted in the proper places in the line--
A DEN I I CAN DOCK
it will read: _Madmen mimic and mock_.
33. The quotation from Shakespeare--
OXXU8 MAAULGIHCTE
NOR
is by interpretation:--“Nothing extenuate, nor set down aught in
malice.”
34. The phonetic nightmare--
Ieukngheaurrhphthewempeighghteaps--
is merely the word _unfortunates_. It can be justified thus by English
spelling of similar sound taken letter by letter:--
u--iew in view; n--kn in know; f--gh in tough; o--eau in beau; r--rrh in
myrrh; t--phth in phthisis; u--ewe; n--mp in comptroller; a--eigh in
neigh; t--ght in light; e--ea in tea; and s--ps in psalm.
35. The word square is completed thus:--
FARM
AREA
RENT
MATE
36. A QUAINT INSCRIPTION
The millers leave the mill,
The wherrymen lower their sail;
The maltsters leave the kiln,
For a drop of the White Swan’s ale.
37. A POET’S PI
TONDEBNIOTOCHUMFOARYHUR
OTDIRECTTHAWHOTERSOFKLSYA;
TIKATESTUBALIGHTSTILLETRUFLYR
OTBOWLALLNFESLEAVARFWYAA
is disentangled thus:--
Don’t be in too much of a hurry
To credit what other folks say;
It takes but a slight little flurry
To blow fallen leaves far away.
38. BURIED PLACES
The five buried places are Deal, London, Esk, Perth, and Baden. The word
is Ourangoutang.
39. It is no offence to conspire in the evening, because what is
treasonable is _reasonable after t_!
40. The bit of botany--
Inscribe an _m_ above a line,
And write an _e_ below,
This woodland flower is hung so fine
It bends when zephyrs blow--
is solved by,
m
-,
e
_an em on e_, the delicately hung wind-flower.
41. A PIED PROVERB
The pied proverb, is “A rolling stone gathers no moss.”
42. The Drop Letter Proverb--
E..t. .e.s..s .a.e .h. .o.. ..i.e, is--_Empty vessels make the most
noise_.
43. The English word of five syllables, which has eight letters, five of
them vowels--namely an a, an e, twice i, and y--is _Ideality_.
44. TORMENT may be turned into RAPTURE, using four links, changing only
one letter each time, and varying the order of the letters, thus:
TORMENT, _portent_, _protest_, _pratest_, _praters_, RAPTURE.
45. The pied sentence--
a a c e e e f f h h i i i i i m n n o o o p r r s s t t t t t
can be cast into the proverb--
“Procrastination is the thief of time.”
46. The English sentence, when the letter _o_ is added, reads:--
“Good old port for orthodox Oxford dons.”
47
One vowel in an English word is found,
Which by eight consonants is hedged around--
is solved by _Strengths_.
48. The letters AAAAABBNNIIRSSTT form the word _Antisabbatarians_.
49. The quotation from Shakespeare,
KINI
stands for “A little more than kin, and less than kind.”
50. The two English words which have the first six letters of the
alphabet among their ten letters are _fabricated_ and _bifurcated_.
51. SHIFTING NUMBERS
The letter _A_ stands at the head of the letters of the alphabet. For
_bed_ 3 of these are used; for _goal_, 4; for _prison_, 6; for _six_, 3;
for _three_, 5. The letter _A_ is not used in the spelling of the name
of any number from 1 to 100, but it makes up, with the other vowels, the
number 6.
52. The prodigal’s letter to his father, “Dear Dad, keep 1000050,” in
reply to a suggestion for safeguarding some of his prospects, was
written in playful impudence; and its interpretation is, “Dear Dad, keep
cool!” for the figures in Roman numerals are COOL.
53. BURIED POETS
The poets’ names buried in the lines--
The sun is darting rays of gold
Upon the moor, enchanting spot;
Whose purpled heights, by Ronald loved,
Up open to his Shepherd cot.
And sundry denizens of air
Are flying, aye, each to his nest;
And eager make at such an hour
All haste to reach the mansions blest.
are Gray, Moore, Byron, Pope, Dryden, Gay, Keats, and Hemans.
54. When _A. B._ gave up the reins of government, and _C.B._ took office
in his place, the two verbs, similar in all respects, except that the
one is longer by one letter than the other, which expressed the change,
were _resigns_--_reigns_.
55
Underdone mutton and onion make between you and me,
A glutton a little seedy after a capital tea.
56
First a _c_ and _a t_, last _a c_ and a _t_,
With a couple of letters between,
Form a sight that our eyes are delighted to see,
Unless in their sight it is seen--
is solved by _Cataract_. The first line reads, First a _c_ and _a t_,
last _a c_ and a _t_, that is _cat_ and _act_.
57. Cuba.
58. The Rebus T S is solved by the words _tones_ and _tans_, _t_ before
_one s_, or _t_ before _an s_.
59. The phonetic phrase--
INXINXIN--
is, _Ink sinks in_!
A GOOD END
60. Finis (F IN IS).
=PART III.=
CONTENTS
PAGE
WORD PUZZLES, MISSING WORDS, LETTER PUZZLES III-1
ANAGRAMS, PICTURE PUZZLES III-48
PALINDROMES III-108
SOLUTIONS III-111
WORD PUZZLES
No. I--AN EARLY CRYPTOGRAM
The use of some sort of grille was not uncommon in olden days among the
many methods then employed for secret correspondence. Here is an early
and interesting specimen:--
[Illustration: VENITE PAUPERES]
An important despatch would appear to be a mere confusion of letters,
until it fell into the right hands, and this perforated key was laid
over it, when the intended instructions were at once revealed, and read
in the openings of the tracery.
No. II.--A MANIFOLD MONOGRAM
Here, by seven straight lines and one circle, a manifold monogram is
formed.
[Illustration]
Within its borders we find a circle, a square, a parallelogram, a
triangle, the vowels a, e, i, o, u; the consonants, C, D, H, K, L, M, T,
W; and other forms and figures.
MISSING WORDS
1. PICKING AND STEALING
What tempting ...... beguiled the boy to sample
Fruit that hung ...... on the parson’s trees?
...... upon ...... shall make him an example
When the stern ...... has brought him to his knees.
The missing words are spelt with the same six letters.
No. III.--A BOOK AND ITS AUTHOR
What well-known book and its author may be represented thus:--
[Illustration]
2. A SWARM OF MISSING WORDS
No less than eight different words, spelt with the same six letters, are
available to fill the gaps in the following lines:--
Man of the dark room, ...... none I find
Upon these ...... of likeness to my features.
...... then nought, O man of evil mind,
Who ...... thus to libel fellow-creatures?
Evil thus done ...... upon the doer,
The ...... in thy conduct, Sir, are many;
...... thy life, and let thy crimes be fewer,
Or all thy ...... of good won’t fetch a penny!
No. IV.--ON THE SHUTTERS
Upon the shutters of a barber’s shop the following legend was painted in
bold letters:--
NO. I
JOHN MARSHALL
IN ATTENDANCE
FROM 8 A.M. DAILY
BARBER AND
HAIR CUTTER
THE BALD CRY ALOUD
FOR HIS CREAMS
AS DISPLAYED IN THIS WINDOW
WHICH MAKE HAIR GLISTEN
CLOSES AFTER 8 P.M.
One evening about 8.30, when it was blowing great guns, quite a crowd
gathered round the window, and seemed to be enjoying some excellent
joke. What was amusing them when one shutter blew open?
3. NO HEART!
False Kate! ... .... . ......’s nest,
.. ..... the Upas tree,
I will not budge, ... .... to rest,
.. .... . coward be.
No, not .... ... enough their sting
To drive me back to thee;
None swifter meet thy beckoning
.... ... the hills I flee.
... .... frosts less my love would quell.
Rather than seek thy side,
Of ... .... horse I love so well
I’ll ... .... hoofs and hide!
The number of letters in each word of the missing phrases is indicated
by dots, and the seven letters in each case are those that spell also
“no heart,” which we give as a title and clue.
No. V.--A PHONETIC MAXIMUM
How far phonetic spelling may be pushed, is illustrated by the following
swarm of variations given in a book published at Enfield in 1829:--
Scissars -- ers -- irs -- ors -- urs -- yrs
Scisars -- „ -- „ -- „ -- „ -- „
Sciszars -- „ -- „ -- „ -- „ -- „
Scizars -- „ -- „ -- „ -- „ -- „
Scizscars -- „ -- „ -- „ -- „ -- „
Scizzars -- „ -- „ -- „ -- „ -- „
Or the word may start with Sis, Siss, Siz, Sys, Syss, Syzz, Syzs, Syz,
Cis, Ciss, Ciz, Cisz, Cysz, Cyz, Cyzz. By substituting “z” for the final
“s” we may double the number, and reach a total of 1224.
4. UNNATURAL HISTORY
’Neath ...... Indian seas fierce battles spread
’Twixt ...... hermit-crabs and other shellfish!
With horrid ...... when their foes are dead,
These crabs declare their shells ......, so selfish!
Each missing word has the same six letters.
No. VI.--SOLVITUR AMBULANDO
On this chequered floor, paved with slabs each a foot square, the
palindrome word ROTATOR can be traced in various ways.
+---+---+---+---+---+---+---+---+---+---+---+---+---+
|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O |=R=| O | T | A | T | O | T | A | T | O |=R=| O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | O |=R=| O | T | A | T | A | T | O |=R=| O | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| A | T | O |=R=| O | T | A | T | O |=R=| O | T | A |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | A | T | O |=R=| O | T | O |=R=| O | T | A | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O | T | A | T | O |=R=| O |=R=| O | T | A | T | O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O | T | A | T | O |=R=| O |=R=| O | T | A | T | O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | A | T | O |=R=| O | T | O |=R=| O | T | A | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| A | T | O |=R=| O | T | A | T | O |=R=| O | T | A |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | O |=R=| O | T | A | T | A | T | O |=R=| O | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O |=R=| O | T | A | T | O | T | A | T | O |=R=| O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|
+---+---+---+---+---+---+---+---+---+---+---+---+---+
If a man walks over it, taking one slab at every step, and never
lengthening his strides, how many steps will he take in tracing every
possible variation of the word, and how many such variations are there?
No. VII.--A CURIOUS CHRONOGRAPH
A bachelor clergyman, whose initials were I.E.V., had built a fernery
with the profits of his tracts on the deceased wife’s sister question.
He dated it on a mural tablet thus:--
| |
-+------------------------------------+-
|My LateVVIfe’ssIsterbVILtthIs VVaLL;|
| bVt I In trVth |
| neVer VVeD any VVIfe at aLL, |
| nor VVont forsooth, |
| saIth I. e. V. |
-+------------------------------------+-
| |
If the Roman numerals are extracted from this inscription, and added
together, they amount to 1884, the desired date.
5
Though ------ secure and ------ in his cage,
Our Polly, when ------, will fly into a rage.
Each missing word has the same six letters.
6
All courtly honours are but light
As grains that from a ------ fly;
And he who wears the ------ bright
May haply in a ------ die.
The missing words are spelt with the same six letters.
7
I’d rather from a ------ eat,
I give my sacred word,
Than dine in slums where ------ meet,
And ------ pedlars herd.
Each missing word has the same six letters.
No. VIII.--AN OLD SAMPLER
In the drawer of a cabinet that had belonged to my grandmother I came
upon an old sampler, beautifully worked in scarlet cross-stitch. Its
very curious legend runs as follows:--
| |
-+-----------------------------+-
| AL. IT. |
|T.L EW. O. MA! |
|N.T. Ho! UGH. AVE. Ryli. |
|T.T. Let. Hi! N.G.I. |
|S.S. We. Et. Erf. Art. Ha!|
|N.S. Ug. Ara. N.D.F. Lo! |
|W.E. R.S.T. Ha! TB. |
|L.O. O! Mins. Pri. |
| N. G. |
-+-----------------------------+-
| |
8
A much married ....... of Cadiz
Once ....... some riotous ladies.
To ....... him they chucked
A ......., but he ducked,
Which ....... these rude ladies of Cadiz.
The five missing words are spelt with the same seven letters.
9. THE LASS AND HER LOVER
A lass and her lover were ------ by the sky
Not to ------ too far where no shelter was nigh.
She lingered behind, and ----- -- old church,
St. ------ by name, and was left in the lurch.
She tried a short cut through a park on the grass,
But sternly the ------- forbade her to pass;
Then helplessly stood the disconsolate maid,
When the lad she was soon to --- --- to her aid.
The missing words are spelt with the same six letters.
No. IX.--THE LANDLORD’S PUZZLE
The following curious Missing Words Puzzle is to be seen on a card which
hangs in the bar of an inn in the Isle of Man:--
I had both-- |by both I set great store |and a--
I lent my-- |and took his word therefor;|to my--
I asked my-- |and nought but words I got.|from my--
I lost my-- |for sue him I would not. |and my--
At length with--|which pleased me very well,|came my--
I had my-- |away quite from me fell: |but my--
If I’d both-- |as I have had before, |and a--
I’d keep my-- |and play the fool no more. |and my--
It is to be read thus:--
I had both _money_ and a _friend_, by both I set great store,
I lent my _money_ to my _friend_, and took his word therefor,
_and so on to the end_.
10
When ------- smiles, and sunbeams play
On flowers that ------- and deck the green,
------- can match the scene so gay
------ they crown the May-day queen?
The missing words are spelt with the same seven letters.
11
’Tis said of William, while his forces rested
On Albion’s ------, when Harold had been bested,
He made the ------ of his ------ fuse
Saxon spear-heads, to fashion into shoes.
Each missing word has the same six letters.
No. X.--DECAPITATED WORDS
The decapitated words are in italics:--
The ship rode in an _eastern_ bay,
Asleep _astern_ the master lay,
A _stern_ and rugged man was he,
And, like a _tern_, at home at sea.
Like swooping _ern_ he caught his prey
Whene’er an _R.N._ came his way;
But while due _N._ the needle kept
He in his cabin lay and slept.
The ern, or erne, is the sea-eagle.
12
Happiness, brighter than ------, is dead;
Life’s battle, sterner and ------ now,
Heals the sore ------ that love left as it fled,
------ remembrance of long broken vow!
The missing words are spelt with the same six letters.
13. AN AUTHOR’S EPIGRAM
Press critics fall on me like sharks;
“A shameless ....... of odds and ends,
No ....... original,” and more remarks
In adverse mood. But stay, my friends,
He ....... best who hath his record clean;
My faults are published, yours are yet unseen!
The missing words have the same seven letters.
14
...... are his ......, fashion-forms of grace
In ...... deftly hinted.
...... soft as ......, crowned by Beauty’s face,
In ...... hues are tinted.
The six missing words are spelt with the same six letters.
No. XI.--AN ANCIENT ANAGRAM
On the front of a church, in the Largo Remedios, at Braga, in Portugal,
there is an inscription which, with its letter-perfect Anagram, runs as
follows:--
| |
-+----------------------------+-
| BEATUS IOANNES MARCUS |
| CHRISTI DOMINI DISCIPULUS |
| ---- |
| ANAGRAM |
| -------------- |
|IS IN MUNDO PIUS EST MEDICUS|
| TUIS INCOLIS, BRACHARA |
| -----*----- |
-+----------------------------+-
| |
which may be rendered--“Blessed John Mark, disciple of Christ the Lord.”
_He in this world is the holy healer of thy people Braga!_
15
When Kate --- -------- ----- -------- displayed
----- ----- --- hide a tear;
“All love is dead --- --------,” he said.
“------- I’ll ----- --------!”
The missing word and groups of words are spelt with the same seven
letters.
16
Some grinding at the ------ must toil,
Down-trodden ------ of to-day;
While other children of the soil
In vast ------ their wealth display.
The missing words are spelt with the same six letters.
No. XII.--STRIKE A BALANCE
This diagram shows that the odd numbers of the 9 digits add up to 25,
and the even numbers to 20.
+----------------------+
/| |\
+-+----------------------+-+
| | 1 | |
| | 3 2 | |
| | 5 4 | |
| | 7 6 | |
| | 9 8 | |
| | -- -- | |
| | 25 20 | |
| | ======== | |
+-+----------------------+-+
\| |/
+----------------------+
Can you arrange the 9 digits in two groups in which the odd numbers and
the even will add up to exactly the same sum?
17
Betrayed by faithless friends, in ------ mood
Man ------ his fellows as the ------ brood.
The missing words are spelt with the same six letters.
18. HONEST INDIAN
With divers ---- his ---- is scarred,
He hangs a bangle in his nose;
Such marks secure his ---- regard,
Exalt his fame, and ---- his foes.
Each missing word is spelt with the same four letters.
No. XIII.--HKISTA!
MRS LR’S SR
MR LR KRS.
“BLR MR LR!”
MRS LR HRS.
How do you read these lines and their title?
19. ON THE OCEAN WAVE
------- who, as we ------- roll,
------- for me the foaming bowl,
And ------- off unfriendly spray
With oilskin cape, thou shalt not say
“In vain I’ve ------- my favours here.”
I’ll think of thee when port is near!
The four missing words are spelt with the same seven letters.
20. THE ZENANA MISSION
With high ------ for hearts and hands,
These ------ ------ for distant lands.
The three missing words are spelt with the same six letters.
21
The ------- of his speech did not
------- his audience a jot.
They greeted all he said thereafter
With -------, smiles, and open laughter.
The missing words have the same seven letters.
22
To convent shrine at break of day
With ----- together nuns repair;
Mid gleaming ----- they kneel and pray,
And chanted ----- allays each care.
Spelt with the same five letters.
No. XIV.--IN MEMORIAM
The following puzzle-epitaph was engraved on a tombstone in Durham
Cathedral:--
| |
-+-------------------------+-
|WEON . CEW . ERET . WO|
|WET . WOM . ADEO . NE|
|NON . EFIN . DUST . WO|
|NO . WLI . FEB . EGO . NE|
| WILLIAM and MARGARET |
| TAYLOR |
| Anno Domini 1665. |
-+-------------------------+-
| |
23
Here once, as a hag is bedizened with paint,
A ----- ----- ----’- in the garb of a saint.
The three missing words are spelt with the same five letters.
