A tricky problem by Ernest Clement Mortimer. This position was reached after Black’s fourth move in a legal chess game. Can you reconstruct the game?
A traveler wants to stay at an inn for seven days. He has no money, but he has a gold chain with seven links. The innkeeper agrees to accept this in payment for the week’s stay, but the traveler is reluctant to part with all seven links at once. He prepares to cut the chain into seven pieces.
The innkeeper stops him. If the traveler is willing occasionally to accept change in the form of links previously paid, then they can work out a plan that minimizes damage to the chain and yet permits the traveler to pay only what he owes on each successive day. How many links must they cut?
A rail one mile long is lying on the ground. If you push its ends closer together by a single foot, so that the distance between them is 5279 feet rather than 5280, how high an arc will the rail make?
By Eric M. Hassberg, New York Post, April 21, 1945. White to mate in two moves.
There are 13 ways to draw four of a kind and 40 possible straight flushes.
Why then does a straight flush beat four of a kind?
Consider the classic story of Henry, a backwoods villager watching a theatrical performance, who leaps to the stage to save the heroine from the clutches of the villain and a horrible death. Of course Henry is mistaken if he thinks he can save the actress. She is not in danger; there is nothing to save her from. But the character she portrays is in danger and does need saving. Can Henry help her, despite the fact that he doesn’t live in her world?
— Kendall L. Walton, “How Remote Are Fictional Worlds From the Real World?”, Journal of Aesthetics and Art Criticism, 1978
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?
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.
“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?
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.”
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?
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?”
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?”
Twenty-five basketball teams compete in a knockout tournament — each team is eliminated after its first loss. How many games must be played to establish a winner?
1. P-K4 P-K4 2. B-B4 P-R4 3. Q-B3 P-R4 4. QxP mate:
That’s a pretty colorless chess game, but Mike Keith points out that the game score makes an alphametic:
P-K4 + P-K4 + B-B4 + P-R4 + Q-B3 + P-R4 + QxP = IWIN
Replace each letter and symbol (-, x) with a digit, leaving the numbers as they are, to produce a valid equation.
1. You are midway through dealing a bridge hand when a nuclear apocalypse destroys civilization. The bridge table is still upright, and your friends are willing to keep playing, but you can’t remember where you left off dealing. How can you finish dealing this hand without having to start over?
2. Can I stand behind you while you stand behind me?
3. My bed is 10 feet from the light switch. But last week I turned off the light, dashed across the room, and was in bed before the room got dark. How did I manage this?
A puzzle by Henry Dudeney:
A robber broke into the belfry of a church, and though he had nothing to assist him but his pocket-knife, he contrived to steal nearly the complete lengths of the two bell-ropes, which passed through holes in the lofty boarded ceiling. How did he effect his purpose? Of course, there was no ladder or aught else to assist him. It is easy to understand that he might steal one rope and slide down the other, but how he cut the two, or any considerable portion of them, without a bad fall, is perplexing.
In a chess game, White plays 1. f3 2. Kf2 3. Kg3 4. Kh4. Black’s fourth move checkmates White. What is the game?
1. f3 e5 2. Kf2 Qf6 3. Kg3 Qxf3+! 4. Kh4 Be7#
White’s play is so suicidal that the task sounds easy, but “this problem is almost impossibly difficult because Qxf3+ is such a horrible move by normal chess standards,” writes former U.S. champion Stuart Rachels. “It is hard for a competent player to consciously consider it.”
Here’s another problem by Sam Loyd:
White to mate in two moves. In 1907 J.H. Blackburne chose this as one of his all-time favorite problems. “It was first published in this country about fifty years ago, and greatly puzzled the solvers of that day, the idea then being entirely new.”
It’s a perfectly fair two-mover — there’s no trickery.
A gold miner lives at point A, 3 miles north of the river and 5 miles upstream from the gold mine at point B, which is 2 miles north of the river. On the way to work he must stop at the river to give his burro a drink. At what point on the river should he stop in order to minimize the length of the trip?
The American Chess Bulletin of October 1917 contains a puzzle story about a boastful player who entered a local club claiming to have beaten one of the best players in the county.
Our first question was: ‘What odds did he give you?’
‘Why, none, of course,’ was the reply. ‘Topnotch was White, and he set up a fierce King’s side attack on my castled K. I had almost given up all hope when I saw that if I could only get my Kt to QR5, and he went on with his attack, I had a mate. So on my 15th move I played Kt-QR5. As I hoped, he overlooked the mate which he could have stopped with a move, and played 16 Kt-KR5, and then, of course, I mated. That is the position.’
And he set it up with the air of a conqueror.
We looked at it, saw the mate (a very commonplace one, by the way), and were turning away, when the Problemist, who was the most ‘fed up’ of us all, said in his quietest voice:
‘S—, you are a beautiful–Ananias.’
We started in surprise; it was so unlike him.
S—, with a red face and heated manner, said: ‘What do you mean? I give you my word of honor that was the position after White’s 16th move.’
‘I don’t dispute it; but still you are not telling the truth.’ And he proceeded to demonstrate to our satisfaction he was right.
During this period S— disappeared and I think it unlikely that we shall receive another visit from him.
Now, what did the Problemist demonstrate?
“Can our solvers unravel this mystery?” wrote the editors. “It is plain that the Problemist synthetically deduced that by no possibility could S— have met this precise position in the course of orthodox chess play.”
Alas, I don’t have the solution! If S— is telling the truth, then in the diagram above the black knight must have moved from b6 and the white knight from f4. Black’s mate would have been something like 16. … Nc3+ 17. bxc3 Qb6+ 18. cxb6 Rxb6+ 19. Ka1 Bxc3#. But none of these observations seems to lead anywhere. Any ideas?
UPDATE: A number of readers have analyzed this, and the strong consensus is that the position above cannot have been reached in 16 moves, as S— says it did. I had dismissed this possibility when the Problemist said “I don’t dispute it,” thinking this meant he accepted S—‘s contended move totals, but now I think that remark meant merely that the Problemist thinks S— generally dishonest. Thanks to everyone who saw more deeply than I did.
SECOND UPDATE: Wait. Another reader points out that perhaps the idea is that White’s position can be reached in 16 moves — if he gave knight odds. This is much more satisfying — the Problemist isn’t disputing the number of moves; he’s pointing out that Topnotch had offered to play with a significant handicap. This would embarrass the boastful S—, giving the whole story a satisfying punchline. It also explains why S— is asked explicitly about odds at the start, and it illuminates the rather canny phrasing about “orthodox” chess play. I’ll bet this is it.