┃ ┃
┃ A - B = 4 ┃
┃ ┃
┃ A ÷ B = 4 ┃
┃ ┃
┗━━━━━━━━━━━━━┛
is that A = 5¹⁄₃ and B = 1¹⁄₃.
No. XXXVI
This is the diamond squared:--
┌───┐
│ s │
┌───┼───┼───┐
│ h │ i │ s │
┌───┼───┼───┼───┼───┐
│ h │ i │ n │ t │ s │
┌───┼───┼───┼───┼───┼───┼───┐
│ s │ i │ n │ u │ o │ u │ s │
└───┼───┼───┼───┼───┼───┼───┘
│ s │ t │ o │ r │ m │
└───┼───┼───┼───┼───┘
│ s │ u │ m │
└───┼───┼───┘
│ s │
└───┘
in which the words read alike from top to bottom, and from left to
right.
No. XXXVII
This is the arrangement of the 32 letters in the 64 cells--
╔═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╗
║ │ A │ │ E │ I │ │ O │ ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ E │ O │ │ │ │ │ A │ I ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ │ │ A │ I │ E │ O │ │ ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ I │ │ O │ │ │ A │ │ E ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ O │ │ I │ │ │ E │ │ A ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ │ │ E │ O │ A │ I │ │ ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ A │ I │ │ │ │ │ E │ O ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ │ E │ │ A │ O │ │ │ I ║
╚═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╝
No A is in the same column, row, or diagonal with another A, no E with
another E, no I with another I, and no O with another O.
No. XXXVIII
This is the anagram square, with the letters, which in the former
diagram spelt the words _vote_, _wove_, _prow_, _call_, _stew_, _news_,
_core_, _nape_, recast into fresh words which now read alike from top to
bottom and from left to right of the square.
╔═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╗
║###│ C │###│ R │###│ O │###│ W ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ C │###│ L │###│ A │###│ W │###║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║###│ L │###│ O │###│ V │###│ E ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ R │###│ O │###│ P │###│ E │###║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║###│ A │###│ P │###│ E │###│ S ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ O │###│ V │###│ E │###│ N │###║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║###│ W │###│ E │###│ N │###│ T ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ W │###│ E │###│ S │###│ T │###║
╚═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╝
The empty squares and diagonal setting are necessary for this particular
puzzle, as the words would not form a word square if their letters were
placed below one another in the usual way.
No. XXXIX
The sentence formed with the ten letters above the line, which is the
key to this sum, is--_Add these up_. If these letters are numbered
consecutively 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, and the corresponding
figures are substituted for the numbers, the sum works out as is shown
below.
D U 2 9
E H 6 5
E D 8 3
A P 1 0
S T 7 4
----- -----
D E A 2 6 1
===== =====
No. XL
The four words, seek, slab, leek, moan, which were placed on the white
squares when recast form the following combination:--
╔═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╗
║###│ M │###│ A │###│ S │###│ K ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ A │###│ B │###│ L │###│ E │###║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║###│ S │###│ L │###│ O │###│ E ║
╟───┼───┼───┼───┼───┼───┼───┼───╢
║ K │###│ E │###│ E │###│ N │###║
╚═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╝
These fresh words read alike from side to side, and zigzag from top to
bottom.
No. XLI
These are the four words, recast by anagram from afar, task, seat, leal,
and which now form a perfect word square.
╔═══╤═══╤═══╤═══╗
║ F │ A │ S │ T ║
╟───┼───┼───┼───╢
║ A │ R │ E │ A ║
╟───┼───┼───┼───╢
║ S │ E │ A │ L ║
╟───┼───┼───┼───╢
║ T │ A │ L │ K ║
╚═══╧═══╧═══╧═══╝
No. XLII
The word square is recast thus--
╔═══╤═══╤═══╤═══╤═══╗
║ c │ r │ e │ s │ s ║
╟───┼───┼───┼───┼───╢
║ r │ e │ a │ c │ h ║
╟───┼───┼───┼───┼───╢
║ e │ a │ g │ e │ r ║
╟───┼───┼───┼───┼───╢
║ s │ c │ e │ n │ e ║
╟───┼───┼───┼───┼───╢
║ s │ h │ r │ e │ d ║
╚═══╧═══╧═══╧═══╧═══╝
Its words are spelt with the same letters as the words _chess_, _greed_,
_canes_, _rears_, _cheer_, which formed the original square, but did not
read alike from top to bottom, and from left to right, as these do.