24. IN PRAISE OF SUSSEX
Sussex! No ----- of a bygone age
Ride through thy ----- to-day with shield and -----,
And ----- no horseflesh so they may engage
To save some damozel from harm or fear.
Who now would give a thought to ----- or peaches?
He truly farms who ----- a golden store;
And, though he cannot ----- the simplest speeches,
----- down expense, and savings has galore!
Each missing word is spelt with the same five letters.
No. XV.--A FRENCH WORD SQUARE
Here is an excellent French Word Square of seven letters:--
+-+-+-+-+-+-+-+
|R|E|N|E|G|A|T|
+-+-+-+-+-+-+-+
|E|T|A|L|A|G|E|
+-+-+-+-+-+-+-+
|N|A|V|I|R|E|S|
+-+-+-+-+-+-+-+
|E|L|I|D|A|N|T|
+-+-+-+-+-+-+-+
|G|A|R|A|N|C|E|
+-+-+-+-+-+-+-+
|A|G|E|N|C|E|R|
+-+-+-+-+-+-+-+
|T|E|S|T|E|R|A|
+-+-+-+-+-+-+-+
This is a worthy companion to the English seven-letter squares on
“Problem” and “Palated,” which are given on other pages.
25
----- in the ----- far away,
Remote alike from heaven and hell,
The silent -----, so poets say,
Who shape the ends of mortals dwell.
Each missing word has the same five letters.
26
In all our ------ the mechanician’s skill
Now compasses the rogue with artful wile.
The patent ------ and the “tell tale” till
Beset his way who ------ the path of guile,
Besotted youth, who ------ to defy
The rule of right, beware his awful fate
Who, sitting down to eat a stolen pie,
------ the eighth commandment on the plate!
Spelt with the same six letters.
No. XVI.--A QUAINT EPITAPH
This epitaph, most of it in some sort of dog Latin, tells its own
pathetic tale on its tablet.
| |
-+------------------------------+-
|IT - OBIT - MORTI - MERA |
|PUBLI - CANO - FACTO - NAM |
|AT - RES - T - M - ANNO - XXX |
|ALETHA - TE - VERITAS |
|TE - DE - QUA - LV - VASTO |
|MI - NE - A - JOVI - ALTO |
|PERAGO - O - DO - NE - AT |
|STO - UT - IN - A - POTOR - AC|
|AN - IV - VAS - NE - VER - A |
| =R - I - P= |
-+------------------------------+-
| |
27
The .... with .... importunate
To rule his .... may try;
His .... is so unfortunate
That .... they may reply!
The missing words are spelt with the same four letters.
28. “TURN AGAIN WHITTINGTON!”
In all the pomp of ---- and chains
He lords it o’er the town;
The ---- of his hopes he gains
Who ---- with half-a-crown.
Each missing word has the same four letters.
No. XVII.--A TRAGIC CALENDAR
| |
-+--------------------------------------+-
|Jan-et was quite ill one day; |
|Feb-rile troubles came her way. |
|Mar-tyr like, she lay in bed, |
|Apr-oned nurses softly sped. |
|May-be, said the leech judicial, |
|Jun-ket would be beneficial. |
|Jul-eps, too, though freely tried, |
|Aug-ured ill, for Janet died. |
|Sep-ulchre was sadly made, |
|Oct-aves pealed and prayers were said.|
|Nov-ices with many a tear |
|Dec-orated Janet’s bier. |
-+--------------------------------------+-
| |
29. A SAUCY JADE
A writer quite devoid of tact,
She valued ------ more than fact.
A wayward ------ she made her muse
On ------ and noble heaped abuse.
Dealt ----- on ------ to prince or peer,
Her ----- wit a paltry jeer.
Each missing word is spelt with the same six letters.
30. MISSING WORDS
Of all destructive country pests
The farmer ..... ..... least;
He cannot yet the puzzle .....
How to suppress the beast!
The missing words have the same five letters.
No. XVIII.--A DIAMOND PALINDROME
Within the four corners of this Mystic Diamond the Palindrome, NAME NO
ONE MAN, can be traced in 16,376 different directions, in straight
lines, or at right angles, starting from the centre or from the borders.
N
NaN
NamaN
NamemaN
NamenemaN
NamenonemaN
NamenooonemaN
NamenoonoonemaN
NamenoonenoonemaN
NamenoonemenoonemaN
NamenoonemamenoonemaN
NamenoonemaNamenoonemaN
NamenoonemamenoonemaN
NamenoonemenoonemaN
NamenoonenoonemaN
NamenoonoonemaN
NamenooonemaN
NamenonemaN
NamenemaN
NamemaN
NamaN
NaN
N
31. TO THE FRESH AIR FUND
OH THE ------ OF THE ------.
The ------ of darkest London are radiant with ------,
You can ----- it in their ----- little faces.
So wherever you ------ let it be your heart’s ------
To ease the ----- and sorrows of all -----.
The missing words in the title and those in the first and third lines
each contain six letters. Those in the second four, and in the fourth
five.
No. XIX.--SHAKESPEARE RECAST
If you start with the right letter in this combination, and then take
every third letter, a well-known quotation from Shakespeare will be
formed.
+----------------------+
|HOUSE.CANOE.AFTER. |
|HOUR.PRINT.CAVE.CHILD |
|SASH.SLEVE.ACORN. |
|AMPLE.SAD.TATTA.HENA |
|MAT.ACHE.CAKE.TACHES. |
|HELIAC.SACQUE.USUAL. |
|ARBOR.SEE.MULCH.JACUR.|
|USE.STOP. |
+----------------------+
32. THE FLIRT THAT FAILED
She ...... in vain, “Men are ......, and as shy
As ...... in October,” she says with a sigh.
The missing words are spelt with the same six letters.
33
When good men lapse the ....... grins,
When one ....... he swears,
And strives to set his former sins
Against his ....... prayers.
Each missing word is spelt with the same seven letters.
No. XX.--A DOUBLE ACROSTIC
An old Italian bird we know
Whose heart is ever touched by snow.
1. None can press me without pain
Pressure is against the grain.
2. I am a king without my head.
3. Here is another king instead.
It is fair to our readers to say that some knowledge of Latin and French
is needed for dealing with this very excellent Acrostic, of which a full
explanation is given with the solution.
34. THE GIPSY LAD
His hands and face were -----, and sad
Upon the ----- a gipsy lad
Lay; as the breeze his temples fanned
He counted ----- on either hand.
Each missing word has the same five letters.
35. THE OLD DIVINE
In yon grey ----- an old divine
Taught me my ----- to decline,
And verbs with ----- of mood and tense;
But while I plodded on apace
I had to keep the ----- of grace,
And close his prayers with loud -----.
Each missing word is spelt with the same five letters.
36. BANZAI!
No reckless ------ of the sword,
He ------ his fatherland to save.
Fighting for freedom, not ------,
Now ------ of the eastern seas.
The four missing words contain six letters.
No. XXI.--HIDDEN PROVERBS
Five familiar proverbs are hidden in this square of 169 letters.
R E N O W N E D T H A N W
S Y O U R C A K E A N D A
S T E T O B E F E A R H R
E A R K S S P O I L E A F
L E O O H E R S N T D V O
O T M O T L I N O H T E U
N O S C A L A G M E H I R
S N I Y G O R S O B A T S
E N G N E N O T S R N P A
I A O A M O O T S O A E W
R C D E V I L A H T D A S
O U O Y N O I L D A E C A
T C I V R E H H T A H E Z
The proverbs are arranged in a regular sequence.
37. OF DOUBTFUL WORTH
A fair ------, though ------ and frayed,
The critic ------ to own,
And it might interest the trade
If ------ by some one known.
The missing words are spelt with the same six letters.
38
In his ------ days, as when he was young,
The ------ indulges in ------ of tongue.
Each missing word is spelt with the same six letters.
No. XXII.--AN ALPHABETICAL TOAST
Lord Duff, who evidently had a turn for puzzles, proposed this
alphabetical toast, which became popular among the Jacobites.
A.B.C. A blessed change.
D.E.F. Down every foreigner.
G.H.J. God help James.
K.L.M. Keep Lord Mar.
N.O.P. Noble Ormond preserve.
Q.R.S. Quickly resolve Stuart.
T.U.V.W. Truss up vile Whigs.
X.Y.Z. Exert your zeal.
Another quaint and ingenious use of separate letters is recorded of the
well-known preacher, Henry Ward Beecher.
Years ago, before his reputation had become world-wide, he was asked to
give a lecture without charge, and assured that it would increase his
fame. His reply was characteristic and very much to the point: “I will
lecture for F.A.M.E.--fifty and my expenses!”
39. MISSING WORDS
(1) A cylindrical lock
Where no key can be found,
(2) An instrument treble
And ringing in sound.
(3) In story-land ranging,
(4) Now chopping and changing;
(5) Broken up, reunited,
Quite whole I am found.
Words, spelt with the same eight letters are indicated in these lines.
There are two words in (1).
No. XXIII.--A MORAL PRECEPT
The following obscure legend was worked on an old sampler, in the red
cross-stitch that found favour when our grandmothers were girls:--
+----------------+
| Elizabeth out |
|Rue Constantine |
|Very thin gloves|
| Way Susan dart.|
+----------------+
This was evidently some excellent moral precept, but it hung on its
frame, a mere puzzle on the school-room wall, until an expert word
juggler came that way, and solved the mystery by reading it off thus:--
“Eliza be thou true, constant in everything. Love sways us, and art.”
40
In the following lines the first missing word has two letters, and the
letters are carried on, with one more added each time, and in varied
order, throughout the verses, either in single words or in groups of
words:--
A lover of .. unkind fair
Were less than ... did he not ....
“Mine is no ..... life, I swear,
It dwells in this ...... alone.
Grant me thy love, like ....... chaste
.. ...... lest thou live unwooed,
..... .. . lowly life to waste
The treasures of sweet ..........”
No. XXIV.--SHAKESPEARE’S MANTLE
Ingenious cryptic efforts have been made to prove that Bacon was the
author of Shakespeare’s plays, but it has been reserved for us to
reveal, by a convincing cryptogram, the modern wearer of his mantle.
The secret is disclosed by a line of capital letters shown below:--
Mac B eth.
Oth E llo.
Comedy of Er R ors.
Merchant of Ve N ice.
Coriol A nus.
Midsummer Night’s D R eam.
Merry Wives of Win D sor.
Measure for Mea S ure.
Much Ado about Not H ing.
Antony and Cleop A tra.
All’s Well that ends W ell.
41. MISSING WORDS
Till a man is as ----- of a ----- as his palm is,
We ----- him from earning his ----- in our armies.
The missing words are spelt with the same five letters.
42. THE PAUPER’S PLAINT
Pale penury that ------ social bands,
And any link that ------ worth to fame,
Take ye the blame for my inactive hands,
I ------ in vain to build upon the sands,
Without a ------ who can make a name?
The missing words are spelt with the same six letters.
No. XXV.--CAPITAL SHORT CUTS
The following example of the use of phonetic capitals and figures is
fresh and original. It contains more than eighty such symbols in its
twenty-four lines:--
A MAID OF ARCADY
A rosy maid of R K D
Is L N in her bower;
Brisk as U C A honey B,
And sweet as N E flower.
Does she S A herself 2 please
(XQQ the saucy miss),
She sings an L E G 2 TT,
Or blows an M T kiss.
“B mine, I say, U bonny J,
B 4 I CC mine L;
When you are gay my hopes D K,
In T sing U X L.”
Without ado she takes the Q,
Her II B 9 and B D,
“O, sir, I do not N V U
I C that U R C D.
“X S of spirits--O D V--
Begins 2 U U U up;
The cure must B a dish of T
With K N in the cup!”
“O L N U I C R true,
Y need I C Q less?
I’ll never D V 8 from U,
But end my cares with S.”
(_caress_).
43. MISSING WORDS
Mr Backslide, afflicted with weakness of mind,
-------- over to Lushington’s inn, where he dined.
He -------- the pledge he had taken as handy,
And emptied forthwith a -------- of brandy.
Each missing word has eight letters.
44
A ------ sat in his ------ grey,
Watching the moonbeams ------ play
On a keg that in the bushes lay,
And these were the words of his song:--
“Thou ------ the weak, thou ------ the strong,
To thee the ------ of bad deeds doth belong.”
And the leaves with a ------ took up the sad song.
Each of these missing words is spelt with the same six letters.
No. XXVI.--SIMPLE SCHOLARSHIP
Three hungry scholars came to a wayside inn, and saw this sign over the
door:
+-----------+
|PLACET ORE |
|STAT ORDINE|
|ORE STABIT |
|ORE AT ABIT|
+-----------+
One of them eager to show his ready wit, translated these Latin words of
welcome roughly into English verse:--
“Good cheer we provide,
Our service is sure;
Their savours abide
Though meats don’t endure!”
The complacent smile faded from his face as a village schoolboy, who had
overheard him, broke in with the real rendering of the words:--“Place to
rest at or dine; O rest a bit, or eat a bit!”
45
In these lines, where the dots occur, insert words, each of which is
longer by one letter than the one before, and so complete the poem. The
same letters are carried on each time in varied arrangement:--
Nature . love .. every land,
On burning plain, by wooded rill;
Where ... is girt by coral strand,
Or .... rears her castled hill.
Then ..... from me the tale to hear,
How, true to one ......, the bee
Once ....... out keeps, year by year,
The ........ by her instinct given,
Which teach her, wheresoe’er she roam,
In every clime beneath the heaven,
To build the same ......... home.
No. XXVII.--WAS IT VOLAPÜK?
| |
-+---------------+-
|FFAH CHTI WT |
|HGU ACT ONE|
|RASD RIB DLO|
-+---------------+-
| |
A schoolmaster in the Midlands, who was a bit of a wag, wrote this on
the blackboard, as a novel exercise for the boys of Standard VI. Can you
decipher it?
46
Here is another ingenious specimen of missing words, spelt each of them
with the same five letters:--
That Samson did a thousand -----
Is not so wondrous strange.
In days like these at ----- such feats
Assume a wider range.
The Press ----- news ----- now,
Enough to scare a sinner,
And any fool who chooses may,
In Samson’s way, his thousands slay
Who chews his ----- at dinner.
No. XXVIII.--ANOTHER EPITAPH
(_On an Old Pie Woman_)
BENE AT hint HEDU S.T.T.H. emo Uldy O
L.D.C. RUSTO F.N.E. L.L.B.
AC. hel orl AT Ely
W ASS hove N.W. how ASS Kill’d
Int heart SOF pi escu Star
D. sand Tart Sand K N ewe,
Ver yus E oft he ove N.W. Hens he
’Dliv’ Dlon geno
UG H.S. hem Ade he R la STP uffap
UF FBY HE RHU
S. B an D. M.
Uchp R.A. is ’D no Wheres He dot
H.L. i.e. TOM a Kead I.R.T.P. Iein hop est
Hat he R.C. Rust W I
L.L.B. ERA IS ’D----!
47. IN A FARM-YARD
All his flock from ------ rough,
To the ------ ran apace,
Where their ------, old and tough,
------, the guardian of his race.
In these lines each missing word is spelt with the same six letters.
48
This is a bright little specimen of a missing words puzzle:--
Come, landlord, fill the flowing ----
Until their ---- run over;
For in this ---- to-night I’ll ----,
To-morrow ---- to Dover!
Each missing word has the same four letters.
No. XXIX.--DOG LATIN
An old worn stone, with the inscription given below just legible, was
found near to some ancient Roman remains, and was the valued possession
of a local antiquarian, who was convinced that it dated back to the days
of the Emperor Claudius:--
BENE
AT . HTH . IS . ST
ONERE . POS . ET
H . CLAUD . COS. TERT
R . I . P
ES . ELLE . RO
F . IMP
IN . G . TONAS . DO
TH . HISCO
N . SORTJ
A . N . E
His pride of possession was, however, shattered when a rival collector
read it off into excellent English:--“Beneath this stone reposeth Claud
Coster, tripe seller, of Impington, as doth his consort Jane.”
49
Here, as quite a novelty, is a double-barrelled missing words puzzle. As
a puzzle, Part I. should stand alone, but the second part forms a
thinly-veiled solution, which throws light upon the missing words. These
are four in number and are spelt differently with the same six letters.
Part I
I tell of voices hushed and still,
I bid men prick their ears,
I help an army’s ranks to fill,
My gleam like gold appears.
Part II
Hushed is the still and ------ voice,
Pricked ears are keen to ------,
Men who ------ make noble choice.
------ like gold will glisten.
No. XXX.--THE PROBLEM SQUARED
P R O B L E M
R E C E I V E
O C T A V E S
B E A C O N S
L I V O N I A
E V E N I N G
M E S S A G E
This is a singularly perfect specimen of a seven-letter Word Square.
50. MISSING WORDS
Some men their -------- escorted on their way,
When “-------- look here!” I heard a driver say:
“It -------- our pluck to toil like -------- all day,
When wanting -------- we starve on wretched pay.”
Each missing word is spelt with the same five letters.
No. XXXI.--BY LEAPS AND BOUNDS
Can you disentangle the eight-line verse which is scattered over these
64 squares? You must leap always from square to square, as a knight
moves on the chess-board.
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| tle | to | a |cat- |life | and |live | In |
| | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| By | tle | ow- |bro | of | non |tle |fall |
| | | |wse | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| ter |tur- | gain| like|land |one’s|quiet| And |
| | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| of | ar | Bet-| me | and |Than | a- |bat- |
| | m | | ad- | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
|bask | Be | lau-| or | tle |ness |done |wan- |
| | t- | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| rel | let |Than |die |With | der | of | smo |
| | | | | | | | ke |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| ter | in |brain|myr- | on | and |har- | un- |
| | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| Ch | or |to |sun |with |work | In |heat |
| ap- | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
The verses begin with “Better to die,” and end with “tle” in the top
left-hand corner.
51. WISDOM WHILE YOU WAIT
As a -------- -------- of facts you’ll find
Our Encyclopedia -------- the mind.
The three missing words are spelt with the same seven letters.
52. MISSING WORDS
You drink that --------, -------- wine, too lavishly at night,
And say a -------- or a swim next morning puts you right,
When night brings you a sudden --------, and morning devils blue,
Then you’ll ------ your careless boast, and own my warning true.
