Part 10
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
The primitive wolf-trap consisted of two circular fences higher than a wolf could scale, with a gate as was shown on the former diagram. To set the trap a lamb was placed in the safe centre, and the gate was opened as is shown below--
[Illustration]
Attracted by the bleating of the lamb, the wolf entered the outer circle, made his way round, and presently pushed aside the gate, which closed with a spring, and shut off all escape.
No. CXII
When you have told someone to think of a number between 5 and 15, and while you are not looking, to count upwards from the lowest card step, and round in the direction indicated by the arrow, until that number is reached, and then, starting afresh with “one” on that card to count backwards round the semi-circle, this time _not including the central upright or the steps below it_, until the number thought of is again reached, you can tell at once which is the final card arrived at, for it will be as many places _upwards on the left_ as there are _step cards and their upright_.
[Illustration]
Thus if there are 3 steps, it must always be the fourth card upwards on the left of the semi-circle. To keep up the puzzle, the number of steps should each time be changed, on the pretext that their number does not signify.
No. CXIII
This diagram shows how the apple may be divided into six pieces by two straight cuts, so that there shall be a gash in each piece.
[Illustration]
First cut the apple through the dotted line, then place the upper piece shown at the side of the larger piece, and make the second cut straight through, where the line is drawn.
No. CXVII
The sixpence under the middle of the tumbler can be easily removed thus--
[Illustration]
Slip larger coins under opposite edges of the tumbler to raise it slightly, and then scratch firmly on the cloth, from just outside the rim, in the direction you wish the sixpence to take. It will at once respond, and makes its own way gradually outside the circle that had surrounded it.
No. CXVIII
This is the way to draw the spiral--
[Illustration]
Tie a piece of strong thread with a loop at its end round the upper part of the windings of a screw. Drive the screw into a board, through the middle of a card, wind the thread down the screw so that its loop just reaches the card, place a pencil in this loop, and draw the spiral freely, unwinding the thread from the grooves of the screw, and keeping it always taut. A perfect spiral is the result.
No. CXXII.
The secret of the talking head is simple indeed when you know it.
[Illustration]
Between the front and two side legs of the table mirrors are fixed, which reflect the similar surroundings, so that the performer, kneeling behind these, and putting his head through a hole in the table top, completely conceals his body and limbs from the audience.
No. CXXV
The picture charade is completed thus--
[Illustration]
My first may blow the candle out, My second then comes in; My whole in water moves about Without an oar or fin--
and is solved by _Puffin_.
No. CXXVI
When the walnuts and cobnuts have been arranged as is shown on the diagram--
[Illustration]
they can be shifted so that they stand alternately, by moving two that are close together at a time, in four moves, as follows:--
(1) Move 2 and 3 beyond 8.
(2) Move 5 and 6 between 1 and 4.
(3) Move what are now 6th and 7th in the gap.
(4) Move what are now 1st and 2nd in the gap, and the alternate arrangement is complete.
No. CXXVII
The question suggested by this picture riddle is: Why is a waiter like a racehorse? And the solution is: Because he runs for cups and plates.
[Illustration]
WORD PLAY SOLUTIONS
1
The paradox--
Two words in our region of puzzledom pose, And claim, through the passage of years, That neither the pages of Johnson disclose, While either in Murray appears.
is solved by the lines--
This key unlocks our puzzle-box, Johnson and Murray both give “neither,” While, to complete the paradox, Murray and Johnson both give “either!”
2
The verse is completed thus--
Rude Eurus murmurs, trustful buds uncurl, Bulbs push, due culture nurtures fruitful flush; Thrush builds, full sunhued plumes furze tufts unfurl, Up bursts, pure flute-fugue, Bulbul’s tuneful gush.
3
The enigma--
I see my first, I see my next, And both I sigh and see Joined to my third, which much perplexed And sorely puzzled me. ’Twas fifty, and ’twas something more, Reversed ’twas scarce an ell, With first and next it forms a whole Clear as a crystal bell. What is my whole? A splendid tear Upheld in cruel thrall; Blow soft, ye gales, bright sun, appear! And bid it gently fall.
is solved by ICICLE.