No. XLIII
The five familiar proverbs hidden in this square of 169 letters are: A
rolling stone gathers no moss. Too many cooks spoil the broth. A live
dog is more to be feared than a dead lion. You cannot eat your cake and
have it. Peace hath her victories no less renowned than war.
R E N O W N E D T H A N W
S Y O U R C A K E A N D A
S T E T O B E F E A R H R
E A R K S S P O I L E A F
L E O O H E R S N T D V O
O T M O T L I N O H T E U
N O S C A L A G M E H I R
S N I Y G O R S O B A T S
E N G N E N O T S R N P A
I A O A M O O T S O A E W
R C D E V I L A H T D A S
O U O Y N O I L D A E C A
T C I V R E H H T A H E Z
No. XLIV
[Illustration]
If the shaded circles are cut out and the diagram is placed squarely
over the jumbled letters, with the I., II., III., IV. in turn at the top
left-hand corner, this sentence is disclosed--
Le premier Supplément du Journal de la Jeunesse a été publié dans le
Numéro du Dix-neuf Juin Mil huit cent soixante-quinze.
No. XLV
This is the way to reconstruct Sam Loyd’s black pony--so that, while its
legs and tail are strangely misplaced, they form the spirited outline of
a white galloping horse.
[Illustration]
No. XLVI
Here is the key to Sam Loyd’s ingenious puzzle--
[Illustration]
which shows the jockeys and horses in full racing trim.
No. XLVII
This is the inevitable result of the boy’s attempt to annex with his
mouth the sugar on the chair--
[Illustration]
No. XLVIII
The leap-frog puzzle is solved in nine hops thus:--
[Illustration]
First jump from stool 2, then from 5, 3, 6, 7, 1, 3, and 6 in turn to
the vacant stools.
No. LV
This diagram shows that the seven wheels, which spin so merrily when the
paper is rotated in the hand, can be divided off into separate
enclosures by only three straight lines--
[Illustration]
No. LVI
The diagram below shows how the market-gardener, keeping one-fourth of
his square field for himself in the shape of a triangle, was able to
divide the remainder so that each of his four sons had an equal portion
of similar shape--
[Illustation]
No. LVII
Here is a drawing of the perfect Latin cross--
[Illustation]
The position of the two long pieces does not readily suggest itself to
those who try to arrange the five on paper with a pencil.
No. LVIII
This diagram shows the effectual means taken by four rich men, whose
houses were further afield, to exclude four poor men from all access to
a central lake, that they might reserve the fishing for themselves.
[Illustration]
They built a high wall on the lines that are indicated which, while it
left a way for each of them to the water, altogether shut it away from
their poor neighbours.
No. LIX
This is the square that can be formed with the ten pattern pieces
given--
[Illustration]
No. LX
The dotted lines in this diagram show how the figure can be divided into
nine parts by four straight cuts
[Illustration]
which can be reunited to form a perfect cross.
No. LXI
This is a simple way by which the figure given can be divided by four
straight cuts into four equal and similar parts--
[Illustration]
No. LXII
This is the way to draw twenty-two straight lines within the circle at
right-angles to each other, so that they divide it into four similar
parts--
[Illustration]
and each part has three dots within its borders.
No. LXIII
These diagrams show how the upper triangle is divided into five parts,
which can be rearranged to form the equilateral triangle below.
[Illustration]
The originator of this ingenious novelty says, “The method of
construction is not shown, but its application is general, and the
result is easily verified by measurement.”
No. LXVI
This is an arrangement of the twenty-seven counters in nine rows, six in
a row, within the borders of an equilateral triangle.