Each missing word is spelt with the same six letters.
No. XXXII.--A BROKEN SQUARE
Can you complete this broken Word Square?
+---------+
| |O| |E| |
+-+-+-+-+-+
|O| | | |E|
+-+-+-+-+-+
| |I| |O| |
+-+-+-+-+-+
|E| | | |E|
+-+-+-+-+-+
| |E| |E|-|
+-+-+-+-+-+
53
The missing words in these lines are all spelt with the same six
letters:--
--- -------- but for rebel act
Without --- -------- should be;
But this --- --- --- end, in fact
None find --- -------- in me.
54. MISSING WORDS
“Oh for a ----- in this vast solitude,
This endless rise and fall of ----- and moor!”
Soliloquised a ----- in sad mood,
As through the lonely hills the staff of life he bore.
Spelt with the same five letters.
No. XXXIII.--A KNIGHT’S TOUR PROVERB
If the letters on these squares are taken in proper sequence they will
form the words of a well-known proverb:--
+-+-+-+-+-+-+-+-+
| | | | | | | | |
+-+-+-+-+-+-+-+-+
| | | | |E| | | |
+-+-+-+-+-+-+-+-+
| | |E| | | |T| |
+-+-+-+-+-+-+-+-+
| | | |L|H| | | |
+-+-+-+-+-+-+-+-+
| |E| |R| |S| | |
+-+-+-+-+-+-+-+-+
| | |E|A|S| | | |
+-+-+-+-+-+-+-+-+
|D| |E| |O| |S| |
+-+-+-+-+-+-+-+-+
| | | |S|P| |M| |
+-+-+-+-+-+-+-+-+
When a starting point has been chosen for trial of this puzzle, the
successive letters must occupy the squares which in every case are
reached by a knight’s move at chess, until a popular proverb is formed.
55. “MONSTRUM HORRENDUM INFORME INGENS”
’Twas in ........ that we saw him play
Like a ........ in his sports, and they
Amuse us as a good ........ may.
Each missing word has the same eight letters.
No. XXXIV.--GUARINI’S PROBLEM
The following curiosity, which is known as _Guarini’s Problem_, dates
back to the year 1512. On a board of 9 squares two white Knights are
placed in the top corners, and two black Knights in the bottom corners,
thus:--
+---+---+---+
| N |...| N |
+---+---+---+
|...| |...|
+---+---+---+
| n |...| n |
+---+---+---+
The problem is to interchange, in as few moves as possible, the
positions of the white and black knights.
56
We call particular attention to the construction of this very curious
couplet, in which the spaces are filled by the same seven letters. In
every case four of the letters of the missing words or phrases are the
same, and keep the same order, and in all but the first the order of the
letters is unchanged throughout, though the meaning always alters, as it
does in that most perfect old Latin motto, “Persevera, per severa, per
se vera,” “persevere through trials, true to thyself.”
Soup is --- ------- for a ------- divine,
Who with --- -------- is ----- -------- to sit down and dine.
No. XXXV.--AN ANAGRAM SQUARE
Can you break up and recast the five words in this square, so that the
fresh words form a perfect Word Square? The initials are A, M, E, N, D,
S.
+-+-+-+-+-+-+
|S|E|N|D|E|R|
+-+-+-+-+-+-+
|O|N|I|O|N|S|
+-+-+-+-+-+-+
|B|A|B|B|L|E|
+-+-+-+-+-+-+
|M|A|N|N|E|R|
+-+-+-+-+-+-+
|S|M|I|L|E|D|
+-+-+-+-+-+-+
|L|I|N|E|A|L|
+-+-+-+-+-+-+
57. MISSING WORDS
Sweet as the ------ and cruel as its thorn,
------ thy power is great, thy pity scorn.
Swift as the ------ that through the forest fly,
Deep as the ------ that deepest hidden lie,
Is thine own ------ to hapless mortals given,
Semblance of darkest hell or brightest heaven.
These missing words are spelt with the same four letters.
58. MISSING WORDS
(_Dedicated to the Fresh Air Fund_)
Good ----- for City -----
My pipe ----- for -- ---- charms, that yield
Pictures and ----- of a children’s day.
Lest conscience ----- I ----- -- down to say
My ----- shall send some city ----- afield.
Each word or group is spelt with the same five letters.
No. XXXVI.--SHAKESPEARE’S PSALM
Quite as cryptic and convincing as any of the curious Shakespeare-Bacon
cyphers is the evidence which connects our great English poet with the
forty-sixth Psalm of the authorised Bible version.
Shakespear, spelt thus, as it often was, contains four vowels and six
consonants. This is the key to the position. If, guided by these
figures, we turn to the _forty-sixth_ Psalm and count from the
beginning, we find the _forty-sixth_ word is “Shake.”
Then, counting from the end, disregarding the “Selah,” which is no part
of the text, we find that the _forty-sixth_ word is “spear.”
Thus, by a startling and perfect succession of affinities, the poet’s
name-number is linked again and again with this Psalm, until it reveals
his name.
If any sceptic asks why the Book of Psalms should thus be turned to, the
answer comes in the curious fact that the actual letters of the name
William Shakespere, another of its different spellings, form this
sentence as their anagram, and thus afford the necessary clue:--
“We are like his Psalm.”
A final point of interest is made when we notice that Shakespeare
himself must have been just _forty-six_ years old when the Psalms were
re-translated.
59. MISSING WORDS
He said “You ------” when one lied,
He said “Don’t ------” when one hied,
His glass held ------ at his side,
He can ------ what he denied.
Each missing word is spelt with the same six letters.
No. XXXVII.--A KNIGHT’S TOUR
The letters on this board, if read aright in the order of a Knight’s
moves at chess, will give a popular proverb.
+-+-+-+-+-+-+-+-+
|R|L|T|E|Y|L|R|O|
+-+-+-+-+-+-+-+-+
|Y|H|L|T|O|B|T|A|
+-+-+-+-+-+-+-+-+
|T|A|A|A| |H|T|I|
+-+-+-+-+-+-+-+-+
|E|L| |E|I|N|E|O|
+-+-+-+-+-+-+-+-+
|D|H|W| |Y|E|S|Y|
+-+-+-+-+-+-+-+-+
|R|T|E|S|D| |B|W|
+-+-+-+-+-+-+-+-+
|Y|N|E|S|N|D|A|E|
+-+-+-+-+-+-+-+-+
|H|A|A|A|W|I|D|E|
+-+-+-+-+-+-+-+-+
Start from the most central E, and you will be able to trace the
proverb.
60. MISSING WORDS
Mr Snip, the --------, was -------- a hill,
With a bag of new -------- for stock;
When a runaway motor-car gave him a spill
Which scattered his doubts with the shock.
Each missing word is spelt with the same eight letters.
No. XXXVIII.--A WORD SQUARE
The pupils of Dr Puzzlewitz found one morning these vowels printed
boldly on the blackboard:--
E * A * E
* A * E *
A * E * *
* E * * E
E * * E *
Under it the doctor had written “Fill in the consonants, so that the
words read alike from top to bottom, and from side to side.” How is this
to be done?
61. MISSING WORDS
----- her fair cheek, and back o’er all
The ----- of years ----- memory.
Those wedding ----- to her recall
The ----- he urged so tenderly.
Each of these missing words has five letters.
62. MISSING WORDS
Two burglars attempted to ----- a house,
The ----- was heard, though as still as a mouse.
When challenged at once he a ----- became,
But caught as a ----- he finished his game.
Each word has the same five letters.
No. XXXIX.--THE SQUAREST WORD
The squarest word in any language is the Latin _time_, which, in
connection with the three other Latin words, _item_, _meti_, _emit_, can
be read, when written as a square, in every possible direction. Thus:--
T I M E
I T E M
M E T I
E M I T
As it seems impossible to go one better, we have been seeking, as a new
nut for our store, some English word which may be a good second. Can you
complete the square which is built up on these lines?
D E L F
* * * *
* * * *
* * * *
Delf is the key word, but it so far falls short of the perfection aimed
at, that other letters are used in four of the vacant places. Still, it
is so constructed that words which begin with D, E, L, or F appear each
of them in four different directions, and is thus quite a notable
example.
No. XL.--A PUZZLE DIAMOND
Can you fill in this diamond with four words that read alike from left
to right, and from top to bottom?
D
. I .
. . A . .
D I A M O N D
. . O . .
. N .
D
63. MISSING WORDS
The -------- fool in olden days
Gave kings advice in jesting phrase;
He’s -------- now; the modern throne
-------- all follies but its own.
Each missing word is spelt with the same eight letters.
64. MISSING WORDS
Days of ------ and times of evil,
Starving girls with ------ do toil,
No man ------ feast or revel,
Hushed is ------ and turmoil.
Each missing word contains the same six letters.
65. MISSING WORDS
Who ------- in his pride and rage,
To ------- vice a prey,
May hope to reach a green old age,
And find ------- his stay.
Each word has the same seven letters.
No. XLI.--A DEFECTIVE DIAMOND
S
. . M
P . . . L
. . N . . A L
S . . . N . . . R
M . . . C . E
L A . . E
L . E
R
The places now occupied by dots are to be filled in with letters so that
a complete diamond is formed, of words that read alike from left to
right, and from top to bottom.
66. A POET’S POLITICS
When Limerick once, in idle whim,
Moore as her member gaily courted,
The boys, for fun’s sake, asked of him
To state what party he supported.
When thus to them the answer ran,
“I’m of no party as a man,
But as a poet ------”
What is the missing word?
67. MISSING WORDS
Is England ------? That this is so
A solemn ------ aspires to show.
By most ignored, the theme -- ---- to some
Who gravely to the same conclusion come.
Like ------ o’er obstacles they soar,
And if an ---- -- ’vert they rave the more.
There are six letters in the missing words and phrases.
No. XLII.--A SPECIMEN MAGIC SQUARE
The following clever word square of the unusual number of seven letters,
in which there is no undue straining of words or inflexions, is by a
master hand, and would be difficult to match:--
P A L A T E D
A N E M O N E
L E V A N T S
A M A S S E S
T O N S U R E
E N T E R E R
D E S S E R T
68. MISSING WORDS
Off to the links is now their cry,
For golf is man’s --------:
Be not -------- or slow,
-------- hit the ball will go.
Each missing word is spelt with the same eight letters.
69. MISSING WORDS
No maid e’er ------- North, South, East, or West,
More ------- than she who ------- Love’s request.
Each missing word is spelt with the same seven letters.
70. OUT IN THE COLD
Though in ......... I be,
It is, alas! ... ......
No ...... ... comes nigh to me.
Each word or phrase has the same nine letters.
No. XLIII.--A LETTER PUZZLE
Can you fill in the places of these 21 asterisks with only 3 different
letters, so arranged that they spell a common English word of 5 letters
in 12 different directions?
* * * * *
* * * *
* * *
* * * *
* * * * *
Two of the five letters are vowels.
71
--------- his pride the Royal James
Came down upon the --------- Thames;
Like --------- his court repair
To breathe -- -------’s freer air.
Each space has the same nine letters.
72. DROP LETTER LINES
With lily leaves his oars are ........,
Her eager hands their treasures .......,
To the fair winds all cares . .....,
And echo faintly answers .....!
The first letter is dropped in each case, so that while the word which
ends line 1 has eight letters, the last word of line 4 has but five.
73. ENIGMA WITH MISSING LETTERS
There was no good ... in the d...y, so the klim.
No. XLIV.--A CANINE CHRONOGRAPH
Some years ago a country parson had the following inscription engraved
upon the tombstone of a favourite dog that died in 1885:--
CarLo
Dear DoggIe
LoVIng faIthfVL anD trVe
she Lost her sIght
bVt not her LoVe
for
I. e. V.
If the large capital letters are treated as Roman numerals, they add up
to the year of the dog’s death, 1885.
74
If the missing letters, indicated by dots, are supplied, and the words
are separated, this will be found to form a line in a well-known poem:--
.u.u.m.r.i.u.d.s.s.e..o.l.w.d.a.t.n.f.l.o.e.f.s.e.
75
Complete this sentence by filling in five words in the gaps, each spelt
with the same five letters:
If you write ----- ----- at ----- do not ----- the -----.
76. SIX MISSING WORDS
A ..... ..... on ....’. strands
Caught Pat’s heart in her meshes;
He left the ..... in Cupid’s hands,
And watched her ..... her tresses;
Tresses of ..... coloured gold,
That did her fairy form enfold.
Each missing word has the same five letters.
No. XLV.--A HIDDEN NAME
“Yes,” said the village wit, as a merry party sat round the tap-room
fire at Stratford-on-Avon, “some wiseacres have tried to prove that
Bacon wrote Shakespeare’s plays, because his name can be found hidden in
some of the lines. Let me show you how easily this sort of thing can be
arranged to suit our fancy.”
Taking a piece of chalk he wrote upon the door--
“Titus Andronicus”
“All’s Well that Ends Well”
“The Merchant of Venice”
“Coriolanus”
“Cymbeline”
“A Midsummer Night’s Dream”
“Much Ado about Nothing”
“Look down the letters under _d_ of these titles of some of
Shakespeare’s plays,” he said, “and you will find the well-known name of
one who certainly did not write them.” What name did he mean? What but
that of the prince of jokers, Dan Leno!
77. MISSING WORDS
Can you supply the missing words in these lines? Each is spelt with the
same five letters:--
A man of ----- had caught a -----,
And it was windy weather;
“Give me my -----,” he cried, “to fix
My fish and ----- together.”
No. XLVI.--A CRYPTIC INSCRIPTION
The following cryptic inscription was engraved, in his own language,
upon a tablet in honour of the great French astronomer and scientist,
Arago:--
+-------------+
| URE |
|AR ERIL|
+-------------+
It has this interpretation:--
AR à gauche,
ERIL à droit,
URE sur tout.
Arago chérit la droiture sur tout.
Arago cherished integrity above all.
78. ON THE LOOSE
When ....., our puppy, sets out for a run,
Over ..... he ....., all frolic and fun.
For no whistle he ..... in his desperate hurry
The cattle to ....., and the slow sheep to worry.
Each word has the same five letters.
79. MISSING WORDS
Buy my ripe ------, my ------ who’ll buy?
Don’t look so ------, but take some and try!
The missing words are spelt with the same six letters. What are they?
No. XLVII.--SQUARE THE CIRCLE
Here is a circle which it is quite possible to square:--
C I R C L E
I . . . E .
R . . E . .
C . E . . E
L E . . E .
E . . E . .
Can you fill it in with English words, that read alike from top to
bottom, and from left to right? Try it before you turn to the solution.
Every E must be worked in as it stands.
80. MISSING WORDS ILLUSTRATED
He who .... may .... at last,
How to .... we show;
Take a sixpence, hold it fast,
Press the .... and blow!
Each missing word has the same four letters.
[Illustration]
No. XLVIII.--A BROKEN SQUARE
We give as clues the complete border, and a diagonal in which the same
letter persists. Can you construct the whole square?
+---+---+---+---+---+---+---+
|_B_|_O_|_A_|_S_|_T_|_E_|_R_|
+---+---+---+---+---+---+---+
|_O_| | | |_E_| |_E_|
+---+---+---+---+---+---+---+
|_A_| | |_E_| | |_S_|
+---+---+---+---+---+---+---+
|_S_| |_E_| | | |_E_|
+---+---+---+---+---+---+---+
|_T_|_E_| | | | |_N_|
+---+---+---+---+---+---+---+
|_E_| | | | | |_T_|
+---+---+---+---+---+---+---+
|_R_|_E_|_S_|_E_|_N_|_T_|_S_|
+---+---+---+---+---+---+---+
ANAGRAMS
Anagrams, as a method of divining and illustrating personal destiny and
character, were quite a craze in the sixteenth and seventeenth
centuries. No specimens of this word juggling have ever been more apt
than the perfect pair of political anagrams evolved from the names of
two of our greatest statesmen.
When the reins of power changed hands, it was found that the letters
which form Gladstone also spell out exactly, “G. leads not,” while the
name of his great rival and successor Disraeli itself announces, when
recast, “I lead, sir!”
No. XLIX.--A CARD PROBLEM
Here is a pretty card problem, akin in its character and arrangement to
a Magic Square.
Take from a pack of cards the four aces, kings, queens, and knaves, and
arrange them so that in each horizontal, vertical, and diagonal row,
each of the four suits and each of the four denominations shall be
represented once, and only once.
IDEAL ANAGRAMS
| |
-+--------------------------------------------------------+-
|Ave Maria, gratiâ plena, Dominus tecum! |
|Virgo serena, pia, munda et immaculata. |
|Regia nata, evadens luctum amari pomi. |
|Eva secunda, Agni immolati pura mater. |
| |
|Hail, Mary, full of grace, the Lord is with thee! |
|A virgin calm, holy, pure and spotless. |
|Of royal kin, free from the penalty of the bitter apple.|
|A second Eve, pure mother of the slain Lamb. |
-+--------------------------------------------------------+-
| |
These wonderful anagrams need no word of praise. Constructed each of
them with the same letters, the lines express with startling emphasis
the character and special attributes of her whom they describe.
No. L.--TURF-CUTTING
I cut eight narrow strips of turf from my lawn, to form a double
rose-border, with sides of the relative lengths shown in the diagram:--
[Illustration]
How can I relay these eight pieces, without turning or breaking them, on
a piece of level soil, so that they enclose three flower-beds of similar
size?
AN ANAGRAM EPITAPH
This was engraved on a slate monument in memory of Marya Arundell, in
Duloe, Cornwall, June 8, 1629:--
| |
-+------------------------------------------------+
| MARYA ARUNDELL--MAN A DRY LAUREL |
| |
|Man to the marigold compared may be, |
|Man may be likened to the laurel tree. |
|Both feede the eye, both please the optic sense,|
|Both soon decay, both suddenly fleete hence. |
|What then infer you from her name but this, |
|Man fades away, _man a dry laurel_ is! |
-+------------------------------------------------+-
| |
No. LI.--A READY RECKONER
Two schoolboys, looking into a small water-butt after a heavy rain,
could not agree as to whether it was quite half full.
