Boxing Day

Death row is overcrowded, so the warden proposes a radical solution. He places 100 boxes in a sealed room. Each contains a slip of paper bearing the name of one of the 100 prisoners on the row.

Each prisoner will enter the room by one door, open 50 boxes, and exit by another door. Unless every prisoner can discover his own name, all 100 will be executed.

The prisoners will be supervised by a guard. They cannot communicate with one another, and they must leave the room as they found it, but the group can prepare a plan in advance and post it on the wall of the room.

If they proceed at random, their chance of succeeding is 1/2¹⁰⁰, or about 0.00000000000000000000000000000008. What should they do?

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The written plan assigns one box to each prisoner. When he enters the room, he opens his assigned box, reads the name on the slip, and opens the box assigned to that prisoner. He continues in this way until he’s opened 50 boxes or found his own name. Remarkably, this strategy raises the chance of success to 31.18 percent. Peter Winkler discusses the idea here; the puzzle originated with Danish computer scientist Peter Bro Miltersen. (Thanks, Steve.)

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October 18, 2011January 29, 2013 | Puzzles

Accordion Commute

A puzzle by David Wells:

Every day I take the subway from Startville to Endville. Today I arrived at the Startville station to find that my train was just departing. I caught the next train to Endville, where I left the station at exactly the same time as if I had caught the first train. How did I manage this? The two trains traveled at the same speed, and I myself did not have to rush to make up the lost time.

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Startville is north of Endville. Normally I arrive at the north end of the Startville station, enter the last car of my regular train, and ride it to Endville, where I leave the train and walk the length of the platform to exit at the south end of the station. Today, when I saw that I had missed my regular train, I walked the length of the Startville platform and arrived at the south end just as the next train arrived. I boarded the first car, rode it to Endville, and debarked at the south end of the Endville station, next to the exit. My normal commute involves walking the length of a subway platform; today I simply did it in Startville rather than Endville.

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October 17, 2011January 29, 2013 | Puzzles

Black and White

black and white

By Auguste D’Orville. White to mate in two moves.

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1. Nd2!, followed by 2. c4#. From Problèmes d’Echecs, composés et dédiés aux amateurs de ce jeu, 1842.

October 5, 2011January 29, 2013 | Puzzles

Black and White

calvi chess problem

By Calvi. White to mate in two moves.

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1. Qg2! and Black cannot stop both 2. Qd2# and 2. Nb7#. From Le Palamède, via Charles Tomlinson, Amusements in Chess, 1845.

September 27, 2011January 29, 2013 | Puzzles

Sudden Death

sudden death chess problem

“Paul Morphy IV” submitted this puzzle to the Journal of Recreational Mathematics in 1974. White might capture Black’s queen at this point, but instead can choose to mate on the move. How?

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It’s a trick. The square in the lower right is dark when it should be light, so we must rotate the board 90 degrees. If we turn it to the right then the black king is in check on White’s move, which is illegal. So turn it to the left: Now White can mate by promoting the d7 pawn to a knight. (“Why Prolong It?”, JRM 7:1, p. 62)

September 20, 2011January 29, 2013 | Puzzles

“A Desperate Woman”

A puzzle from Henry Dudeney:

Her eyes were filled with tears, her face was flushed with anger, and her expression was one of indignation at the brutal injury to which she had been subjected.

“You monster of cruelty!” she cried, “I have borne with you too long! The very foundations of my being you have injured. Day by day I have endured your tortures. When first we met your ease and polish attracted me, and when you became my own my friends envied me. Yet see what I have suffered for your sake! You offer every opposition to my advancing myself. Your understanding is far too small for a large soul like mine. My standing in society you have entirely ruined. Had we never met I might have walked in peace. Begone! We part for ever.”

There was a moment’s convulsive breathing, a grinding of teeth, and a quick sigh. It was all over between them. One supreme effort, and she cast it from her —

“‘Whom?’ perhaps the reader will ask. That is the question. I leave you to fill in the blank.”

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“The blank should be filled in with the words ‘her shoe.’ On reading the account again, everything will become quite clear.”

September 19, 2011May 2, 2013 | Puzzles

Fatal Attraction

You have two straight iron bars that look the same. One is a magnet and one is not. How can you tell which is which only by touching them together?

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Touch one to the other in the form of a T. If they stick together, the unmagnetized bar is the crossbar.

September 15, 2011January 28, 2013 | Puzzles

False Fealty

Written in prison by Arthur Connor, a prominent figure in the Irish Rebellion of 1798:

The pomps of Courts and pride of kings
I prize above all earthly things;
I love my country, but the King,
Above all men, his praise I sing.
The Royal banners are displayed,
And may success the standard aid.

I fain would banish far from hence
The “Rights of Man” and “Common Sense.”
Confusion to his odious reign,
That foe to princes, Thomas Paine.
Defeat and ruin seize the cause
Of France, its liberties and laws.

Connor escaped in 1807 and made his way to France, where he became a general in the army. “These two apparently loyal verses, if properly read, bear a very different meaning,” writes Henry Dudeney. “Can you discover it?”

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“Read the first line of the first verse, then the first line of the second verse, next the second line of the first verse, then the second line of the second verse, and so on, when the treasonable character of the lines will be apparent.”

September 13, 2011January 28, 2013 | History · Puzzles

Black and White

sam loyd chess problem

By Sam Loyd. White to mate in two moves.

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1. Rxh6! and Black will be mated along the first rank. From Alain C. White, Sam Loyd and His Chess Problems, 1913.

September 10, 2011January 28, 2013 | Puzzles

A Puzzling Figure

A poser from Jerome S. Meyer’s Puzzle Quiz and Stunt Fun (1956):

“The mark above is the mark of evil. It is the symbol of murder and terror. Millions have died for it and millions have died because of it. Can you tell what it is?”

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It’s Hitler’s signature.

September 7, 2011January 28, 2013 | Puzzles