*
╱ ╲
╱ ╲
* *
╱ ╲ ╱ ╲
╱ ╲ ╱ ╲
* * *
╱ ╲ ╱ ╲ ╱ ╲
╱ ╲ ╱ ╲ ╱ ╲
╱ * * ╲
╱ ╱ ╲ ╱ ╲ ╲
╱ ╱ ╲ ╱ ╲ ╲
╱ ╱ * ╲ ╲
╱ ╱ ╱ ╲ ╲ ╲
╱ ╱ ╱ ╲ ╲ ╲
╱ ╱ ╱ ╲ ╲ ╲
*─────*─────*───────*─────*─────*
╱ ╱ ╱ ╲ ╲ ╲
*─────*─────*───────────*─────*─────*
╱ ╱ ╱ ╲ ╲ ╲
*─────*─────*───────────────*─────*─────*
No. LXVII
All the cards of one colour, when placed alternately, can be brought
together in four moves, two at a time, thus--
┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐
│ A │ │ 2 │ │ 3 │ │ 4 │ │ 5 │ │ 6 │ │ 7 │ │ 8 │
│ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
│ ♠ │ │ ♡ │ │ ♣ │ │ ♢ │ │ ♣ │ │ ♢ │ │ ♣ │ │ ♡ │
└───┘ └───┘ └───┘ └───┘ └───┘ └───┘ └───┘ └───┘
Place two and three beyond eight; Place five and six between one and
four; Place eight and two between four and seven; Place one and five
between seven and three.
No. LXVIII
You can in a moment tell the number chosen on these cards, when you are
told on which of them it appears,
╔════════════════════════════════════════════════════════════════════╗
║┌───────────────┐┌───────────────┐┌───────────────┐┌───────────────┐║
║│ I. ││ II. ││ III. ││ IV. │║
║│ ││ ││ ││ │║
║│ 1 33 65 97││ 2 34 66 98││ 4 36 68 100││ 8 40 72 104│║
║│ 3 35 67 99││ 3 35 67 99││ 5 37 69 101││ 9 41 73 105│║
║│ 5 37 69 101││ 6 38 70 102││ 6 38 70 102││ 10 42 74 106│║
║│ 7 39 71 103││ 7 39 71 103││ 7 39 71 103││ 11 43 75 107│║
║│ 9 41 73 105││ 10 42 74 106││ 12 44 76 108││ 12 44 76 108│║
║│ 11 43 75 107││ 11 43 75 107││ 13 45 77 109││ 13 45 77 109│║
║│ 13 45 77 109││ 14 46 78 110││ 14 46 78 110││ 14 46 78 110│║
║│ 15 47 79 111││ 15 47 79 111││ 15 47 79 111││ 15 47 79 111│║
║│ 17 49 81 113││ 18 50 82 114││ 20 52 84 116││ 24 56 88 120│║
║│ 19 51 83 115││ 19 51 83 115││ 21 53 85 117││ 25 57 89 121│║
║│ 21 53 85 117││ 22 54 86 118││ 22 54 86 118││ 26 58 90 122│║
║│ 23 55 87 119││ 23 55 87 119││ 23 55 87 119││ 27 59 91 123│║
║│ 25 57 89 121││ 26 58 90 122││ 28 60 92 124││ 28 60 92 124│║
║│ 27 59 91 123││ 27 59 91 123││ 29 61 93 125││ 29 61 93 125│║
║│ 29 61 93 125││ 30 62 94 126││ 30 62 94 126││ 30 62 94 126│║
║│ 31 63 95 127││ 31 63 95 127││ 31 63 95 127││ 31 63 95 127│║
║└───────────────┘└───────────────┘└───────────────┘└───────────────┘║
║ ┌───────────────┐┌───────────────┐┌───────────────┐ ║
║ │ V. ││ VI. ││ VII. │ ║
║ │ ││ ││ │ ║
║ │ 16 48 80 112││ 32 48 96 112││ 64 80 96 112│ ║
║ │ 17 49 81 113││ 33 49 97 113││ 65 81 97 113│ ║
║ │ 18 50 82 114││ 34 50 98 114││ 66 82 98 114│ ║
║ │ 19 51 83 115││ 35 51 99 115││ 67 83 99 115│ ║
║ │ 20 52 84 116││ 36 52 100 116││ 68 84 100 116│ ║
║ │ 21 53 85 117││ 37 53 101 117││ 69 85 101 117│ ║
║ │ 22 54 86 118││ 38 54 102 118││ 70 86 102 118│ ║
║ │ 23 55 87 119││ 39 55 103 119││ 71 87 103 119│ ║
║ │ 24 56 88 120││ 40 56 104 120││ 72 88 104 120│ ║
║ │ 25 57 89 121││ 41 57 105 121││ 73 89 105 121│ ║
║ │ 26 58 90 122││ 42 58 106 122││ 74 90 106 122│ ║
║ │ 27 59 91 123││ 43 59 107 123││ 75 91 107 123│ ║
║ │ 28 60 92 124││ 44 60 108 124││ 76 92 108 124│ ║
║ │ 29 61 93 125││ 45 61 109 125││ 77 93 109 125│ ║
║ │ 30 62 94 126││ 46 62 110 126││ 78 94 110 126│ ║
║ │ 31 63 95 127││ 47 63 111 127││ 79 95 111 127│ ║
║ └───────────────┘└───────────────┘└───────────────┘ ║
╚════════════════════════════════════════════════════════════════════╝
by adding together the numbers at the top left-hand corner of these.