[Illustration]
They appealed to the gardener, as there were no means of measurement at
hand, and he, being a shrewd, practical man, was able to decide the
point. How did he do this?
TWIN ANAGRAMS
Paradise lost.
_Reap sad toils._
Paradise regained.
_Dead respire again!_
No. LII.--A TRANSFORMATION
Can you turn this flat-headed 3 into a 5 by one continuous line, without
scratching out any portion of the 3?
[Illustration]
ADVANCE AUSTRALIA
What were “The Australian Cricketers?”
ANSWERED BY ANAGRAM
_Clinkers! Each a true artist._
BUNYAN’S ANAGRAM
John Bunyan, in the conclusion of the advertisement of his “Holy War,”
has these quaint lines (using i for j):--
“Witness my hand, if Anagrammed to thee
The letters make ‘Nu hony in a B.’”
OLD POLITICAL ANAGRAMS
“The Earl of Beaconsfield.”
_Chief one of all debaters._
“William Ewart Gladstone.”
_Wit so great will lead man._
No. LIII.--A CLEAR COURSE
These diagrams show two of the many ways in which eight pieces of
chessmen or draughtsmen can be so placed upon the board that each of
them has a clear course in every direction, along straight or diagonal
lines.
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| |.X.| |...| |...| |...| | |...| |...| |.X.| |...|
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
|...| |...| |...| X |...| | |...| |...| X |...| |...| |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| X |...| |...| |...| |...| | |.X.| |...| |...| |...|
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
|...| |...| |...| |.X.| | |...| |...| |...| |...| X |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| |...| |.X.| |...| |...| | |...| |...| X |...| |...|
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
|...| |...| |...| |...| X | |...| |...| |...| |.X.| |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| |...| X |...| |...| |...| | X |...| |...| |...| |...|
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
|...| |...| |.X.| |...| | |...| |.X.| |...| |...| |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
We will give a table in the solutions which shows a large number of
similar possible positions. Meantime our solvers may like to trace some
for themselves.
APPOSITE AND OPPOSITE
Three most excellent anagrams are formed with the letters of the great
name Thomas Carlyle. Two of them seem to point to the rugged sage of
Chelsea in life, and one to his repose in death. They are:--
Mercy! lash a lot.
Cry shame to all!
A calm holy rest.
A ROYAL ANAGRAM
(Adsit omen!)
“Albert Edward and Alexandra.”
_All dear bread and war tax end!_
No. LIV.--QUARRELSOME NEIGHBOURS
Three families, who were not on speaking terms, lived in three houses
within the same enclosing fence. Determined to avoid each other, they
built covered ways from the doors of their houses to their gates, so
that they might never cross each other’s paths. The family in A had
their gate at A, those in B at B, and those in C at C. How were these
covered ways arranged so as to secure their complete separation?
[Illustration]
HIS HOBBY
William Ewart Gladstone.
_A man will go wild at trees._
A SOLDIER’S ANAGRAM
Lord Kitchener of Khartoum.
_Oh firm rod! the knack to rule!_
No. LV.--A PRETTY TRICK
Ask some one to place five cards (not court cards) in a row, to add up
their pips, and to place two cards representing that number below, for
subtraction, as is shown in the diagram.
/-------\ /-------\ /-------\ /-------\ /-------\
| ♠ | | ♦ | | ♣ ♣ | | ♥ ♥ | | ♦ ♦ |
| | | | | | | ♥ | | ♦ ♦ |
| | | ♦ | | ♣ ♣ | | ♥ ♥ | | ♦ | = 28.
| | | | | | | ♥ | | ♦ ♦ |
| ♠ | | ♦ | | ♣ ♣ | | ♥ ♥ | | ♦ ♦ |
\-------/ \-------/ \-------/ \-------/ \-------/
/-------\ /-------\
| ♣ | | ♠ ♠ |
| | | ♠ |
| | | ♠ ♠ |
| | | ♠ |
| ♣ | | ♠ ♠ |
\-------/ \-------/
/-------\ /-------\ /-------\ /-------\ /-------\
| ♥ | | ♣ | | ♠ ♠ | | ♦ ♦ | | |
| | | | | | | | | |
| | | ♣ | | ♠ ♠ | | ♦ ♦ | | ♥ |
| | | | | | | | | |
| ♥ | | ♣ | | ♠ ♠ | | ♦ ♦ | | |
\-------/ \-------/ \-------/ \-------/ \-------/
Let him then place cards to represent the result of subtraction, remove
which one he pleases of these, and tell you the sum of the remaining
pips.
You can at once tell him the value of the card removed by deducting the
number of pips in that remainder from the next highest multiple of 9.
Thus, in the instance shown above, if one of the sixes is removed, the
sum of the remaining pips is 12, and 18 - 12 = 6. A space must be left
for any 0.
BOAT-RACE ANAGRAMS
Here is a batch of anagrams, all letters perfect, which show how, by a
little ingenuity, words may be twisted into opposite and appropriate
meanings.
“The Oxford and Cambridge annual boat-race.”
ANAGRAMS
Hard race, but Cantab gained lead from Oxon.
Ah! bad rudder line for Cantab cox to manage.
Cantab blue had raced in an extra good form.
No. LVI.--THE CROSS-KEYS
This pretty puzzle can be made at home by anyone who is handy with a
fret-saw.
[Illustration]
Cut three pieces of hard wood according to the patterns given in this
diagram, and try to fit the three sections together so that they form a
firm symmetrical figure with six projecting ends.
ANGLO-JAPANESE ANAGRAMS
“The Anglo-Japanese treaty of Alliance.”
Yea, Fate enjoins to help a gallant race
or
Hail, gallant East! Fear not, enjoy peace
or
A peace angel, then joy to all in far East.
A WONDERFUL ANAGRAM
If the letters which spell the names of the twelve months are shaken up
and recast, these appropriate lines and their title are formed--
POEM
Just a jury by number, each a scrap of year,
A number recording every jumble, tumble, tear!
No. LVII.--THE NABOB’S DIAMONDS
An Indian Nabob left a casket of valuable diamonds to his children under
the following conditions:--The first was to take a diamond and
one-seventh of the remainder; the second was to take two and a seventh
of the then remainder; the third three and a seventh of the rest, and so
on, on similar lines, till all the diamonds were taken. Each of the
children had then exactly an equal share. How many diamonds were there,
and how many children?
A PRIZE ANAGRAM
It would be difficult to find a more ingenious and appropriate anagram
than this, which took a prize in _Truth_ in 1902, and connects the
King’s recovery with the Coronation.
The sentence was--
“God save our newly crowned King and Queen!
Long life to Edward and Alexandra!”
The letters of this were recast thus--
Can we wonder an anxious devoted England followed drear danger
quakingly?
A GOOD ANAGRAM
Sir Francis Bacon, the Lord Keeper.
_Is born and elect for rich speaker._
THE DREAMER’S ANAGRAM
“Imagination”--_I’m on it again!_
A SEASONABLE ANAGRAM
“Spring, Summer, Autumn, Winter.”
_We murmur--“Time’s running past!”_
No. LVIII.--A CARD CHAIN
The cardboard chain in this diagram is formed of unbroken links cut from
one card.
[Illustration]
There are no joinings in these links, no paste or gum is used, and the
chain is fairly cut from a single card.
APPROPRIATE
Very apt indeed, in these days of books and papers without end, is the
descriptive anagram which we find involved in
“The Alphabet,” _That be a help_.
A TOUR DE FORCE
Made with the letters which form the names of the twelve months, each
being used once, and only once:--
Merry durable just grace
My every future month embrace,
No jars remain, joy bubble up apace!
No. LIX.--STRAY DOTS
These represent the four quarters of a torn design, on which large black
dots had been so drawn that no two of them stood on the same row,
column, or diagonal.
+--+--+--+--+--+--+--+--+ +--+--+--+--+--+--+--+--+
|\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /|
+--+-----+-----+-----+--+ +--+-----+-----+-----+--+
|/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /|
+--●-----+-----+-----+--+ +--+-----●-----+-----+--+
|/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /|
+--+-----+-----●-----+--+ +--+-----+-----+-----+--+
|/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /|
+--+-----+-----+-----+--+ +--+-----+-----●-----+--+
|/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \|
+--+--+--+--+--+--+--+--+ +--+--+--+--+--+--+--+--+
+--+--+--+--+--+--+--+--+ +--+--+--+--+--+--+--+--+
|\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /|
+--+-----+-----+-----+--+ +--+-----+-----+-----+--+
|/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /|
+--●-----+-----+-----+--+ +--●-----+-----+-----+--+
|/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /|
+--+-----+-----+-----+--+ +--+-----+-----+-----+--+
|/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /|
+--+-----+-----+-----●--+ +--+-----+-----+-----●--+
|/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \|
+--+--+--+--+--+--+--+--+ +--+--+--+--+--+--+--+--+
Can you copy out these four pieces, and place them in close contact, so
that the proper edges come together to reproduce the original effect?
AN OLD POLITICAL ANAGRAM
The initials of Brougham, Russell, Allthorp, and Grey,
If rightly disposed the word “brag” will display;
Transpose them and “grab” will appear to the view,
Which hints at what many assert to be true,
That they, like some others, still follow the plan
To _brag_ what they’ll do, and then _grab_ what they can!
No. LX.--THE OPEN DOOR
A prisoner placed in the cell marked _A_ is promised his release on the
condition that he finds his way out of the door at _X_ by passing
through all the cells, entering each of them once only.
+---+---+---+---+---+---+---+---+
| A |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| _x_|
+---+---+---+---+---+---+---+ +
How can he do this?
A ROYAL ANAGRAM
The following remarkable anagram is recast from the name and title of
the daughter of George IV., who was direct heir to the throne:--
“Princess Charlotte Augusta of Wales.”
ANAGRAM
_P. C. her august race is lost, O fatal news!_
No. LXI.--THE SHEPHERD’S PUZZLE
When a farmer told his shepherd to put 21 sheep into 4 pens at the fair,
and added, “I wish you could put an odd number into each pen, as there
is luck in odd numbers, but that is impossible,” he did not take into
account the shrewdness of the shepherd, who very cleverly folded them
thus:--
+---------------------------------+
| * * * |
| +-------------------------+ |
| | * * | |
| | +-----------------+ | |
| | | * * | | |
| | | +---------+ | | |
| | | | * * | | | |
| * | | | * | | | * |
| | | | * * | | | |
| | | +---------+ | | |
| | | * * | | |
| | +-----------------+ | |
| | * * | |
| +-------------------------+ |
| * * * |
+---------------------------------+
Each fold or pen has by this arrangement an odd number of sheep within
the hurdles that form its outer boundaries, and in this sense the
farmer’s wish was satisfied.
We are familiar, most of us, with what is called Macaronic verse or
prose, in which the letters and syllables of Latin words can be read so
as to form English sentences.
It would seem to be too much to expect that there could be any
connection in meaning between these Latin and English words, but there
is one striking exception to this general rule. “Non est” means exactly
“it is not,” and “No nest” conveys precisely the same idea, when a bird
finds that its home has been destroyed.
No. LXII.--LEAP-FROG
Here is an interesting puzzle which can be worked out with coins or
counters on a corner of a chess or a draughtboard.
[Illustration]
At starting only the central point is vacant. A piece that is moved to a
vacant spot must leap over two other pieces if it goes along the solid
black lines, and can only move over one of the dotted diagonals at a
time to an adjoining point. Try, on these lines, to enable the frog, now
in the second hole of the lowest row, to reach the centre in the fewest
possible moves, leaving its own original point vacant, and at the last
surrounded by the words “leap-frog” as they now stand.
Moves can only be made to vacant places.
LXIII.--MUSIC HATH CHARMS
[Illustration]
Transpose two letters, and the lad
Who grinds his organ in the Strand,
Can sing “my music is not bad,
I wake it with a master hand!”
How did he justify this ambitious claim?
No. LXIV.--GRIST FOR THE MILL
If the letters P E A R S O N S are printed on small wafers or buttons,
and set at hap-hazard and out of order on the points which they now
occupy, a very pretty game of patience will result from the attempt to
restore them to their places.
[Illustration]
Any letter can be pushed along one of the lines to a vacant place, and
those on the mill sails can be moved to or from the central spot. There
is no fixed limit to the number of moves, but the puzzle is to restore,
in as few moves as possible, the broken and disordered word to its
proper reading round the mill.
No. LXV.--YOUR WATCH A COMPASS
We are indebted to Sam Loyd, the famous American problem composer and
puzzle king, for the following very practical curiosity, which is so
closely akin to a puzzle that it is well worth giving for the benefit of
our readers when they are out on holiday. If you are uncertain as to
your bearings, lay your watch flat on the palm of your hand so that the
hour-hand points in the direction of the sun. The point exactly midway
between the hour-hand and the figure 12 will be due south at any time
between 6 in the morning and 6 in the afternoon. During any other hours
our rule will give the _north_ point, and in the southern hemisphere the
rules will be reversed.
[Illustration]
In the days of Pope Pio Nono someone extracted from the Papal title
“Supremus Pontifex Romanus” an anagram, which cut at the very foundation
of the faith. It ran thus: “O non sum super petram fixus”--“O I am not
founded on the rock.”
This held its place as a clever topical anagram, until in a moment of
happy inspiration a son of the Church discovered that if the first words
are recast and rearranged, a splendidly appropriate motto for the then
reigning pontiff leaps to sight, “Sum Nono, super petram fixus,” “I am
Nono, founded on the rock!”
No. LXVI.--A MYSTIC SQUARE
This is an arrangement of numbers in 9 cells, so that no cell contains
the same figure as appear in any other, and the two upper rows, the two
side columns, the two long diagonals, and the four short diagonals all
add up to 18:--
+-------------+-------------+-------------+
| | | |
| | 5 + 5| 2 |
| 1 + 1 + 1 |5 + 5 + -----| 2 + - |
| | 5 | 2 |
| | | |
+-------------+-------------+-------------+
| | | |
| | | 4 + 4 |
| 3 + 3 | 6 | 4 + ----- |
| | | 4 |
| | | |
+-------------+-------------+-------------+
| | | |
| 7 + 7 | 9 + 9 + 9| 8 |
| 7 + ----- |9 + ---------| 8 + - |
| 7 | 9 | 8 |
| | | |
+-------------+-------------+-------------+
Though not, strictly speaking, a Magic Square, this is a most ingenious
fulfilment of the conditions of the puzzle.
UP-TO-DATE ANAGRAMS
Good up-to-date anagrams are:--Chamberlain, “Rich able man,” and
Pierpont Morgan, “Man prone to grip.”
No. LXVII.--A SWARM OF WORDS
In each of the five crosses of this mystic figure the same letters are
to be inserted where there are asterisks, so that seven different
English words are formed, which can be read altogether in 64 different
ways and directions.
*
*
* * D * *
*
*
* +---/*\---+ *
* | * | *
* * D * *|* * D * *|* * D * *
* | * | *
* +---\*/---+ *
*
*
* * D * *
*
*
There will then be in all the five crosses 320 readings of these seven
words, three of them having 80 variations and four of them having 20,
and only three different letters are used.
SEASONABLE ANAGRAMS
| |
-+---------------------------------------+-
| “_A Merry Christmas and a Happy |
| New Year._” |
|My prayer and wishes reach many a part.|
| _or_ |
|Many a sad heart can whisper my prayer.|
-+---------------------------------------+-
| |
No. LXVIII.--AFTER SOME SAD REVERSE
We admit this most miserable picture of a discontented outcast into our
bright pages, to “point a moral,” if it does not “adorn a tale.”
[Illustration]
Can our readers gather from it the lesson, that when things seem to be
at the worst, a turn of fortune’s wheel may set them on their legs
again, and change the merest melancholy to the merriest mirth? A reverse
of another sort will set things right. Turn the page round!
A lady, to whom the momentous question had been put with some
diffidence, handed to her lover a slip of paper, telling him that it
embodied her reply. Nothing was written but the word “stripes,” which
seemed at first to be of sinister omen; but to his relief and joy the
fateful letters presently resolved themselves into a message of direct
encouragement, and never was an anagram more welcome than this which
bade him “persist.”
No. LXIX.--THE EXPLOSIVE RAFT
With eight large wooden matches form a miniature raft, as is shown in
the diagram:--
[Illustration]
Place the little raft on a wine-glass, and apply a lighted match to one
of its corners. The tension on its parts will cause the whole
construction to fly asunder as soon as the pressure on any point is
removed.
A NOTABLE HISTORIC ANAGRAM
It is very remarkable that the letters which form the sentence--
“The Jubilee Day of Victoria, Queen and Empress,” also exactly spell--
_Joys are never quite complete if a husband die._
No. LXX.--A PICTURE PUZZLE
Much is bad, and much is sad,
And life has many woes.
[Illustration]
May we keep clear from year to year
Of what this picture shows!
Can you interpret it?
CONTRADICTION BY ANAGRAM
Logica, Latin for logic, can be resolved into the strangely
contradictory anagram, _caligo, darkness_; and, in seeming support of
this perversion, our word logic can be turned into _I clog_!
Here are two good anagrams connected with the land of the Pharaohs:--
David Livingstone,
“Go and visit Nile, D.V.”
Cleopatra’s Needle on the Thames Embankment,
“An Eastern emblem; then take me to Cheops’ land.”
Danes should be _dark men_, according to the anagram of “Denmark.”
No. LXXI.--PATCHWORK PICTURES
This is good fun for old and young as a round game. Each player draws on
the upper part of a slip of paper some fancy head and folds it back,
leaving just enough in sight to guide his left-hand neighbour, who takes
it and adds a body. Again the slips are handed on for the final addition
of legs of any sort, some continuation being always indicated.
[Illustration]
Then these completed patchwork pictures are thrown into a central bowl,
shaken up, drawn out, and passed round for inspection and merry comment.
The folds are the dotted lines.
A HOUSEHOLD WORD
The wounded and sick soldiers whom Florence Nightingale nursed so
tenderly in the Crimea would have acclaimed her beautiful anagram--“Flit
on, cheering angel!”