4
The charade--
Take for my first a quadruped, Transpose one for my second; My whole, a biped, quick or dead Is dainty reckoned.
is solved by _Pigeon_ (_one_ becomes _eon_).
5
Byron’s enigma--
I am not in youth, nor in manhood, nor age, But in infancy ever am known; I’m a stranger alike to the fool and the sage, And though I’m distinguish’d in history’s page I always am greatest alone.
I am not in earth, nor the sun, nor the moon; You may search all the sky--I’m not there; In the morning and evening--though not in the noon-- You may plainly perceive me--for, like a balloon, I am midway suspended in air.
Though disease may possess me, and sickness and pain, I am never in sorrow nor gloom; Though in wit and in wisdom I equally reign, I’m the heart of all sin, and have long lived in vain, Yet I ne’er shall be found in the tomb!
is solved by the letter I.
6
I am bright as a whole Till you cut off my head; Then as black as a coal, Or a mortal instead. Shaken up and recast We with science are found, Read us back from the last And we live underground.
is solved by _Star_, _tar_, _arts_, _rats_.
7
Horace Smith’s charade--
In arts and sciences behold my first the watchword still, All prejudice must bend the knee before its iron will; Yet “Onward!” is the Briton’s cry--a cry that doth express A holy work but half begun, and speaks of hopefulness. In palace or in lonely cot its name alike is heard, And in the Senate’s lordly halls sit my second and my third. Strange paradox, though for my first my total is designed, Sad marks of vice and ignorance we in that whole may find.
is solved by _Reformatory_.
8
Untouched I tell of budding growth and life; Beheaded I lead upward more or less; Again--with varied fragrance I am rife; Again--but little value I express.
is solved by _Nascent_, _ascent_, _scent_, _cent_.
9
The enigma--
Search Holy Writ and you will see A victory was won by me. Behead me, and I may be found In water or on hilly ground. Behead again, and then transpose, A snare my letters now disclose. If yet again my head you sever, No matter how sharp-set or clever, ’Tis all in vain you look about, For no one yet has found me out.
is solved by _Sling_, _ling_, _gin_, _in_.
10
The charade--
Said a lawyer aside to his friend in the court, “Now I’d bet, were we not in this place, That my first is my second a bottle of port,” Then bright with my whole shone his face.
is solved by _Pleasure_.
11
The answer to the problem--
Six horse ’buses and four motor ’buses travel each hour from Temple Bar to the Bank. The horses take 15 minutes, and the motors 10 minutes on the journey.
If I come to Temple Bar, and wish to reach the Bank as soon as possible, shall I take the first horse ’bus that turns up, or wait for a motor? It must be assumed that I can only see a ’bus as it actually passes me--
is (1) Take a motor if it comes first.
(2) Take a horse ’bus if it comes first, and comes within 2¹⁄₂ minutes of waiting.
(3) Wait for a motor if a horse ’bus comes first, but does not come till after 2¹⁄₂ minutes.
As I may have to wait 0 minutes or 15 minutes, the average time of waiting will be 7¹⁄₂ minutes.
If I wait _x_ min., and a horse ’bus arrives, I should reach the Bank in 15 mins, if I took it.
If I waited longer for a motor, which, on the average, will now turn up in 7¹⁄₂ - _x_ mins., I should reach the Bank in 17¹⁄₂ - _x_ mins.
If, therefore, _x_ is greater than 2¹⁄₂, the motor is the quicker.
12
The historical charade--
My first, if foolishly or rashly taken, May mar the future prospects of your life. My second, by her fickle lord forsaken (Sad type of many a gentle, patient wife). May toil and moil to feed his many babies, While he goes flirting off with other ladies. The thrifty monarch of a former age My whole a place in Britain’s history fills. Immortalised in Shakespeare’s magic pages As one who’d fain reform his tailor’s bills!
is solved by _Stephen_ (Step-hen).
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My _second_, worn with pompous pride, My _first_ had dangling at his side, On chain securely hooked. My _first_ he came from o’er the sea, A bundle of conceit looked he, And he was all he looked.
She led him to the village green, Where in desponding mood was seen My _whole_, with drooping head. “Behold,” she said, “a perfect, true And striking likeness, sir, of you!” And, laughing, gaily fled.
is solved by _Donkey_.
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