No. LXIX
This diagram shows that the postman can take a course which involves
fewer turnings than that indicated, when he had to pass round eighteen
corners.
●┅┅┅●┅┅┅●┅┅┅●┅┅┅●┅┅┅●┅┅┅●┅┅┅●
┇ ┇
● ●┅┅┅●┅┅┅●┅┅┅●┅┅┅●┅┅┅● ●
┇ ┇ ┇ ┇
● ● ●┅┅┅●┅┅┅●┅┅┅● ● ●
┇ ┇ ┇ ┇ ┇ ┇
● ● ● ●┅┅┅○ ● ● ●
┇ ┇ ┇ ┇ ┇ ┇ ┇ ┇
● ● ● ● ● ● ● ●
┇ ┇ ┇ ┇ ┇ ┇ ┇ ┇
● ● ● ● ● ● ● ●
┇ ┇ ┇ ┇ ┇ ┇ ┇ ┇
● ● ● ● ● ●┅┅┅● ●
┇ ┇ ┇ ┇ ┇ ┇
●┅┅┅● ●┅┅┅● ●┅┅┅●┅┅┅●┅┅┅●
It will be seen that he has to turn only fifteen times.
No. LXX
This shows how a square can be divided into three parts, so that these
can be reunited to form No. 2 and No. 3 of the diagram.
[Illustration]
[Illustration: 1.]
[Illustration: 2.]
[Illustration: 3.]
Try it with scissors and paper or cardboard.
No. LXXI
┏━━━┯━━━┯━━━┯━━━┯━━━┯━━━┯━━━┯━━━┓
┃ │###│ │###│ │###│ │###┃
┠───┼───┼───┼───┼───┼───┼───┼───┨
┃###│ │###│ │###│ │###│ ┃
┠───┼───┼───┼───┼───┼───┼───┼───┨
┃ │###│ │###│ │###│ │###┃
┠───┼───┼───┼───┼───┼───┼───┼───┨
┃###│ │#♘#│ ♖ │#♚#│ ♖ │###│ ┃
┠───┼───┼───┼───┼───┼───┼───┼───┨
┃ │###│ │###│ │###│ │###┃
┠───┼───┼───┼───┼───┼───┼───┼───┨
┃###│ │###│ │###│ │###│ ┃
┠───┼───┼───┼───┼───┼───┼───┼───┨
┃ │###│ │###│ │###│ │###┃
┠───┼───┼───┼───┼───┼───┼───┼───┨
┃###│ │###│ │###│ │# #│###┃
┗━━━┷━━━┷━━━┷━━━┷━━━┷━━━┷━━━┷━━━┛
This position fulfils the conditions of the puzzle. Obviously it could
not occur in actual play.
No. LXXV
The dotted lines in this diagram show where the flag with a cross taken
out from its centre must be cut, so that the two pieces can be rejoined
to form a perfect flag.
[Illustration]
The piece on the right is moved upward, and to the left.
No. LXXVI
This is a way in which the eleven parts can be readjusted to form a
square:--
[Illustration]
No. LXXVIII
This shows the shortest course--
[Illustration]
This track takes him completely round every block, passing only once
round four of them.