No. LXXII.--A WINTER NIGHT’S DREAM
Mr Jolliboy, chubby and active, had been dancing until the small hours
at a house in the suburbs, which was the home of sweet Lucy, the lady of
his love.
The full moon shone down upon him as he walked happily to his own modest
quarters, and the “man in the moon” seemed to smile and wink at him most
knowingly.
[Illustration]
Letting himself in presently with his latch-key, Mr Jolliboy was soon in
bed and fast asleep, when in his dreams the full moon shone again,
showing at one moment a likeness of his own round face, at another two
smiling profile views of his Lucy, and at times all the three mixed.
Here, changed by a few touches, are the three moon-faces to be seen in
one moon!
When the great Tichborne trial was still dragging its slow length along,
a barrister with a turn for anagrams amused himself and his learned
friends by constructing the following really remarkable specimen:--Sir
Roger Charles Doughty Tichborne, Baronet, “Yon horrid butcher Orton,
biggest rascal here.”
No. LXXIII.--POINTS AND PICTURES
Among the many openings for pleasant fun in the home circle, there is
none which appeals more easily to young and old than the good old puzzle
of drawing off-hand some fanciful figure, based on five dots placed at
random, which must fall on the face, hands, and feet of the subject
chosen.
[Illustration]
This spirited specimen shows how well it may be done, and similar
efforts, more or less successful, will provoke much amusement. Try it
with pencil or pen and ink.
ANOTHER BOAT-RACE ANAGRAM
Among the many points which have to be taken into account by those who
in successive years are responsible for the selection of the Oxford
eight, there is one which is thus neatly expressed by an anagram:--
“The Oxford and Cambridge annual boat-race.”
_Much extra load on board can bring a defeat._
No. LXXIV.--A NERVOUS SHOCK
This is the astounding portrait of himself, which presented itself to
our scientific professor in his dreams. What very poor justice it does
to the real lines of his benevolent and shrewd old countenance will be
seen in a moment if this weird picture is reversed.
[Illustration]
HOLIDAY HAUNTS
_Divination by Name_
Whenever we are making our plans, some of us for a holiday abroad, some
for a few weeks at the seaside, there is a special interest in these
descriptive anagrams:--
Davos Platz, Engadine.
“Stop, gaze, and live!”
Weston-super-Mare, Somerset.
“A sweet open summer’s resort.”
A very appropriate anagram that exactly describes its subject is
this:--Cleopatra’s Needle, London--“An old lone stone replaced.” Very
suggestive, too, are these short ones, which assure us that skeletons
are “not sleek,” and that editors are “so tired!”
No. LXXV.--HOGARTH’S PUZZLE
A soldier, a dog, and a door can be thus drawn by only three strokes of
a pen:--
[Illustration]
It is said that this originated with Hogarth, who made a bet with his
boon companions that he would draw a soldier, a dog, and a door in three
strokes. For the bayonet he drew a pike.
No. LXXVI.--A REBUS
Why is this “Joker” like a poor joke?
[Illustration]
Because he is _in an E_ (inane).
Here are three ingenious instances of what may be called answers by
anagram:--
What is the protector of “wealth?”
_The law._
Where would a “cart-horse” be unhandy?
In an _orchestra_.
What is the “Daily Express?”
_Pressa die lux._
Concise daily light.
(u is used for y.)
It is curious that Mary, a name so sweet and simple, has as its anagram
“army.” The conflicting thoughts suggested by these two words are very
happily harmonised by George Herbert in his quaint style:--
“How well her name an army doth present,
In whom the Lord of Hosts doth pitch His tent!”
No. LXXVII.--THREE SQUARES
Here is quite a simple method of arranging nine matches so that they
represent three squares.
[Illustration]
The figure also includes at its sides two equilateral triangles.
A ROYAL ANAGRAM
Victoria the First, Queen of Great Britain and Ireland, and Empress of
India. These letters also spell exactly:--
Fit for a bard I claim inspiréd strain:--
The sad and even tenor of a quiet reign.
POLITICAL ANAGRAMS
Here are two very perfect specimens:--
Earl Beaconsfield.
An able force is led_,
or,
_A free lance is bold_.
No. LXXVIII.--A TRANSPARENCY
When the plebiscite was taken in France to decide whether Napoleon III.
should be Emperor, the number of votes cast in his favour was 7,119,791.
Against him there were 1,119,000 votes.
[Illustration: 7119791/1119]
If these numbers are written down quite plainly, as is shown above, with
a dividing line, and without the three cyphers, and the paper or card on
which they are strongly marked is reversed and held up against the
light, the very word with which they were concerned, “empereur,” stands
out with startling distinctness.
It can be drawn on thin cardboard with good effect.
AN IMPERIAL ANAGRAM
A sa Majesté impériale le Tsar Nicolas, souverain et autocrat de
toutes les Russies.
The same letters exactly spell--
O, ta vanité sera ta perte. O, elle isole la Russie; tes successeurs
te maudiront à jamais!
This most remarkable anagram was published in the early days of the
Crimean war.
This curiously apposite anagram was formed letter by letter from the
surnames of the Oxford and Cambridge crews:--
April first nineteen hundred and five. How all warm, as arms, strong as
light or dark blue crew’s, all ply oars on very smooth Thames! Oh! shall
Cam’s boat lose?
No. LXXIX.--FOR THE CHILDREN
Here is an excellent and amusing pastime for the winter evenings. Cover
a square of stout cardboard with glazed black paper, and divide it as is
shown in this diagram:--
[Illustration]
With a little ingenuity and some sense of fun, any number of grotesque
figures can be constructed with the pieces, such as those which we give
here as samples. Try it.
The truth that there is often much in common between puzzles and
politics is borne out by the following up-to-date anagram:--This Eastern
question--“Is quite a hornet’s nest.”
Quite a good anagram, appropriate to the name of a great author, and one
of his works runs thus:--
Charles Dickens: Oliver Twist.
“Now C. D. strikes till vice hears.”
Confessions of an Opium-Eater
The same letters recast spell--
_If so man, refuse poison at once!_
No. LXXX.--JUDGING DISTANCE
(For the Children)
Can you, without measuring, say which two of these posts are farthest
apart?
[Illustration]
A JAPANESE ANAGRAM
“Oyama is Field-Marshal.”
_Fame aid his loyal arms!_
A TOPICAL ANAGRAM
“North Sea outrage.”
_A ghost near route!_
APPROPRIATE ANAGRAMS
Madame Rachel.
_Deal me a charm._
A. Tennyson.
_Any sonnet._
A FOURFOLD ANAGRAM
“Notes and Queries”
_A question sender._
_Enquires on dates._
_Reasoned inquest._
_I send on a request._
No. LXXXI.--HIT IT HARD
Place the two parts of a common wooden match-box, empty, and in good
condition, in the position shown below.
[Illustration]
Now challenge any one to break them with a smart downward blow of the
edge of the hand. What will happen? Try it.
It is well to take care that no people are sitting, or children
standing, near the box, as it might fly into their faces.
An amusing sequence and a note of warning run through these three
anagrams:--Sweetheart, “There we sat;” Matrimony, “Into my arm;” One
hug, “Enough.”
No. LXXXII.--A RE-“BUS”
The driver of a London ’bus the other day broke out into florid language
as he nearly collided with a brand new motor omnibus.
[Illustration]
One of the travesties of “motor-’bus” which he hurled at his rival is
depicted in this diagram. What was it?
A PRIZE ANAGRAM
This letter-perfect anagram could not be more apposite if the words had
been chosen from a dictionary:--“Abdul Hamid Khan, Sultan of the Ottoman
Empire.”--“Inhuman despot, that maketh Armenia bloodful.”
The words in italics in--
One lovely _May morn it_ chanced that I set
My all on a new speculation;
But the venturesome step I can never regret,
For my prize has surpassed expectation,
find in _Matrimony_ their anagram, which is also the solution of the
lines.
No. LXXXIII.--ROUSING DEAD DOGS
A GOOD OLD PUZZLE
These dogs are dead, we all should say;
Give them four strokes, they run away!
[Illustration]
A MEAL OF ANAGRAMS
Mute hen.
Your posset.
Try our steak.
One solid lamb.
Steamed or tossed.
Mince sole.
This is solved thus:--
The Menu.
Oyster soup.
Roast turkey.
Boiled salmon.
Dressed tomatoes.
Lemon ices.
Each corresponding sentence is a perfect anagram.
_Earl of Beaconsfield_ is spelt with the same letters as the sentence “O
able dealer in scoff!”
If a lion with an ear for music were to hear the sound of an “oratorio,”
he might say, as an answer by anagram, _I roar too_!
No. LXXXIV.--LIKE A BLACK SWAN
(_Nigroque simillima cygno._)
Here is quite a good “shadowgraph.”
[Illustration]
With a strong light and a little practice, any one may easily produce
this effect with the shadow thrown by arms and hands.
ANSWERS BY ANAGRAM
What is Russia?--Russia _is ursa_ (a bear).
What did a Prime Minister say of the _Saturday Review_?
That _it was a very rude_ periodical.
BEANS AND BACON
What appropriate advice might be given by anagram to those who support
the “Shakespeare-Bacon” controversy?
_Soak cheaper beans._
No. LXXXV.--CHEQUERS AND STRIPES
Here is a particularly charming domino puzzle:--
+---+ +---+ +---+ +---+ +---+
| 2 | | | | 3 | | | | 3 |
| | | | | | | | | |
| 2 | | | | 1 | | | | 3 |
+---+ +---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+ +---+
| | | 1 | | | | 3 | | |
| | | | | | | | | |
| | | 4 | | | | 4 | | |
+---+ +---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+ +---+
| 1 | | | | 3 | | | | 5 |
| | | | | | | | | |
| 5 | | | | 5 | | | | 5 |
+---+ +---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+ +---+
| | | 3 | | | | 5 | | |
| | | | | | | | | |
| | | 6 | | | | 6 | | |
+---+ +---+ +---+ +---+ +---+
Place any twenty stones, as is shown in the diagram, so that in every
row their fronts and backs alternate. How can you change the picture by
only two movements, so that, retaining its present form, you alter its
chequers into stripes?
The answer by anagram to--What helps to make “bakers fat?” is
_Breakfast_.
No. LXXXVI.--HANG THE MATCHES!
Here is an amusing method of turning wax matches to quaint account:--
[Illustration]
If the wax is slightly melted, and perhaps shredded for some effects,
all sorts of fanciful figures can be thus contrived.
ANSWER BY ANAGRAM
What does an editor say to each “ream of paper?” _Appear for me._
LEWIS CARROLL’S WILL PUZZLE
Here is a most ingenious will puzzle, by Lewis Carroll, which will be
new to most of our readers. Each of the following five questions has to
be answered by a different sentence, nine letters long, and each
sentence is spelt with the same letters used in varied order:--
When are you going to make your will?
Shall I write it for you in pencil?
When may a man leave all his money to charities?
What did the uncle say when he heard this?
What did the nephew say when the uncle made him his heir?
The anagram answers to the five questions in Lewis Carroll’s will puzzle
are as follows:--
When are you going to make your will?
_Now I think._
Shall I write it for you in pencil?
_No, with ink._
When may a man leave all his money to charities?
_With no kin._
What did the uncle say when he heard this?
_Hint, I know._
What did the nephew say when the uncle made him his heir?
_Think I won!_
No. LXXXVII.--A PARROT CRY
The good old Rebus--
[Illustration]
may stand for the proverb--
“Honesty is the best policy.” (On ST is the best poll I see!)
No. LXXXVIII.--A PICTURE PUZZLE
Can you find eight animals that are concealed in this wood?
[Illustration]
If we may go by its anagram the _gardenia_ needs careful “drainage.”
DEFINITIONS BY ANAGRAM
What is the “soldiers’” anagram?
_Lo I dress._
What motto befits “Christianity?”
_I cry that I sin._
No. LXXXIX.--A SHADOWGRAPH
Here is a good old sample of an effect produced by supple fingers in a
strong light on the wall:--
[Illustration]
Adjust the fingers as is shown, so as to secure the bright spot for the
eye, and then life-like movements can easily be made with legs and ears.
The characteristic for the moment of the gaol-bird who began to tear his
clothing, crying out, “I mean to rend it!” was _determination_, which
contains exactly the same letters.
Those who, according to their anagram, are best equipped for a “sea
trip” are _Pirates_.
AN ANSWER BY ANAGRAM
What is most unlike a festival?--_Evil fast_.
The three words in italics in the verse below form also a long single
word, of which the lines themselves give a vivid description:--
While many greet the friends they meet,
I know no face, I press no hand.
Though busy feet may throng the street,
I _sit alone, sirs_, in the land.
“Solitariness.”
No. XC.--A REBUS
Can you interpret this word-picture?
[Illustration]
It represents the name of a famous man.
ANSWER BY ANAGRAM
Should you wish to go by rail,
Hasten to the station;
“Train on time” can never fail
To reach its destination.
If you need a further clue
Keep your journey’s end in view.
_Termination._
We may expect to find “Anarchists” involved _in rash acts_ according to
their anagram.
When his patient has recovered, a “surgeon,” can say by anagram _go
nurse_!
ANSWER BY ANAGRAM
What momentous event of the last century forms in two words an anagram
of the three words appropriate to it, “violence run forth?”
_French Revolution._
No. XCI.--ON THE WALL
Here is a picturesque head, which in a strong light can be thrown upon
the wall by anyone who is handy with his fingers.
[Illustration]
The peaked cap seems to suggest a French soldier.
ANSWERS BY ANAGRAM
What manner of men has “Eton” produced?
Men of _tone_ and _note_.
What worries the “postman?”
_No stamp._
What are to be seen at “Epsom Races?”
_Some pacers._
No. XCII.--ILLUSTRATED EGGS
As an excellent illustration of how much expression can be given by
quite a few simple lines, if the pen or pencil is in artistic hands, we
give the outlines of half a dozen eggs, on which by a few deft touches
varied emotions of the human face are cleverly depicted.
[Illustration]
Here is a hint for fun in the home circle, with a basket of eggs, a
sheaf of pencils, and a prize for the best rapid design. There is room
for two contrasting faces on each egg.
ANSWERS BY ANAGRAM
What did “Henry Wadsworth Longfellow” do for America?
He _Won half the New World’s glory_.
What was the happy result of patriotic “sentiment” in our colonies
during the Boer war?
_It sent men._
No. XCIII.--THE FIVE STRAWS
Take five straws, each about four inches long, and a shilling, and
arrange them so that by holding an end of one of the straws you can lift
them all.
[Illustration]
The diagram given above shows how, by properly interlacing the five
straws, the shilling may be so inserted as to form a wedge which locks
them all together.
ANSWERS BY ANAGRAM
What can you say when using a “fire-escape?”
_I creep safe._
What is the extreme of “slow reading?”
_A single word._
How might a “Poorhouse” in olden days have been described by its own
letters?--_O sour hope!_
What is “Old England” to her sons and daughters?--_Golden land._
The battle of “Inkermann” tells by its anagram of _men in rank_.
No. XCIV.--EQUIVALENT REDISTRIBUTION
In the problem known as “The Flighty Nuns,” the Abbess in the central
cell was satisfied so long as she could count nine of her charges in the
cells on each of the four sides. Here are diagrams which show how the
thirty-six inmates could on these terms absent themselves without
discovery, 2, 4, 8, 10, 12, 16, and even 18 at a time by re-arrangement
of their numbers in the cells.
+-+-+-+ +-+-+-+ +-+-+-+
|0|9|0| |1|8|0| |2|5|2|
+-+-+-+ +-+-+-+ +-+-+-+
|9|A|9| |8|A|8| |5|A|5|
+-+-+-+ +-+-+-+ +-+-+-+
|0|9|0| |0|8|1| |2|5|2|
+-+-+-+ +-+-+-+ +-+-+-+
+-+-+-+ +-+-+-+ +-+-+-+
|2|5|2| |2|4|3| |3|3|3|
+-+-+-+ +-+-+-+ +-+-+-+
|5|A|5| |4|A|4| |3|A|3|
+-+-+-+ +-+-+-+ +-+-+-+
|2|5|2| |3|4|2| |3|3|3|
+-+-+-+ +-+-+-+ +-+-+-+
+-+-+-+ +-+-+-+ +-+-+-+
|2|2|5| |4|1|4| |5|0|4|
+-+-+-+ +-+-+-+ +-+-+-+
|2|A|2| |1|A|1| |0|A|0|
+-+-+-+ +-+-+-+ +-+-+-+
|5|2|2| |4|1|4| |4|0|5|
+-+-+-+ +-+-+-+ +-+-+-+
The clue by anagram to those in search of “hidden treasure” who sought
to discover a dish-cover is _dish under a tree_.
No. XCV.--THE PUZZLED CARPENTER
To stop a serious leak a carpenter sought for a board a foot square. The
only piece he could find was two feet square, but it was pierced with
sixteen holes, as in the diagram below:--
[Illustration]
How did he contrive to cut a square from this of the necessary size?
The answer by anagram to “What should we all welcome, if the Chancellor
of the Exchequer could ‘introduce’ it into his Budget?” is _reduction_.
Things that we know to be “transient” must be looked at, according to
their anagram, _instanter_.
A MUSICAL ANAGRAM
Sweet Mary, the Maid of the Mill, arranged an ingenious signal by song,
by which, in olden days, she could assure her father that all was well
when mischief was abroad. If he heard her singing, “Do, re, mi, fa, sol,
la, si,” he was sure that nothing was amiss. When these syllables are
shaken up, and recast as an anagram, what reassuring sentence do they
form?
The musical syllables, sung as a reassuring signal to her father, by
Mary, the Maid of the Mill, “Do, re, mi, fa, sol, la, si,” when shaken
up and recast as an anagram form the sentence “A mill door is safe.”
No. XCVI.--NOT EASY WHEN YOU KNOW
Of the many “match puzzles” the following seems to be the most confusing
to the ordinary solver, and any variation of its original position is
enough to create fresh confusion.
+-----+-----+-----+
| | | |
| | | |
+-----+-----+-----+
| | | |
| | | |
+-----+ +-----+
Re-arrange three of these matches and form four squares.
The enigma anagram--
They were orthodox as beadles,
But in business tricks and wheedles
They were “sharp I see” as needles--
is solved by _Pharisees_.
