The Haberdasher’s Problem

Can you make three cuts in a square of cloth and rearrange the pieces to form an equilateral triangle?

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March 28, 2007January 15, 2013 | Puzzles · Science & Math

Knotty Thinking

Dudeney dungeon

The “Death’s-head Dungeon,” from Henry Dudeney’s Canterbury Puzzles (1908), in which a youth rescues a noble demoiselle from a dungeon belong to his father’s greatest enemy:

“… Sir Hugh then produced a plan of the thirty-five cells in the dungeon and asked his companions to discover the particular cell that the demoiselle occupied. He said that if you started at one of the outside cells and passed through every doorway once, and once only, you were bound to end at the cell that was sought. Can you find the cell? Unless you start at the correct outside cell it is impossible to pass through all the doorways once, and once only.”

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“‘Some here have asked me,’ continued Sir Hugh, ‘how they may find the cell in the dungeon of the Death’s Head wherein the noble maiden was cast. Beshrew me! but ’tis easy withal when you do but know how to do it. In attempting to pass through every door once, and never more, you must take heed that every cell hath two doors or four, which be even numbers, except two cells, which have but three. Now, certes, you cannot go in and out of any place, passing through all the doors once and no more, if the number of doors be an odd number. But as there be but two such odd cells, yet may we, by beginning at the one and ending at the other, so make our journey in many ways with success. I pray you, albeit, to mark that only one of these odd cells lieth on the outside of the dungeon, so we must perforce start therefrom. Marry, then, my masters, the noble demoiselle must needs have been waiting in the other.’ “The drawing makes this quite clear to the reader. The two ‘odd cells’ are indicated by the stars, and one of the many routes that will solve the puzzle is shown by the dotted line. It is perfectly certain that you must start at the lower star and end at the upper one; therefore, the cell with the star situated over the left eye must be the one sought.”

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March 20, 2007January 15, 2013 | Puzzles

Chess Detective Work

Retrograde analysis involves looking into a chess game’s past, rather than its future. Here’s an example from Henry Ernest Dudeney (1917):

Dudeney retrograde analysis

“Strolling into one of the rooms of a London club, I noticed a position left by two players who had gone. This position is shown in the diagram. It is evident that White has checkmated Black. But how did he do it? That is the puzzle.”

The solution is unique. Can you find it?

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The earlier game must have reached this position: From here, White played e5+, and Blacked responded … f5 (the only move). Then White captured the pawn en passant, exf5 e.p., producing the final position.

March 15, 2007January 15, 2013 | Puzzles

“To — — –“

Here’s a valentine written by Edgar Allan Poe in 1846. His sweetheart’s name is hidden in it — can you find it?

For her these lines are penned, whose luminous eyes,
Brightly expressive as the starts of Leda,
Shall find her own sweet name that, nestling, lies
Upon the page, enwrapped from every reader.
Search narrowly these words, which hold a treasure
Divine — a talisman, an amulet
That must be worn at heart. Search well the measure —
The words — the letters themselves. Do not forget
The smallest point, or you may lose your labor.
And yet there is in this no gordian knot
Which one might not undo without a sabre
If one could merely comprehend the plot.
Upon the open page on which are peering
Such sweet eyes now, there lies, I say, perdus,
A musical name oft uttered in the hearing
Of poets, by poets — for the name is a poet’s too.
In common sequence set, the letters lying,
Compose a sound delighting all to hear —
Ah, this you’d have no trouble in descrying
Were you not something, of a dunce, my dear —
And now I leave these riddles to their Seer.

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Poe wrote the poem for Frances Sargent Osgood: For her these lines are penned, whose luminous eyes, BRightly expressive as the starts of Leda, ShAll find her own sweet name that, nestling, lies UpoN the page, enwrapped from every reader. SearCh narrowly these words, which hold a treasure DivinE — a talisman, an amulet That muSt be worn at heart. Search well the measure — The wordS — the letters themselves. Do not forget The smallEst point, or you may lose your labor. And yet theRe is in this no gordian knot Which one miGht not undo without a sabre If one could mErely comprehend the plot. Upon the open pAge on which are peering Such sweet eyes Now, there lies, I say, perdus, A musical name ofT uttered in the hearing Of poets, by poets — fOr the name is a poet’s too. In common sequence Set, the letters lying, Compose a sound deliGhting all to hear — Ah, this you’d have no trOuble in descrying Were you not something, Of a dunce, my dear — And now I leave these ridDles to their Seer. (He misspelled her middle name.)

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March 12, 2007January 15, 2013 | Poems · Puzzles

Suburban Physics

You’re driving a car. The windows are closed. In the back seat is a kid holding a helium balloon.

You turn right. You and the kid sway to the left. What does the balloon do?

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The balloon sways to the right, into the turn and away from you and the kid. As you turn right, inertia pulls the air in the cabin to the left, displacing the balloon.

March 8, 2007January 15, 2013 | Puzzles · Science & Math

Safety First

On an average weekend, the emergency room at the John Radcliffe Hospital in Oxford treats 67 children for injuries sustained in accidents.

On two recent weekends, however — June 21, 2003, and July 16, 2005 — only 36 children needed treatment. Can you guess why?

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Each of those weekends saw the release of a new Harry Potter book (Harry Potter and the Order of the Phoenix in 2003 and Harry Potter and the Half-Blood Prince in 2005). So presumably many kids were too busy reading to get into accidents. This may spark a new trend in public health. “It may … be hypothesised,” wrote a team of researchers in the British Medical Journal, “that there is a place for a committee of safety conscious, talented writers who could produce high quality books for the purpose of injury prevention.”

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March 5, 2007January 15, 2013 | Puzzles

Requiescat In Pace

William Andrews, Curious Epitaphs, 1899

A puzzle from 1796. “This curious inscription is humbly dedicated to the penetrating geniuses of Oxford, Cambridge, Eton, and the learned Society of Antiquaries.” Can you decipher it?

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Just ignore the punctuation: “Beneath this stone reposeth Claud Coster, tripe-seller, of Impington, as doth his consort Jane.” (Cited in William Andrews, Curious Epitaphs, 1899)

February 15, 2007January 15, 2013 | Puzzles

Highway Robbery

A stranger called at a shoe store and bought a pair of boots costing six dollars, in payment for which he tendered a twenty-dollar bill. The shoemaker could not change the note and accordingly sent his boy across the street to a tailor’s shop and procured small bills for it, from which he gave the customer his change of fourteen dollars. The stranger then disappeared, when it was discovered that the twenty-dollar note was counterfeit, and of course the shoemaker had to make it good to the tailor. Now the question is, how much did the shoemaker lose?

— H.E. Licks, Recreations in Mathematics, 1917

February 12, 2007November 19, 2010 | Puzzles

Connection Puzzle

connection puzzle

Here’s a simplified version of a classic puzzle by Sam Loyd. Connect each square to its triangle with a line. The lines must stay within the boundary and may not cross one another.

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January 31, 2007January 16, 2013 | Puzzles

Alcohol Problem

Fill one glass with wine and another with water. Transfer a teaspoonful of wine from the first glass into the second. Then transfer a teaspoonful of that mixture back into the first glass. Now, is there more wine in the water or water in the wine?

Most people will predict it’s the former, but in fact the two quantities will always be the same. Can you see why?

January 11, 2007November 22, 2010 | Puzzles · Science & Math