No. LXXIX
Here is a very simple and symmetrical arrangement, by which on a board
of 36 squares twelve counters are so placed that there are two, and two
only, on each line, column, and diagonal.
╔═══╤═══╤═══╤═══╤═══╤═══╗
║ ◎ │ │ │ │ │ ◎ ║
╟───┼───┼───┼───┼───┼───╢
║ │ │ ◎ │ ◎ │ │ ║
╟───┼───┼───┼───┼───┼───╢
║ │ ◎ │ │ │ ◎ │ ║
╟───┼───┼───┼───┼───┼───╢
║ │ ◎ │ │ │ ◎ │ ║
╟───┼───┼───┼───┼───┼───╢
║ │ │ ◎ │ ◎ │ │ ║
╟───┼───┼───┼───┼───┼───╢
║ ◎ │ │ │ │ │ ◎ ║
╚═══╧═══╧═══╧═══╧═══╧═══╝
There are other arrangements which fulfil the conditions.
No. LXXXI
In this nest of triangles of five tiers there are 1196 separate
triangles, or nearly double the number (653) of a similar nest of four
tiers.
[Illustration]
In such a figure with 10,000 tiers there would be 6,992,965,420,332
different triangles!
No. LXXXII
The match puzzle, in which eight matches set in a row are to be
rearranged in four pairs, by passing one match over two four times--
║ ║ ║ ║ ║ ║ ║ ║
║ ║ ║ ║ ║ ║ ║ ║
║ ║ ║ ║ ║ ║ ║ ║
║ ║ ║ ║ ║ ║ ║ ║
║ ║ ║ ║ ║ ║ ║ ║
║ ║ ║ ║ ║ ║ ║ ║
is solved, if the matches are numbered 1, 2, 3, 4, 5, 6, 7, 8, by moving
4 to 7, 6 to 2, 1 to 3, and 5 to 8.
No. LXXXIII
The lower diagram shows how, when three matches are removed from the
four squares, the remaining nine can be readjusted to represent three
squares--
══════ ══════
║ ║ ║
║ ║ ║
║ ║ ║
═══════ ══════
║ ║ ║
║ ║ ║
║ ║ ║
══════ ══════
/-----\/-----\
/-----\
═════ ═════
║ ║ ║ ║ ║
║ ║ ║ ║ ║
═════ ═════
No. LXXXIV
This diagram shows how different arrangements of four matches are
possible in all the thirty-six cells of the square.
│ ╲ ╱ │
│ ╳ │ = 1
│ ╱ ╲ │
│ │ │
│ │ ── │ = 1
│ │ │
___
╱ │
╲ ╱ │ = 1
V │
│ │ │
│ ──+── │ = 2
│ │ │
│ │
│ │
│ │
─── = 2
│
│
│
│ │ │ │
│ │ │ │ = 4
│ │ │ │
╲ ╱ │
╲ ╱ ── │ = 4
V │
╲ ╱
╲ ╱
V
───── = 5
│
│
│
___
╱ │
╱ ── │ = 6
╱ │
___
╱
╱
╱
─── = 7
│
│
│
╲ ╱ │ │
╲ ╱ │ │ = 7
V │ │
╲ ╱ │
╳ ── │= 9
╱ ╲ │
│ │ │
│ │ ── │ = 10
│ │ │
╲ ╱
╳
╱ ╲
─── = 10
│
│
│
│ │
│ │
│ │
─── = 11
│
│
│
╲ ╱ │ │
╳ │ │ = 12
╱ ╲ │ │
│ ╱│
│ ─┼─ = 14
│ │
╲ ╱ ╲ ╱
╳ ╲ ╱ = 15
╱ ╲ V
╲ ╱ ╲ ╱
╳ ╳ = 20
╱ ╲ ╱ ╲
╲ ╱ │
╳ │ = 40
╱ ╲ │___
╱│ │
─+─ │ = 41
│ │
│ │
│ ─── │ = 49
│___ │
│
│
│___
───── = 50
│
│
│
│ │ │
│ │ │ = 52
│___ │ │
│ ╲ ╱
│ ╳ = 60
│___ ╱ ╲
___
│ │ ╱
│ │ ╱ = 117
│ │ ╱
___
│ ╱ │
│ ╱ │ = 171
│ ╱ │
___
╱ │ │
╱ │ │ = 711
╱ │ │
│╲ ╱│
│ V │ = 1000
│ │
────
│ │
│ │ = 0
│ │
────
│
│
│ 1
─── = ───
│ │ 2
│ │
│ │
│
│
│ 1
───── = ───
╲ ╱ 5
╲ ╱
V
│
│
│ 1
──── = ───
___ 7
╱
╱
╱
│
│
│ 1
─── = ───
╲ ╱ 10
╳
╱ ╲
│
│
│ 1
─── = ───
│ │ 11
│ │
│ │
│
│
│ 1
──── = ───
│ 50
│
│__
In every case a whole number or a fraction is represented, with such
signs or lines as are necessary, and only four matches are used.