The question--Where did we buy “our fancy mat?”--is answered by anagram
at the _manufactory_.
No. XCVII.--SIMPLICITY
Construct this figure with five matches:--
/\
/ \
/ \
----
\ /
\ /
\/
Remove three of the matches, and then replace two of them so as to form
a similar figure.
A common and much-appreciated “dose at meat shop” is, according to its
anagram, _mashed potatoes_.
Tiglath-Pileser was the name of the king which can be resolved into the
anagram, “I till the grapes.”
“Art? I begin art!” is an anagram for _Great Britain_.
If heartily administered, _nine thumps_, the anagram of “punishment,”
would fall deservedly upon the shoulders of a wife-beater.
ANSWER BY ANAGRAM
Our strongest “armaments” are _men-at-arms_.
No. XCVIII.--OVER THE WINE AND WALNUTS
Can you build a bridge with three wooden matches, which shall connect
three wine-glasses, and be solid enough to support a fourth set upon it?
[Illustration]
This picture shows how it is to be done.
The _elephant_, according to its anagram, is the animal to which the
command “Leap then!” would be the least appropriate.
The answer by anagram to “Whom should we employ to make ‘alterations’ in
our overcoats?” is _Neat tailors_.
Where do we go to remedy “disease?”
To the _seaside_.
Who should make a good “manager?”
_A German._
No. XCIX.--FROM THE MATCHBOX
Here is quite a simple match problem:--
----- ----- -----
| | | |
| | | |
----- ----- -----
| | | |
| | | |
----- ----- -----
| | | |
| | | |
----- ----- -----
Can you remove eight of these matches, that now form nine squares, so as
to leave only two squares upon the table?
When Cato and Chloe, at the Popular Café, decided to order for their
afternoon tea a pot of what is formed by the mixture of the letters of
their names, they called for _Chocolate_.
The answer by anagram to “Why may the scenery round Bournemouth be said
to be ‘quite spruce’?” is--because it is _picturesque_.
Lord Roberts’ motto, “Virtute et Valore,” is by its anagram _True to
avert evil_, a happy indication of his character.
No. C.--LIFT NINE WITH ONE
To arrange ten matches on a table, so that with one hand you can lift
nine of them with the tenth, lay them, as is shown in Fig. 1, with the
heads of eight pillowed on one, and pointing in opposite directions, and
the tenth placed across the ridge at the top.
[Illustration: Fig. 1]
[Illustration: Fig. 2]
Then lift all, as shown in Fig. 2.
A MAN HIS OWN ANAGRAM
The enigma--
Behold in me a man forlorn,
Who, though with sound limbs he was born,
His anagram alas is!
For he has found out to his cost,
While all his nimbleness is lost,
How slippery wet grass is!
is solved by _Male, lame_.
The answer by anagram to the question, “Whom do ‘our big hens’
frequently annoy?” is _neighbours_.
No. CI.--FREEHAND DRAWING
This is the way to draw in three strokes an old woman looking out of a
window:--
[Illustration]
Here is a puzzle anagram:--
Tell how to spell my name,
As on the stall you spy me,
For the letters are the same
Which bid you how to buy me.
_Peach--cheap._
The eglantine is the flower which quite contradicts its anagram,
_inelegant_.
The touching epitaph in memory of little Alice formed from the letters
of her name was _à ciel_!
No. CII.--A NOTABLE ANAGRAM
sparkle
+-------+
| Cats |
we | on | on.
| Truck |
+-------+
Yes!
Treated as an anagram the words “Cats on truck” can be recast into _Nuts
to crack_, and the surrounding motto, “Yes! we sparkle on” into
_Pearsons Weekly_; so that the whole design resolves itself into--_Nuts
to crack, in Pearson’s Weekly_.
The old saying that a man who is his own doctor has a fool for his
patient, seems to be borne out by the curious fact that the words,
“Dangers of amateur physicking,” resolve themselves into the perfect
anagram--“_The sick men pay for drugs again_.”
A ’VARSITY ANAGRAM
What every “undergraduate” hates--
_A great rude dun_.
The food for a crocodile which seems to be indicated by its name is
_cool’d rice_!
No. CIII.--WITH DRAWN SWORD
Here is a very simple and ingenious method of representing roughly an
officer with drawn sword.
[Illustration]
Six wax vestas, shredded to form the hair and sword-belt, are fastened
together by the application of a little heat.
Anyone with handy fingers and an ingenious turn of mind can easily
construct other quaint figures in this style.
“Time and tide wait for no man.”
ITS ANAGRAMS
A fine mandate to mind, I trow.
_and_
A firm intent made, a “do it now.”
No. CIV.--SHADOWGRAPHS
Here are three excellent shadowgraphs, which can be produced with good
effect by flexible fingers in a strong light on the wall.
[Illustration]
“Norway’s Olaf is in old England.”
ITS ANAGRAMS
Elf-lad, so loyal and so winning.
A darling son and noisy fellow.
Of winning lads, lead, royal son!
On London’s air wing safely lad.
ANSWERS BY ANAGRAM
Why should _city life_ be happy?
Because the same letters spell _felicity_.
What is the best proof that “real stickphast paste sticks?”
The same letters spell--_Keep this, stick scraps at last_!
ANSWERS BY ANAGRAM
What place have our puzzles “in magic tale?”
They are _enigmatical_.
What great assembly would seem from its name to consist of “partial
men?”
_Parliament._
CHARACTER BY ANAGRAM
What did Douglas Jerrold, by his name anagram, declare himself to be?
_Sure, a droll dog I!_ (_i for j_)
What in the old-fashioned days caused “the wig” to be discarded?
_Weight._
The following curious peace anagrams are appropriate in these days of
disturbance. Each set of words between inverted commas contain exactly
the same letters:--
“To escape fray” I ever “stay for peace,”
In “quiet times,” too, “I’m quite set” at ease:
Let no “vile words” provoke the “evil sword,”
Lest “red war” come, and bring its own “reward.”
Why does the old proverb “Birds of a feather flock together” form a
mystic link between us and our cousins in America?
Because the same letters recast spell out the patriotic sentence, _It
rocks the broad flag of the free_!
What, by their anagram, are “platitudes?”
_Stupid tales._
Why is there a measure to “disappointment?”
Because it is _made in pint pots_.
What is the purpose of a “catalogue?”
It is _got as a clue_.
If “porcus” is Latin for pig, what is Latin for its body?
_Corpus._
What may “laudation” easily become?
_Adulation._
What is “revolution?”
_To love ruin._
Define “The Griffin” (Temple Bar).
_Fine fright._
Why is there room for variety in “twelve sentences?”
Because we can _select new events_.
How do we know that “potatoes” in the singular should not have an “e” at
the end?
Because they spell _O stop at e_!
What should be done to a “misanthrope?”
_Spare him not._
What was the owl of “Minerva?”
_A vermin!_
These, wherever they are found,
Cluster lightly overhead.
Should you chance to turn them round
Blows may tell of weight instead.
Twisted in a foreign tongue,
You will see them as they are.
Changed again they need a bung
When you move them full and far.
This is solved by the anagram words _nuts_, _stun_, _sunt_, _tuns_.
(_Sunt_ is Latin for “they are.”)
IPSISSIMA VERBA
A discussion arose one day, in the winter season, between several
members of a West-end Club, as to the value of flannel underwear. A
London physician, who was appealed to, upheld the need for this, and it
was afterwards found that his name, Alfred James Andrew Lennane, treated
as an anagram, becomes “Man needs aired flannel wear.” This was
singular, but a much more curious coincidence of similar sort was
discovered by an expert in anagrams.
Another member took quite an opposite view, and declared that all should
wear linen. By a wonderful chance his name, Edward Bernard Kinsila,
resolves itself into the _actual words_ that came from his lips--“A
d---- bad risk Dr., wear linen!”
A CHRISTMAS CARD
| |
-+----------------------------------+-
| AN ANAGRAM |
| |
|“Christmas comes but once a year.”|
|So by Christ came a rescue to man.|
-+----------------------------------+-
| |
PALINDROMES
OR
SENTENCES THAT READ BOTH WAYS
NAPOLEON’S PALINDROME
Able was I ere I saw Elba.
ADAM AND EVE’S PALINDROME
Madam, I’m Adam!
When Charles Grant, Colonial Secretary, was made Lord Glenelg, in 1835,
he was called Mr Facing-both-ways, because his title Glenelg was a
perfect palindrome, that could be read with the same result from either
end.
It was a member of the same family who sought to prove the antiquity of
his race by altering an “i” into an “r” in his family Bible, so that the
text ran, “there were Grants on the earth in those days.”
A GOOD PALINDROME
“Roma, ibi tibi sedes, ibi tibi amor,” which may be rendered, “At Rome
you live, at Rome you love;” is a sentence which reads alike from either
end.
A QUAINT PALINDROME
Eve damned Eden, mad Eve!
This sentence reads alike from either end.
A good specimen of a palindrome is this German saying that can be read
from either end:--
Bei Leid lieh stets Heil die Lieb
(In trouble comfort is lent by love.)
Here are some ingenious palindromes, which can be read from either
end:--
Repel evil as a live leper.
Dog, as a devil deified, lived as a god.
Do Good’s deeds live never even? Evil’s deeds do O God!
A SCHOOLBOY’S PALINDROME
“Subi dura a rudibus”
“I have, endured roughness from the rod” which can be read alike from
either end.
Very notable as a long palindrome, even if it is not true record of the
great surgeon’s experience, is this quaint sentence:--“Paget saw an
Irish tooth, sir, in a waste gap.”
A PEACE PALINDROME
Snug & raw was I ere I saw war & guns.
This sentence reads alike from either end.
A PALINDROME PUZZLE
A turning point in every day,
Reversed I do not alter.
One half of me says haste away!
The other bids me falter.--_Noon._
Very remarkable for its length and good sense combined is the following
palindrome, which can be read from either end with the same
result:--“No, it is opposed, art sees trades opposition.”
A PERFECT PALINDROME
Perhaps the most perfect of English palindromes is the excellent adage--
“Egad, a base tone denotes a bad age.”
Here is the most remarkable Latin palindrome on record:--
SATOR AREPO TENET OPERA ROTAS
Its distinguishing peculiarity is that the first letters of each
successive word unite to form the first word, the second letters spell
the second word, and so on throughout the five words; and as the whole
sentence is a perfect palindrome, this is also true on reversal.
[Illustration]
SOLUTIONS
No. III.--A BOOK AND ITS AUTHOR
The well-known book and its author which are represented by
[Illustration: A||]
are “Innocents Abroad,” by Mark Twain. (In no sense A broad, by mark
twain.)
No. IV.--ON THE SHUTTERS
+-----------------+-----------------+
| No.|I |
| JOHN MAR|SHALL |
| IN ATTEN|DANCE |
| FROM 8 A.M.|DAILY |
| BARBER|AND |
| HAIR C|UTTER |
| THE BALD CRY A|LOUD |
| FOR HI|S CREAMS |
| AS DISPLAYED|IN THIS WINDOW |
|WHICH MAKE HAIR G|LISTEN |
| CLOSES|AFTER 8 P.M. |
+-----------------+-----------------+
The shutter on the left blew open, leaving the other to tell its strange
tale.
No. VI.--SOLVITUR AMBULANDO
A man, tracing step by step the various readings of ROTATOR on this
chequered floor, can exhaust all of them, according to the arrangement
on our diagram, in 21,648 steps, spelling out the word as he goes in the
many directions 3608 separate times!
+---+---+---+---+---+---+---+---+---+---+---+---+---+
|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O |=R=| O | T | A | T | O | T | A | T | O |=R=| O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | O |=R=| O | T | A | T | A | T | O |=R=| O | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| A | T | O |=R=| O | T | A | T | O |=R=| O | T | A |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | A | T | O |=R=| O | T | O |=R=| O | T | A | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O | T | A | T | O |=R=| O |=R=| O | T | A | T | O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O | T | A | T | O |=R=| O |=R=| O | T | A | T | O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | A | T | O |=R=| O | T | O |=R=| O | T | A | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| A | T | O |=R=| O | T | A | T | O |=R=| O | T | A |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | O |=R=| O | T | A | T | A | T | O |=R=| O | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O |=R=| O | T | A | T | O | T | A | T | O |=R=| O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|
+---+---+---+---+---+---+---+---+---+---+---+---+---+
This large total is due mainly to the fact that ROTATOR is a palindrome,
and lends itself to both backward and forward reading. The man, a
veritable rotator, will thus have walked more than four miles within a
compass of one hundred and forty-four square feet.
No. VIII.--AN OLD SAMPLER
| |
-+----------------------------+-
| AL. IT. |
|T.L. EW. O. MA! |
|N.T. Ho! UGH AVE. Ryli. |
|T.T. Let. Hi! N.G.I. |
|S.S. We. Et. Erf. Art. Ha!|
|N.S. Ug. Ara. N.D.F. Lo! |
|W.E. R.S.T. Ha! TB. |
|L.O. O! Mins. Pri. |
| N. G. |
-+----------------------------+-
| |
The cross-stitch legend on the old sampler, if its letters are read in
regular sequence, runs thus:--
A little woman, though a very little thing,
Is sweeter far than sugar, and flowers that bloom in spring.
No. XII.--STRIKE A BALANCE
This diagram shows how, while the odd and even numbers of the nine
digits add up to 25 and 20 respectively, they can be arranged in two
groups so that the odd and the even add up to exactly the same sum.
+----------------------+
/| |\
+-+----------------------+-+
| | 1 | |
| | 3 2 | |
| | 5 4 | |
| | 7 6 79 | |
| | 9 8 5¹⁄₃ 84²⁄₆ | |
| | -- -- ----- ----- | |
| | 25 20 84¹⁄₃ 84¹⁄₃ | |
| | ==================== | |
+-+----------------------+-+
\| |/
+----------------------+
No. XIII.--PUZZLE LINES
The puzzle lines--
HKISTA!
MRS LR’S SR
MR LR KRS.
“BLR MR LR!”
MRS LR HRS--
when read according to the usual pronunciation of Mr and Mrs, and taking
the title from the Greek, become, by affinity of sound--
_He kissed her!_
Mrs Lister’s sister
Mr Lister kisses.
“Blister Mr Lister!”
Mrs Lister hisses.
No. XIV.--IN MEMORIAM
The puzzle epitaph--
| |
-+-------------------------+-
|WEON . CEW . ERET . WO |
|WET . WOM . ADEO . NE |
|NON . EFIN . DUST . WO |
|NO . WLI . FEB . EGO . NE|
| WILLIAM and MARGARET |
| TAYLOR |
| Anno Domini 1665 |
-+-------------------------+-
| |
reads thus--
We once were two,
We two made one.
None find us two
Now life be gone.
No. XVI.--A QUAINT EPITAPH
| |
-+------------------------------+-
|IT - OBIT - MORTI - MERA|
|PUBLI - CANO - FACTO - NAM |
|AT - RES - T - M - ANNO - XXX |
|ALETHA - TE - VERITAS |
|TE - DE - QUA - LV - VASTO |
|MI - NE - A - JOVI - ALTO |
|PERAGO - O - DO - NE - AT |
|STO - UT - IN - A - POTOR - AC|
|AN - IV - VAS - NE - VER - A |
| =R - I - P= |
-+------------------------------+-
| |
reads into English thus:--
“I Tobit Mortimer, a publican of Acton, am at rest. Man, no treble X ale
that ever I tasted equal was to mine. A jovial toper, a good one at
stout in a pot or a can, I was never a rip!”
No. XIX.--SHAKESPEARE RECAST
If you start with the first =T= in this combination, and then take every
third letter--
+----------------------+
|HOUSE.CANOE.AFTER. |
|HOUR.PRINT.CAVE.CHILD |
|SASH.SLEVE.ACORN. |
|AMPLE.SAD.TATTA.HENA |
|MAT.ACHE.CAKE.TACHES, |
|HELIAC.SACQUE.USUAL. |
|ARBOR.SEE.MULCH.JACUR.|
| USE.STOP. |
+----------------------+
you will form the popular quotation, “Thrice is he armed that hath his
quarrel just.”
No. XX.--A DOUBLE ACROSTIC
The excellent double Acrostic--
An old Italian bird we know
Whose heart was ever touched by snow.
1. None can press me without pain,
Pressure is against the grain.
2. I am a king without my head.
3. Here is another king instead.
is solved thus:--
CORNIX
1. C or N
2. (R) O -- I
3. R e X
We may tell those of our readers who have not studied the dead languages
that _cornix_ is the Latin for a crow, and that the word can be broken
up into _cor_, heart, and _nix_, snow, while _rex_ is, of course, a king
in Latin, as _roi_ is in French. The double meaning of corn is brought
out by “against the grain.”
No. XXI.--HIDDEN PROVERBS
The five hidden proverbs are:--
“A rolling stone gathers no moss.”
“Too many cooks spoil the broth.”
“A live dog is more to be feared than a dead lion.”
“You cannot eat your cake and have it.”
“Peace hath her victories no less renowned than war.”
Start from the central A, and work round and round.
No. XXVII.--WAS IT VOLAPÜK?
Read backwards it becomes “Old birds are not caught with chaff.”
No. XXVIII.--ANOTHER EPITAPH
(_On an Old Pie Woman_)
BENE AT hint HEDU S.T.T.H. emo Uldy O
L.D.C. RUSTO F.N.E. L.L.B.
AC. hel orl AT Ely
W ASS hove N.W. how ASS Kill’d
Int heart SOF pi escu Star
D. sand Tart Sand K N ewe,
Ver yus E oft he ove N.W. Hens he
’Dliv’ Dlon geno
UG H.S. hem Ade he R la STP uffap
UF FBY HE RHU
S. B an D. M.
Uchp R.A. is ’D no Wheres He dot
H L. i.e. TOM a Kead I.R.T.P. Iein hop est
Hat he R.C. Rust W I
L.L.B. ERA IS’D----!
This puzzle epitaph, written aright, runs thus:--
Beneath in the dust the mouldy old crust
Of Nell Bachelor lately was shoven,
Who was skilled in the arts of pies, custards, and tarts,
And knew every use of the oven.
