The Smith Jones Robinson Riddle

On a train, Smith, Robinson, and Jones are the fireman, the brakeman, and the engineer (not necessarily respectively). Also aboard the train are three passengers with the same names, Mr. Smith, Mr. Robinson, and Mr. Jones.

(1) Mr. Robinson is a passenger. He lives in Detroit.

(2) The brakeman lives exactly halfway between Chicago and Detroit.

(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.

(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.

(5) Smith is not a passenger. He beats the fireman in billiards.

(6) The passenger whose name is the same as the brakeman’s lives in Chicago.

Who is the engineer?

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We know that the brakeman doesn’t live in Detroit (2) and that his nearest neighbor is a passenger (4). So that passenger can’t be Mr. Robinson, who lives in Detroit (1). From (3) and (4) we know that the brakeman’s nearest neighbor also can’t be Mr. Jones (because Mr. Jones earns $20,000 per year, which is not evenly divisible by 3). Thus, if the brakeman’s nearest neighbor is not Mr. Jones and not Mr. Robinson, it must be Mr. Smith. Now, if Mr. Robinson lives in Detroit (1) and Mr. Smith lives halfway between Chicago and Detroit (as we’ve just deduced), then the third passenger, Mr. Jones, must be the one referred to in (6) and thus lives in Chicago. That means, also from (6), that the brakeman’s name is Jones. And if Smith is not the fireman (5), then by elimination Smith must be the engineer.

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May 15, 2007January 16, 2013 | Puzzles

Syllogism

Nothing is better than eternal happiness.

Eating a hamburger is better than nothing.

Therefore, eating a hamburger is better than eternal happiness.

April 18, 2007April 18, 2007 | Language · Puzzles

Holiday for Vowels

“In an old church in Westchester county, N.Y., the following consonants are written beside the altar, under the Ten Commandments. What vowel is to be placed between them, to make sense and rhyme of the couplet?”

P.R.S.V.R.Y.P.R.F.C.T.M.N.
V.R.K.P.T.H.S.P.R.C.P.T.S.T.N

— Charles Bombaugh, Facts and Fancies for the Curious From the Harvest-Fields of Literature, 1860

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PERSEVERE YE PERFECT MEN EVER KEEP THESE PRECEPTS TEN.

April 5, 2007January 15, 2013 | Language · Puzzles · Religion

The Spider and the Fly

dudeney, the spider and the fly

Another puzzle from Henry Ernest Dudeney, The Canterbury Puzzles, 1908:

“Inside a rectangular room, measuring 30 feet in length and 12 feet in width and height, a spider is at a point on the middle of one of the end walls, 1 foot from the ceiling, as at A, and a fly is on the opposite wall, 1 foot from the floor in the centre, as shown at B. What is the shortest distance that the spider must crawl in order to reach the fly, which remains stationary? Of course the spider never drops or uses its web, but crawls fairly.”

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“Though this problem was much discussed in the Daily Mail from 18th January to 7th February, 1905, when it appeared to create great public interest, it was actually first propounded by me in the Weekly Dispatch of 14th June, 1903. “Imagine the room to be a cardboard box. Then the box may be cut in various different ways so that the cardboard may be laid flat on the table. I show four of these ways and indicate in every case the relative positions of the spider and the fly and the straightened course which the spider must take, without going off the cardboard. These are the four most favourable cases, and it will be found that the shortest route is in No. 4, for it is only 40 feet in length (add the square of 32 to the square of 24 and extract the square root). It will be seen that the spider actually passes along five of the six sides of the room! Having marked the route, fold the box up (removing the side the spider does not use), and the appearance of the shortest course is rather surprising. If the spider had taken what most persons will consider the obviously shortest route (that shown in No. 1), he would have gone 42 feet! Route No. 2 is 43.174 feet in length and route No. 3 is 40.718 feet. I will leave the reader to discover which are the shortest routes when the spider and fly are 2, 3, 4, 5, and 6 feet from the ceiling and floor respectively.”

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April 2, 2007January 15, 2013 | Puzzles

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