No. LXXXV
It will be seen from the diagram below that the sentence, when filled in
as required, is “Rise to vote, sir.”
╔═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╗
║ R | I | S | E | T | O | V | O | T | E | S | I | R ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ I | I | | | | | | | | | | I | I ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ S | | S | | | | | | | | S | | S ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ E | | | E | | | | | | E | | | E ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ T | | | | T | | | | T | | | | T ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ O | | | | | O | | O | | | | | O ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ V | | | | | | V | | | | | | V ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ O | | | | | O | | O | | | | | O ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ T | | | | T | | | | T | | | | T ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ E | | | E | | | | | | E | | | E ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ S | | S | | | | | | | | S | | S ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ I | I | | | | | | | | | | I | I ║
╟───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───╢
║ R | I | S | E | T | O | V | O | T | E | S | I | R ║
╚═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╝
As this sentence is a perfect palindrome, and reads alike from either
end, it can be traced in a great number of different directions.
No. LXXXVII
This subtraction sum may be very neatly worked, without reducing the
distances to inches, thus:--
╔═══════════════════════════════════════════════╗
║miles furlongs rods yards feet inches║
║ 1 „ 0 „ 0 „ 0 „ 0 „ 0 ║
║ 7 „ 39 „ 5 „ 1 „ 5 ║
║ ─────────────────────────────────────────── ║
║ 0 „ 0 „ 0 „ 0 „ 0 „ 1 ║
║ ═══════════════════════════════════════════ ║
║ ║
╚═══════════════════════════════════════════════╝
Instead of borrowing one foot, we borrow half-a-foot--_i.e._, 6 inches;
taking 5 from the 6 we have 1 as a remainder; now carrying the 6 inches
to the 1 foot, and borrowing half a yard, and subtracting, we have 0 as
remainder; carrying the half-yard to the 5 yards, we borrow the full
5¹⁄₂ yards, which are one rod, and proceed in the usual manner
afterwards, with the result that is shown.
No. LXXXIX
This is an arrangement of nine counters on the irregular board of 67
squares.
┏━━━┯━━━┯━━━┯━━━┯━━━┯━━━┯━━━┯━━━┯━━━┓
┃###| |###| |###| |###| |#●#┃
┗━━━╅───┼───┼───┼───┼───┼───┼───╆━━━┛
┃###| |#●#| |###| |###┃
┠───┼───┼───┼───┼───┼───┼───┨
┃ ● |###| |###| |###| ┃
┠───┼───┼───┼───┼───┼───┼───┨
┃###| |###| |###| ● |###┃
┗━━━╅───┼───┼───┼───┼───╆━━━┛
┃#●#| |###| |###┃
┏━━━╃───┼───┼───┼───┼───╄━━━┓
┃###| |###| |#●#| |###┃
┠───┼───┼───┼───┼───┼───┼───┨
┃ |###| |###| |###| ● ┃
┏━━━╃───┼───┼───┼───┼───┼───┼───╄━━━┓
┃ ● │###| |###| |###| |###│ ┃
┠───┼───┼───┼───┼───┼───┼───┼───┼───┨
┃###| |###| |#●#| |###| |###┃
┗━━━┷━━━┷━━━┷━━━┷━━━┷━━━┷━━━┷━━━┷━━━┛
No two counters are in the same row, column, or diagonal.