When she’d liv’d long enough she made her last puff,
A puff by her husband much prais’d;
Now here she doth lie to make a dirt pie,
In hopes that her crust may be rais’d.
No. XXXI.--BY LEAPS AND BOUNDS
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| tle | to | a |cat- |life | and |live | In |
| | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| By | tle | ow- |bro | of | non |tle |fall |
| | | |wse | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| ter |tur- | gain| like|land |one’s|quiet| And |
| | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| of | ar | Bet-| me | and |Than | a- |bat- |
| | m | | ad- | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
|bask | Be | lau-| or | tle |ness |done |wan- |
| | t- | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| rel | let |Than |die |With | der | of | smo |
| | | | | | | | ke |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| ter | in |brain|myr- | on | and |har- | un- |
| | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| Ch | or |to |sun |with |work | In |heat |
| ap- | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
The “Knight’s Tour” verses run as follows:--
Better to die with harness on
In smoke and heat of battle,
Than wander and browse, and fall anon
In quiet of meadow-land cattle.
Better to gain, by arm or brain,
Chaplet of laurel or myrtle,
Than bask in sun, with work undone,
And live one’s life like a turtle,
beginning with “Bet,” and ending in the top left-hand corner.
No. XXXII.--A BROKEN SQUARE
The Broken Word Square is made perfect thus--
S O B E R
O L I V E
B I S O N
E V O K E
R E N E W
No. XXXIII.--A KNIGHT’S TOUR PROVERB
+-+-+-+-+-+-+-+
| | | | | | | |
+-+-+-+-+-+-+-+
| | | | |E| | |
+-+-+-+-+-+-+-+
| | |E| | | |T|
+-+-+-+-+-+-+-+
| | | |L|H| | |
+-+-+-+-+-+-+-+
| |E| |R| |S| |
+-+-+-+-+-+-+-+
| | |E|A|S| | |
+-+-+-+-+-+-+-+
|D| |E| |O| |S|
+-+-+-+-+-+-+-+
| | | |S|P| |M|
+-+-+-+-+-+-+-+
To solve the “Knight’s Tour” proverb start with M, and by a succession
of moves, as of a knight on the chess-board, you can spell out the
proverb “More haste less speed.”
No. XXXIV.--GUARINI’S PROBLEM
The solution of Guarini’s Problem, to transpose the positions of the
white and black knights on the subjoined diagram on which they appear,
is made clear by following the moves on the lettered diagram:--
+---+---+---+
| N |...| N |
+---+---+---+
|...| |...|
+---+---+---+
| n |...| n |
+---+---+---+
+---+---+---+
| a | C | d |
+---+---+---+
| D | | B |
+---+---+---+
| b | A | c |
+---+---+---+
First move the pieces from a to A, from b to B, from c to C, and from d
to D. Then move them from A to d, from B to a, from C to b, and from D
to c. The effect so far is as if the original square had been rotated
through one right angle. Repeat the same sequence of moves, and the
required change of positions is completed.
No. XXXV.--AN ANAGRAM SQUARE
This is the solution of the Word Square.
+-------------+
| A M E N D S |
| M I N I O N |
| E N A B L E |
| N I B B L E |
| D O L L A R |
| S N E E R S |
+-------------+
No. XXXVII.--A KNIGHT’S TOUR
The letters on the board below, read aright in the order of a Knight’s
moves at chess, starting from the most central E form the following
popular proverb:--
+-+-+-+-+-+-+-+-+
|R|L|T|E|Y|L|R|O|
+-+-+-+-+-+-+-+-+
|Y|H|L|T|O|B|T|A|
+-+-+-+-+-+-+-+-+
|T|A|A|A| |H|T|I|
+-+-+-+-+-+-+-+-+
|E|L| |E|I|N|E|O|
+-+-+-+-+-+-+-+-+
|D|H|W| |Y|E|S|Y|
+-+-+-+-+-+-+-+-+
|R|T|E|S|D| |B|W|
+-+-+-+-+-+-+-+-+
|Y|N|E|S|N|D|A|E|
+-+-+-+-+-+-+-+-+
|H|A|A|A|W|I|D|E|
+-+-+-+-+-+-+-+-+
“Early to bed, and early to rise,
Is the way to be healthy, and wealthy, and wise.”
No. XXXVIII.--A WORD SQUARE
Dr Puzzlewitz completed his Word Square thus:--
E R A S E
R A V E N
A V E R T
S E R V E
E N T E R
No. XXXIX.--THE SQUAREST WORD
This is completed thus:--
D E L F
E V I L
L I V E
F L E D
It will be seen that there are four distinct readings of each word.
No. XL.--A PUZZLE DIAMOND
The Diamond is completed thus:--
D
T I P
T I A R A
D I A M O N D
P R O U D
A N D
D
No. XLI.--A DEFECTIVE DIAMOND
The Defective Diamond is completed thus:--
S
G E M
P E R I L
G E N E R A L
S E R E N A D E R
M I R A C L E
L A D L E
L E E
R
No. XLIII.--LETTER PUZZLE
The word is _Level_, filled in thus:--
L E V E L
E E E E
V V V
E E E E
L E V E L
No. XLVII.--THE CIRCLE SQUARED
The Circle can be squared thus:--
C I R C L E
I N U R E S
R U L E S T
C R E A S E
L E S S E E
E S T E E M
No. XLVIII.--A BROKEN SQUARE
This is the completed Square:--
+-+-+-+-+-+-+-+
|B|O|A|S|T|E|R|
+-+-+-+-+-+-+-+
|O|B|S|C|E|N|E|
+-+-+-+-+-+-+-+
|A|S|S|E|R|T|S|
+-+-+-+-+-+-+-+
|S|C|E|P|T|R|E|
+-+-+-+-+-+-+-+
|T|E|R|T|I|A|N|
+-+-+-+-+-+-+-+
|E|N|T|R|A|N|T|
+-+-+-+-+-+-+-+
|R|E|S|E|N|T|S|
+-+-+-+-+-+-+-+
No. XLIX.--A CARD PROBLEM
Here is the arrangement of the aces, kings, queens, and knaves of a pack
of cards in a kind of Magic Square:--
+--------+--------+--------+--------+
| CLUBS | SPADES | HEARTS |DIAMONDS|
| ACE | KING | QUEEN | KNAVE |
+--------+--------+--------+--------+
|HEARTS |DIAMONDS| CLUBS | SPADES |
| KNAVE | QUEEN | KING | ACE |
+--------+--------+--------+--------+
|DIAMONDS| HEARTS | SPADES | CLUBS |
| KING | ACE | KNAVE | QUEEN |
+--------+--------+--------+--------+
| SPADES | CLUBS |DIAMONDS| HEARTS |
| QUEEN | KNAVE | ACE | KING |
+--------+--------+--------+--------+
In each row, column, and diagonal, one, and one only, of the four suits
and of the four denominations is represented.
No. L.--TURF-CUTTING
The eight thin strips of turf, cut from my lawn to form the four sides
of two square rose-borders, can be placed on a level surface of soil
thus without being broken or bent:--
[Illustration]
This forms a framework for the three flower-beds of similar shape and
size.
No. LI.--A READY RECKONER
The gardener decided that the water-butt was more than half-full thus:--
[Illustration]
He tilted it steadily, and some of the water ran over its edge before
the bottom corner _A_ came into sight; but as soon as the water level
stood at _A B_ the cask was exactly half full.
No. LII.--A TRANSFORMATION
The flat-headed 3 can be turned into a 5 by one continuous line, without
scratching out any portion of the 3, by treating the flat top of the 3
as part of a square drawn round the 5, thus:--
[Illustration]
No. LIII.--A CLEAR COURSE
Here is a list of ninety-two positions, in which eight pieces can be
placed upon the chess or draughtboard so that each has a clear course in
every direction.
++==+====+====+==+====+====+==+====+====+==+====+====++
|| 1|1586|3724|24|3681|5724|47|5146|8273|70|6318|5247||
|| 2|1683|7425|25|3682|4175|48|5184|2736|71|6357|1428||
|| 3|1746|8253|26|3728|5146|49|5186|3724|72|6358|1427||
|| 4|1758|2463|27|3728|6415|50|5246|8317|73|6372|4815||
|| 5|2468|3175|28|3847|1625|51|5247|3861|74|6372|8514||
|| 6|2571|3864|29|4158|2736|52|5261|7483|75|6374|1825||
|| 7|2574|1863|30|4158|6372|53|5281|4736|76|6415|8273||
|| 8|2617|4835|31|4258|6137|54|5316|8247|77|6428|5713||
|| 9|2683|1475|32|4273|6815|55|5317|2864|78|6471|3528||
||10|2736|8514|33|4273|6851|56|5384|7162|79|6471|8253||
||11|2758|1463|34|4275|1863|57|5713|8642|80|6824|1753||
||12|2861|3574|35|4285|7136|58|5714|2863|81|7138|6425||
||13|3175|8246|36|4286|1357|59|5724|8136|82|7241|8536||
||14|3528|1746|37|4615|2837|60|5726|3148|83|7263|1485||
||15|3528|6471|38|4682|7135|61|5726|3184|84|7316|8524||
||16|3571|4286|39|4683|1752|62|5741|3862|85|7382|5164||
||17|3584|1726|40|4718|5263|63|5841|3627|86|7425|8136||
||18|3625|8174|41|4738|2516|64|5841|7263|87|7428|6135||
||19|3627|1485|42|4752|6138|65|6152|8374|88|7531|6824||
||20|3627|5184|43|4753|1682|66|6271|3584|89|8241|7536||
||21|3641|8572|44|4813|6275|67|6271|4853|90|8253|1746||
||22|3642|8571|45|4815|7263|68|6317|5824|91|8316|2574||
||23|3681|4752|46|4853|1726|69|6318|4275|92|8413|6275||
++==+====+====+==+====+====+==+====+====+==+====+====++
The numbers indicate the position on the eight successive columns of the
cells on which the men are to be placed. Of course, many similar
arrangements arise from merely turning the board.
No. LIV.--QUARRELSOME NEIGHBOURS
This diagram shows, by the dotted lines, how the three unfriendly
neighbours made the covered pathways to their gates, so that they might
never meet or cross each other’s paths.
[Illustration]
No. LVI.--THE CROSS KEYS
The Cross Keys puzzle when put together takes the form shown below.
[Illustration]
The method is as follows:--Hold _a_ upright between forefinger and thumb
of left hand. With the right hand push _b_ through the slot until the
further edge of the middle slot is nearly even with the outer edge of
_a_. Then lower _c_, held with the short arm of the cross nearest to
you, over the top of _a_, so that the central portion passes through the
cross cut in _b_. Finally push _b_ towards the centre, until the
transverse cut is hidden, and the puzzle is completed.
No. LVII.--THE NABOB’S DIAMONDS
When the children of the Indian Nabob divided his diamonds, the first
taking one stone and a seventh of the remainder, the second two stones
and a seventh of what was left, the third three under similar
conditions, and so on till all were taken, there were 36 diamonds and 6
children.
The division is prettily illustrated thus:--
○○○○○
○○○○○● ○○○○○
○○○○○● ○○○○○
○○○○○● ○○○○○
○○○○○● ○○○○○
○○○○○● ○○○○○
○○○○○● ●●●●●●
○○○○
○○○○● ○○○○
○○○○● ○○○○
○○○○● ○○○○
○○○○● ○○○○
○○○○● ○○○○
○○○○● ●●●●●●
○○○
○○○● ○○○
○○○● ○○○
○○○● ○○○
○○○● ○○○
○○○● ○○○
○○○● ●●●●●●
This shows how the first three took their shares, indicated by black
dots, the remainder being carried down each time, and by similar process
three more claimants would exhaust all the diamonds.
No. LVIII.--A CARD CHAIN
To solve the Card Chain puzzle take a card about 5 in. by 3 in., as
shown below, draw a light pencil line from _A_ to _B_ and from _C_ to
_D_, lay the card in water till you can split its edges down to the
pencil lines, and put it aside to dry.
With a sharp knife cut quite through the straight lines, but only half
through the dotted lines on the split edges. The corresponding figures
show the bar of each link, marking its two parts, which are connected by
the upper and under halves of the split portion. A little patient
ingenuity will now release link after link, and thus complete the chain.
[Illustration]
No. LIX.--STRAY DOTS
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
|\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /|
+--+-----+-----+-----+--+--+-----+-----●-----+--+
|/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /|
+--+-----+-----+-----●--+--+-----+-----+-----+--+
|/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /|
+--+-----●-----+-----+--+--+-----+-----+-----+--+
|/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /|
+--+-----+-----+-----+--+--●-----+-----+-----+--+
|/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--●--+
|\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /|
+--+-----+-----+-----+--+--+-----+-----+-----+--+
|/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /|
+--●-----+-----+-----+--+--+-----+-----+-----+--+
|/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /|
+--+-----+-----●-----+--+--+-----+-----+-----+--+
|/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \|
|\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /|
+--+-----+-----+-----+--+--+-----●-----+-----+--+
|/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
No. LX.--THE OPEN DOOR
+-+-+-+-+-+-+-+-+
|A |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| |
+ + + + + + + + +
| x |
+-+-+-+-+-+-+-+-+
The prisoner who is placed in the cell marked A, and is promised his
liberty if he can reach the door at _X_ by passing through all the
cells, entering each once only, gains his freedom by passing from _A_ to
the cell below, and thence _returning_ to _A_, and leaving it again _by
the other door_; his further course then is quite simple.
No. LXII.--LEAP FROG
[Illustration]
Move 9 to 13, 3 to 9, 7 to 3, 22 to 7, 18 to 22, 24 to 18, 9 to 24, 13
to 9, 7 to 13, 3 to 7, 18 to 3, 22 to 18.
No. LXIII.--MUSIC HATH CHARMS
is explained by the couplet--
“From _Handel_ I learn
As my _handle_ I turn.”
No. LXVII.--A SWARM OF WORDS
This is the key
M
A
M A D A M
A
M
If these letters form each of the five crosses the conditions are all
fulfilled.
[Illustration]
In each cross the words Madam, Adam, Ada can be traced in sixteen
different directions, and the words Dam, am and a in four directions, so
that there are no less than three hundred and twenty readings of these
words in the whole mystic cross, and sixty-four in each separate cross,
though only three different letters are used.
No. LXVIII.--AFTER SOME SAD REVERSE
[Illustration]
No. LXX.--A PICTURE PUZZLE
“A misunderstanding between friends.”
No. LXXIV.--A NERVOUS SHOCK
[Illustration]
No. LXXVIII.--A TRANSPARENCY
[Illustration: 7119791/1119]
No. LXXXII.--A RE-BUS
It was _Incubus_ that the driver of a London Road car hurled as a
scornful charge, at his rival on a motor car.
No. LXXXV.--CHEQUERS AND STRIPES
+---+ +---+ +---+ +---+ +---+
| 2 | | 1 | | 3 | | 3 | | 3 |
| | | | | | | | | |
| 2 | | 4 | | 1 | | 4 | | 3 |
+---+ +---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+ +---+
| | | | | | | | | |
| | | | | | | | | |
| | | | | | | | | |
+---+ +---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+ +---+
| 1 | | 3 | | 3 | | 5 | | 5 |
| | | | | | | | | |
| 5 | | 6 | | 5 | | 6 | | 5 |
+---+ +---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+ +---+
| | | | | | | | | |
| | | | | | | | | |
| | | | | | | | | |
+---+ +---+ +---+ +---+ +---+
Put a finger on one of the black backs in the top row, and move that
stone round to the bottom of its column, then push upward, so that each
stone rises into the row above it. Repeat this with the other back, and
the stripes are formed.
No. LXXXVIII.--A PICTURE PUZZLE
The eight animals hidden in this wood are-- _Giraffe_, _Lion_, _Camel_,
_Elephant_, _Hog_, _Horse_, _Bear_, _Hound_.
[Illustration]
No. XC.--A REBUS
[Illustration]
The solution is _Wellington_.
No. XCV.--THE PUZZLED CARPENTER
The carpenter, anxious to stop a leak, was able to cut a board a foot
square from a board two feet square, which was pierced at regular
intervals by sixteen holes, by the following ingenious method:--
[Illustration]
No. XCVI.--NOT EASY WHEN YOU KNOW
The solution of the puzzling match rearrangement is as follows:--We
repeat the original five square diagram, from which four squares were to
be formed by rearranging three matches, and its solution below.
+-----+ +-----+
| | | |
| | | |
+-----+-----+-----+
| | | |
| | | |
+-----+-----+-----+
+-----+ +-----+
| | | |
| | | |
+-----+-----+-----+-----+
| | | |
| | | |
+-----+ +-----+
No. XCVII.--SIMPLICITY
When we have constructed this figure with five matches, we can remove
three of the matches, and then replace two of them so as to form a
similar figure, by moving any three of them a short distance, and then
replacing the two that are left behind, in their original positions!
This “catch” finds many victims.
/\
/ \
/ \
------
\ /
\ /
\/
No. XCIX.--FROM THE MATCHBOX
The diagram below shows how eight matches can be removed from the
nine-square arrangement so as to leave two squares on the table.
----- ----- -----
| |
| |
-----
| | | |
| | | |
-----
| |
| |
----- ----- -----
MISSING WORDS SOLUTIONS
1
What tempting _sprite_ beguiled the boy to sample
Fruit that hung _ripest_ on the parson’s trees?
_Stripe_ upon _stripe_ shall make him an example
When the stern _priest_ has brought him to his knees.
2
Man of the dark room, _traces_ none I find
Upon these _cartes_ of likeness to my features.
_Carest_ thou naught, O man of evil mind,
Who _racest_ thus to libel fellow creatures?
Evil thus done _reacts_ upon the doer,
The _carets_ in thy conduct, sir, are many;
_Recast_ thy life, and let thy crimes be fewer,
Or all thy _crates_ of good won’t fetch a penny!
3
The missing words all spelt with the same
seven letters, are _tho’ near_, _a hornet_, _or neath_, _nor
hate_, _or then a_, _near hot_, _than o’er_, _ten hoar_, _the
roan_, and _eat horn_.
