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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.
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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:--