No. XC
This is the arrangement of nine cards in ten rows, three in each row--
┌───┐ ┌───┐ ┌───┐
│ K │ │ Q │ │ K │
│ │ │ │ │ │
│ ♢ │ │ ♠ │ │ ♡ │
└───┘ └───┘ └───┘
┌───┐ ┌───┐ ┌───┐
│ A │ │ A │ │ A │
│ │ │ │ │ │
│ ♣ │ │ ♢ │ │ ♠ │
└───┘ └───┘ └───┘
┌───┐ ┌───┐ ┌───┐
│ 1 │ │ K │ │ J │
│ 0 │ │ │ │ │
│ ♡ │ │ ♣ │ │ ♢ │
└───┘ └───┘ └───┘
No. XCI
The following diagram shows how the two ladies and their squires
represented by white Knights and black, and dressed to impersonate
Light, Liberty, Love, and Learning, started from the four comer squares,
and stepped a figure which exhibited at each pause a revolving square,
and in three paces came together in the centre, by a course traced upon
the lines of their combined monograms.
[Illustration]
No. XCII
The 5 maxims in these 36 cells--
╔════════╤════════╤════════╤════════╤════════╤════════╗
║ │ │ │ │ │ he ║
║ tell │you know│ tells │ knows │ tells │ should ║
║ │ │ │ │ │ not ║
╟────────┼────────┼────────┼────────┼────────┼────────╢
║ │ you │ │ thinks │ │ is ║
║ do │ think │ does │ of │ does │ not ║
║ │ of │ │ │ │ good ║
╟────────┼────────┼────────┼────────┼────────┼────────╢
║ │ │ │ │ │ ║
║ believe│you hear│believes│ hears │believes│is false║
║ │ │ │ │ │ ║
╟────────┼────────┼────────┼────────┼────────┼────────╢
║ │ │ │ │ │ ║
║ spend │you have│ spends │ has │ spends │he needs║
║ │ │ │ │ │ ║
╟────────┼────────┼────────┼────────┼────────┼────────╢
║ │ │ │ │ │ is ║
║ judge │ you see│ judges │ sees │ judges │ not ║
║ │ │ │ │ │ there ║
╟────────┼────────┼────────┼────────┼────────┼────────╢
║ │ │ │ │ │ ║
║ never │ all │ he who │ all he │ often │ what ║
║ │ │ │ │ │ ║
╚════════╧════════╧════════╧════════╧════════╧════════╝
are disentangled by reading the lowest line with each of the upper ones
in turn. Thus the first maxim runs:--“Never tell all you know, he who
tells all he knows often tells what he should not,” and so on
throughout.
No. XCIII
The dislocated circle is solved by making a single cut through the
dotted line shown in the diagram below, and join up the pieces.
[Illustration]
The second diagram shows how this figure is arrived at, by drawing three
similar and intersecting circles, which have their centres at the angles
of an equilateral triangle. The piece cut off by the dotted line
corresponds to the section that completes the circle below.
No. XCV
The catch-words Cleans, Scrubs, Scours, Polishes, which proclaim the
merits of an “Old Dutch Cleanser” on the sails of this windmill,
[Illustration]
can be recast so that the same letters form the singularly appropriate
sentence--
“O rub on, sir, success spells cash!”
No. XCVI
The following diagram shows the solution of this new chess puzzle, and
fulfils its conditions that no Queen should attack a Queen, no Rook a
Rook, no Bishop a Bishop, and no Knight a Knight.
