Part 9

are 18, 26, 32, 24, _Rose_; 25, 33, 34, 28, 35, _Tulip_; 35, 28, 27, 21, _Pink_; 31, 32, 25, 24, 18, _Aster_; and, in similar ways, _Verbena_; _Salvia_; _Ivy_; _Lily_; _Lilac_; _Heliotrope_; _Fern_; and _Bell_.

No. XXXV

The solution of this little problem, set by Dr Puzzlewitz on his blackboard to test the powers of his young pupils--“What are the values of A and B, when 4 is the result of dividing A by B, or of subtracting B from A?”--

┏━━━━━━━━━━━━━┓ ┃ ┃ ┃ 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

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.

No. XLVI

Here is the key to Sam Loyd’s ingenious puzzle--

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--

No. XLVIII

The leap-frog puzzle is solved in nine hops thus:--

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--

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.

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--

No. LX

The dotted lines in this diagram show how the figure can be divided into nine parts by four straight cuts

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--

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--

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.

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.

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.

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:--

No. LXXVIII

This shows the shortest course--

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.

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.

No. XCII

The 5 maxims in these 36 cells--