4
’Neath _bluest_ Indian seas fierce battles spread
’Twixt _subtle_ hermit-crabs and other shellfish!
With horrid _bustle_ when their foes are dead
These crabs declare their shells _sublet_, so selfish.
5
Though _seated_ secure and _sedate_ in his cage,
Our Polly, when _teased_, will fly into a rage.
6
All courtly honours are but light
As grains that from a _grater_ fly;
And he who wears the _Garter_ bright
May haply in a _garret_ die.
7
I’d rather from a _manger_ eat,
I give my sacred word,
Than dine in slums where _ragmen_ meet,
And _German_ pedlars herd.
8
A much married _grandee_ of Cadiz
Once _angered_ some riotous ladies.
To _derange_ him they chucked
A _grenade_, but he ducked,
Which _enraged_ these rude ladies of Cadiz.
9
A lass and her lover were _warned_ by the sky
Not to _wander_ too far where no shelter was nigh.
She lingered behind, and _drew an_ old church,
St. _Andrew_ by name, and was left in the lurch.
She tried a short cut through the park on the grass,
But sternly the _warden_ forbade her to pass.
Then helplessly stood the disconsolate maid,
When the lad she was soon to _wed ran_ to her aid.
10
When _weather_ smiles, and sunbeams play
On flowers that _wreathe_ and deck the green,
_Whate’er_ can match the scene so gay
_Whereat_ they crown the May-day queen?
11
’Tis said of William, while his forces rested
On Albion’s _shores_, when Harold had been bested,
He made the _shoers_ of his _horses_ fuse
Saxon spear-heads, to fashion into shoes.
12
Happiness, brighter than _rubies_, is dead;
Life’s battle, sterner and _busier_ now,
Heals the sore _bruise_ that love left as it fled,
_Buries_ remembrance of long-broken vow!
13
Press critics fall on me like sharks:
“A shameless _patcher_ of odds and ends,
No _chapter_ original,” and more remarks
In adverse mood. But stay, my friends,
He _carpeth_ best who hath his record clean;
My faults are published, yours are yet unseen!
14
_Plates_ are his _staple_, fashion-forms of grace
In _pastel_ deftly hinted.
_Pleats_ soft as _petals_, crowned by Beauty’s face,
In _palest_ hues are tinted.
15
When Kate _no heart_ _nor heat_ displayed
_He ran to_ hide a tear;
“All love is dead _on earth_,” he said.
“_Another_ I’ll _not hear_!”
16
Some grinding at the _tholes_ must toil,
Down-trodden _helots_ of to-day;
While other children of the soil
In vast _hotels_ their wealth display.
17
Betrayed by faithless friends, in _sadder_ mood
Man _dreads_ his fellows as the _adder’s_ brood.
18
With divers _inks_ his _skin_ is scarred,
He hangs a bangle in his nose;
Such marks secure his _kin’s_ regard,
Exalt his fame, and _sink_ his foes.
19
_Steward_, who, as we _west’ard_ roll,
_Drawest_ for me the foaming bowl,
And _wardest_ off unfriendly spray
With oilskin-cape, thou shalt not say
“In vain I’ve _strawed_ my favours here.”
I’ll think of thee when port is near!
20
With high _ideals_ for hearts and hands,
These _ladies_ _sailed_ for distant lands.
21
The _premiss_ of his speech did not
_Impress_ his audience a jot.
They greeted all he said thereafter
With _simpers_, smiles, and open laughter.
22
To convent shrine at break of day
With _palms_ together nuns repair;
Mid gleaming _lamps_ they kneel and pray,
And chanted _psalm_ allays each care.
23
Here once, as a hag is bedizened with paint,
A _devil_ _lived_, _veil’d_ in the garb of a saint.
24
The missing words of the lines “In praise of Sussex,” are _apers_,
_rapes_, _spear_, _spare_, _pears_, _reaps_, _parse_, _pares_, all spelt
with the same letters.
25
The missing words are _there_, _ether_, and _three_.
26
The missing words are _trades_, _daters_, _treads_, _darest_, and
_read’st_.
27
The _Tsar_ with _arts_ importunate
To rule his _tars_ may try;
His _star_ is so unfortunate
That “_rats_” they may reply!
28
The missing words are _mace_, _acme_, and _came_.
29
The missing words are _esprit_, _sprite_, _priest_, _stripe_, and
_ripest_.
30
Of all destructive country pests
The farmer _loves_ _voles_ least;
He cannot yet the puzzle _solve_
How to suppress the beast!
31
The “Fresh Air Fund” missing words are given below in italics:--
OH THE _LUSTRE_ OF THE _RESULT_
The _slimes_ of darkest London are radiant with _smiles_,
You can _read_ it in their _dear_ little faces:
So wherever you _reside_ let it be your heart’s _desire_
To ease the _cares_ and sorrows of all _races_!
32
She _rouges_ in vain, “Men are _rogues_, and as shy
As _grouse_ in October,” she says with a sigh.
33
When good men lapse the _Serpent_ grins,
When one _repents_ he swears;
And strives to set his former sins
Against his _present_ prayers.
34
His hands and face were _swart_, and sad
Upon the _straw_ a gipsy lad
Lay: as the breeze his temples fanned
He counted _warts_ on either hand.
35
In yon grey _manse_ an old divine
Taught me my “_mensa_” to decline,
And verbs with _names_ of mood and tense;
But while I plodded on apace
I had to keep the _means_ of grace,
And close his prayers with loud _amens_.
36
No reckless _drawer_ of the sword,
He _warred_ his fatherland to save.
Fighting for freedom, not _reward_,
Now _warder_ of the eastern seas.
37
A fair _design_, though _singed_ and frayed,
The critic _deigns_ to own,
And it might interest the trade
If _signed_ by some one known.
38
In his _latter_ days, as when he was young,
The _tatler_ indulges in _rattle_ of tongue.
39
The missing words indicated in the lines which begin
A cylindrical lock
Where no key can be found.
are a _ringlet_, _triangle_, _relating_, _altering_, and _integral_,
which are all spelt with the same eight letters.
40
The lines with missing words, which are increased each time by one
letter, run thus:--
A lover of _an_ unkind fair
Were less than _man_ did he not _moan_,
“Mine is no _nomad_ life, I swear,
It dwells in this _domain_ alone.
Grant me thy love, like _diamond_ chaste
_On diadem_, lest thou live unwooed,
_Doomed in a_ lonely life to waste
The treasure of sweet _maidenhood_.”
41
The missing words are _bared_, _beard_, _debar_, _bread_.
42
THE PAUPER’S PLAINT
Pale penury that _rivest_ social bands,
And any link that _rivets_ worth to fame,
Take ye the blame for my inactive hands,
I _strive_ in vain to build upon the sands,
Without a _stiver_, who can make a name?
43
Mr Backslide, afflicted with weakness of mind,
_Cantered_ over to Lushington’s inn, where he dined.
He _recanted_ the pledge he had taken as handy,
And emptied forthwith a _decanter_ of brandy.
44
The missing words are indicated below by italics:--
A _sutler_ sat in his _ulster_ grey,
Watching the moonbeams _lustre_ play
On a keg that in the bushes lay;
And these were the words of his song:--
“Thou _rulest_ the weak, thou _lurest_ the strong,
To thee the _result_ of bad deeds doth belong.”
And the leaves with a _rustle_ took up the sad song.
It would be difficult to find a better specimen than this of seven words
spelt with the same letters.
45
In these lines each of the words in italics is longer by one letter than
the one before, the same letters being carried on in varied order:--
Nature _I_ love _in_ every land,
On burning plain, by wooded rill;
Where _Ind_ is girt by coral strand,
Or _Edin_ rears her castled hill.
Then _deign_ from me the tale to hear,
How, true to one _design_, the bee
Once _singled_ out keeps year by year
The _leadings_ by her instinct given,
Which teach her, wheresoe’er she roam,
In every clime beneath the heaven,
To build the same _six-angled_ home.
46
The missing words are _smite_, _times_, _emits_, _items_, and _mites_.
47
The missing words of the Farmyard puzzle are printed in italics:--
All his flock from _danger_ rough,
To the _garden_ ran apace,
Where their _gander_, old and tough,
_Ranged_, the guardian of his race.
48
Come, landlord, fill the flowing _pots_,
Until their _tops_ run over;
For in this _spot_ to-night I’ll _stop_,
To-morrow _post_ to Dover!
49
The four missing words are _silent_, _listen_, _enlist_, and _tinsel_,
which are all spelt with the same letters.
50
Some men their _teams_ escorted on their way,
When “_Mates_ look here!” I heard a driver say:
“It _tames_ our pluck to toil like _steam_ all day,
When, wanting _meats_, we starve on wretched pay.”
51
WISDOM WHILE YOU WAIT
As a _general_ _gleaner_ of facts you’ll find
Our Encyclopædia _enlarge_ the mind.
52
The missing words are _nectar_, _Cretan_, _canter_, _trance_, _recant_.
53
_I Satan_ but for rebel act
Without _a stain_ should be;
But this _is at an_ end, in fact
None find _a saint_ in me.
54
“Oh for a _break_ in this vast solitude,
This endless rise and fall of _brake_ and moor!”
Soliloquised a _baker_ in sad mood,
As through the lonely hills the staff of life he bore.
55
THE SEA SERPENT
’Twas in _mid-ocean_ that we saw him play,
Like a _demoniac_ in his sports, and they
Amused us, as a good _comedian_ may.
56
Soup is _on table_ for a _notable_ divine,
Who with _no table_ is _not able_ to sit down and dine.
57
Sweet as the _rose_ and cruel as its thorn,
_Eros_ thy power is great, thy pity scorn.
Swift as the _roes_ that through the forest fly,
Deep as the _ores_ that deepest hidden lie,
Is thine own _sore_ to hapless mortals given,
Semblance of darkest hell or brightest heaven.
58
The missing words, dedicated to the Fresh Air Fund, read thus:--
GOOD _TIMES_ FOR CITY _MITES_
My pipe _emits_ for _me its_ charms, that yield
Pictures and _items_ of a children’s day.
Lest conscience _smite_ I _sit me_ down to say
My _mites_ shall send some City _mites_ afield.
59
He said “you _Cretan_,” when one lied,
He said “don’t _canter_,” when one hied,
His glass held _nectar_ at his side,
He can _recant_ what he denied.
60
Mr Snip, the _agnostic_, was _coasting_ a hill,
With a bag of new _coatings_ for stock;
When a runaway motor-car gave him a spill
Which scattered his doubts with the shock.
61
_Pales_ her fair cheek, and back o’er all
The _lapse_ of years _leaps_ memory.
Those wedding _peals_ to her recall
The _pleas_ he urged so tenderly.
62
Two burglars attempted to _rifle_ a house,
But the _filer_ was heard, though as still as a mouse.
When challenged at once he a _flier_ became,
But caught as a _lifer_ he finished his game.
63
The _licensed_ fool in olden days
Gave kings advice in jesting phrase;
He’s _silenced_ now: the modern throne
_Declines_ all follies but its own.
64
Days of _dearth_, and times of evil,
Starving girls with _thread_ do toil,
No man _dareth_ feast or revel,
Hushed is _hatred_ and turmoil.
65
Who _reineth_ in his pride and rage,
To _neither_ vice a prey,
May hope to reach a green old age,
And find _therein_ his stay.
66
This is the full text of Moore’s witty reply, when Limerick courted him
as her member, and the “boys for fun’s sake” asked him to what party he
belonged:--
“I’m of no party as a man,
But as a poet _am--a--tory_!”
67
Is England _Israel_? That this is so
A solemn _serial_ aspires to show.
By most ignored, the theme _is real_ to some,
Who gravely to the same conclusion come.
Like _Ariels_ o’er obstacles they soar,
And if an _earl is_ ’vert they rave the more.
68
Off to the links is now their cry,
For golf is man’s _idolatry_:
Be not _dilatory_ or slow,
_Adroitly_ hit the ball will go.
69
No maid e’er _resided_, North, South, East, or West,
More _desired_ than she who _derides_ Love’s request.
70
Though in _adversity_ I be,
It is, alas! _sad verity_
No _vestry aid_ comes nigh to me.
71
_Mastering_ his pride the royal James
Came down upon the _streaming_ Thames;
Like _emigrants_ his court repair
To breath _St Germain_’s freer air.
72
The drop letter lines are as follows:--
With lily leaves his oars are _trifling_,
Her eager hands their treasures _rifling_.
To the fair winds all cares _I fling_,
And echo faintly answers _fling_!
73
The solution of the enigma with missing letters:--
“There was no good ... in the d...y, so the klim,” is--
There was no good air in the dairy, so the milk turned.
74
But unmerciful disaster followed fast and followed faster.
75
If you write _stale_ _tales_, at _least_ do not _steal_ the _slate_.
76
The six missing words are _Siren_, _risen_, _Erin’s_, _reins_, _rinse_,
_resin_.
77
A man of _parts_ had caught a _sprat_,
And it was windy weather;
“Give me my _strap_,” he cried, “to fix
My fish and _traps_ together.”
78
The missing words are _Cesar_, _acres_, _races_, _cares_, _scare_.
79
Buy my ripe _melons_, my _lemons_ who’ll buy?
Don’t look so _solemn_, but take some and try!
80
He who _nips_ may _snip_ at last,
How to _spin_ we show;
Take a sixpence, hold it fast,
Press the _pins_ and blow!
[Illustration]
PRINTED BY M‘LAREN AND CO., LTD., EDINBURGH.
Transcriber’s Notes
Inconsistent spelling, hyphenation, capitalisation, etc. and lay-out
have been retained, except as mentioned below. The same applies to
repetitions, (factual) errors, mistakes, unclarities and
contradictions in the puzzles, riddles etc. and in the solutions
provided.
Depending on the hard- and software and their settings used to read
this text, not all elements may display as intended. Several of the
puzzles will only display as intended if a fixed-width font is used.
An attempt has been made to include, where possible, the illustrations
in this text. These are only rough approximations; the actual
illustrations (and therefore better representations of the book’s
contents) are available in the other formats provided at
in the available width. Some of the symbols used for this graphic
representation are used to approximate the symbols used in the book
rather than for their usual meaning.
Domino tiles are represented by blocks with the number of pips
inscribed rather than by the pip patterns (or they are left blank to
indicate back sides). For the chess problems, a schematic
representation has been used, in which dots represent black squares,
and K, Q, B, R, N, P and k, q, b, r, n, and p represent white and
black king, queen, bishop, rook, knight and pawn respectively.
Page I-7, Monster Magic Square: row 2 column 2 should be 48, not 41;
row 3 column 9 should be 92, not 72.
Page I-30, magic triangle, bottom row 0 should be 8 (as in the
solution on page I-150).
Page I-89, "on opposite sides of the central line": this should be
read "on opposite sides of the central lines" (both horizontal and
vertical).
Page I-130, mens’ tears: as printed in the source document.
Page I-131, An Illusion of Type: the phenomenon described may not work
with every font.
Page I-136, For the Children, last sentence: the opposite is true: If
this is an even quantity the coins or sweets in the right hand are
odd, and in the left even; if it is odd the contrary is the case.
Page II-130, number 81: some words were misprinted or missing
altogether; these have been added based on the context: ... the man
[fe]ll sick ...; [Ho]w ought his estate ...; and ... to [the] widow,
son and daughter.
Page II-148, Notable Chronogram: IAVDES should have read LAVDES, which
would result in the year 1894 (when the organ was blessed).
Page II-176, Solution LXXX: The positions of the dots are indicated in
the text only, not in the diagram.
Page II-204, Solution 65, 12 + ¹⁄₂ = ¹³⁄₂: the calculation only works
if the 12 were replaced with ¹²⁄₂ (or 6), which would be in accordance
with the description.
Page II-206, Solution 77: _two_ and _twenty_ pence should probably
read _two and twenty_ pence.
Page III-3 and III-111, No. III: The illustration in the question is
not the same as the one in the answer.
Page III-25, Begins 2 U U U up: possibly an error for Begins 2 UU U up
(cf. other repeated letters).
Page III-35, No. XXXV, five words: there are six words in the puzzle
(and in the solution).
Page III-53, No. LIII: the occupied squares on the chess board are
indicated by an X.
Page III-77, inspiréd strain: as printed in the source document.
Changes made
Some obvious minor typographical and punctuation errors and misprints
have been corrected silently.
Some minor lay-out inconsistencies have been standardised without
further remarks; where necessary, table and text-elements have been
re-arranged and aligned in accordance with the description given.
The part numbers have been inserted on the blank pages preceding each
part.
Throughout the book, items from one category (preceded by an Arabic
number) are occasionally printed split over two pages, with one or
more items from other categories (often preceded by a Roman numeral)
between the several parts. For this text, these split items have been
recombined on the page where they originally started, and references
to their respective parts have been deleted.
The part numbers (I, II and III) have been added to the page numbers
for easier reference.
Page I-141: "cigars" changed to "cigares" (French, 2x).
Page II-99, 6¹ changed to 6¹⁄₂.
Pages II-113 and II-185, illustration: reference letter "F" added.
Page II-199: "there they sold" changed to "these they sold".
Page II-225, Solution 6: "f _on_ d l _over_" changed to "a f _on_ d l
_over_".
Page III-7, No. VII: "BVT In trVth" changed to "bVt In trVth".
Page III-7 and III-44, No. VII and XLIV: The chronographs were printed
in small capitals and upper case letters; the former have been
transcribed as lower case letters to retain the meaning according to
the description.
Page III-41, No. 67: "And if -- ---- is ’vert" changed to "And if an
---- -- ’vert".
Page III-46: "chêrit" changed to "chérit".
Page III-67, illustration: unprinted asterisk added to the right-hand
arm of the cross.
Page III-78: "a jamais" replaced with "à jamais".
Page III-108: "stats" replaced with "stets".
Page III-123, Solution XLIII: V inserted in bottom line cf. puzzle.
Page III-124: "stripes" changed to "strips" cf. puzzle.
Page III-128: "86 diamonds and 6 children" changed to "36 diamonds and
6 children".
*** End of this LibraryBlog Digital Book "Twentieth Century Standard Puzzle Book - Three Parts in One Volume" ***
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