╔═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╗
║ B ║#B#║ B ║#B#║ Q ║#R#║ B ║#B#║
╟───┼───┼───┼───┼───┼───┼───┼───║
║###║ N ║#R#║ N ║###║ N ║###║ Q ║
╟───┼───┼───┼───┼───┼───┼───┼───║
║ N ║#R#║ N ║#Q#║ N ║###║ N ║#B#║
╟───┼───┼───┼───┼───┼───┼───┼───║
║#Q#║ N ║###║ N#║ R#║ N ║###║ B ║
╟───┼───┼───┼───┼───┼───┼───┼───║
║ B ║###║ N ║###║ N ║###║ Q ║#R#║
╟───┼───┼───┼───┼───┼───┼───┼───║
║#B#║ Q ║###║ N ║###║ N ║#R#║ N ║
╟───┼───┼───┼───┼───┼───┼───┼───║
║ N ║###║ N ║#R#║ N ║#Q#║ N ║###║
╟───┼───┼───┼───┼───┼───┼───┼───║
║#R#║ B ║#Q#║ N ║#B#║ B ║#B#║ N ║
╚═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╝
Mr Dudeney explains that only 8 Queens or 8 Rooks can be thus placed
upon the board, while the greatest number of Bishops is fourteen, and of
Knights thirty-two. But as all Knights must be placed on squares of the
same colour, while the Queens occupy four of each colour, and the
bishops seven of each colour, it follows that only twenty-one Knights
can be placed, and the arrangement shown above contains the maximum
number of these pieces under the conditions.
No. CII
This diagram shows the order in which the syllables or words of the
eight-line verse are to be read on the course of a Knight’s moves at
chess--
╔══════╤══════╤══════╤══════╤══════╤══════╤══════╤══════╗
║ 14 │ 55 │ 22 │ 37 │ 12 │ 51 │ 18 │ 35 ║
║ sor │ to │ king │ good │ say │ luck │ loy │ eth ║
╟──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────╢
║ 23 │ 38 │ 13 │ 54 │ 17 │ 36 │ 11 │ 50 ║
║ and │ moth │ a │ soon │ dis │ our │ to │ bad ║
╟──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────╢
║ 56 │ 15 │ 40 │ 21 │ 52 │ 9 │ 34 │ 19 ║
║ place│ ry │church│ his │ force│ is │ hat │ al ║
╟──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────╢
║ 39 │ 24 │ 53 │ 16 │ 33 │ 20 │ 49 │ 10 ║
║ er │ queen│ him │ wight│ he │ to │ may │ truth║
╟──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────╢
║ 2 │ 57 │ 28 │ 41 │ 8 │ 61 │ 32 │ 47 ║
║ man │ his │ and │ and │ chess│ es │knight│ op’s ║
╟──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────╢
║ 25 │ 42 │ 1 │ 60 │ 29 │ 48 │ 7 │ 62 ║
║ a │ sneer│ the │ and │ un │ lawn │ of │ tates║
╟──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────╢
║ 58 │ 3 │ 44 │ 27 │ 64 │ 5 │ 46 │ 31 ║
║ cas │ that │ at │ less │ pawn │ no │ bish │ lant ║
╟──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────╢
║ 44 │ 26 │ 59 │ 4 │ 45 │ 30 │ 63 │ 6 ║
║ eth │ faith│ tles │ hath │ the │ gal │ in │ love ║
╚══════╧══════╧══════╧══════╧══════╧══════╧══════╧══════╝
They run thus:--
The man that hath no love of chess,
Is, truth to say, a sorry wight;
Disloyal to his King and Queen,
A faithless and ungallant Knight.
He hateth our good mother Church,
And sneereth at the bishop’s lawn;
May bad luck force him soon to place
His castles and estates in pawn!
No. CV
If such a network as is shown in the diagram below is drawn on clear
tracing-paper and placed on the page of a book, it will conceal the
words beneath it.
[Illustration]
But if, while lying close to the page, it is moved quickly round and
about, the letters and words will be distinctly seen, just as objects on
the other side of close lattice-work become visible as we pass them
quickly in a train.
No. CVI
These are the results of cutting, in the direction of the dotted lines,
completely round a simple paper ring, a ring with one twist, and a ring
with a double twist.
[Illustration]
We have (1) two simple rings; (2) one large-twisted ring; (3) two rings
linked together. If a third twist is given before cutting, a curious
knot is formed.
CVII
The string when it has been placed in the position shown in the diagram,
and two buttons larger than the hole have been fixed upon its ends can
be easily removed if the narrow slip of the leather is drawn through the
hole.
[Illustration]
CVIII
The scissors, when securely fastened, as is shown in the diagram,
[Illustration]
can be easily released by passing the loop upward through the handle,
and then completely over them.
CIX