Rest Stop

rest stop puzzle

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?

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“An End-Game Curio”

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.

School Reform

A classroom contains 25 desks arranged in 5 rows and 5 columns. The teacher asks each student to move to the desk in front of, behind, to the left of, or to the right of her current desk. The students at the edges have limited choices — will every child be able to find a new seat?

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Parting Words

The tombstone of James Leeson (1756-1794) in New York’s Trinity Churchyard bears a curious inscription.

It remained a local puzzle until 1889, when the Trinity Record discovered its meaning.

Can you unriddle the cipher?

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The Counterfeit Coin

You have nine coins and a balance scale. One of the coins is lighter than the others. Is it possible to identify it in only two weighings?

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Match Point

Henrietta wants a yacht. Her parents think she’s too young. Like all rich people, they settle disagreements by playing competitive lawn tennis.

Henrietta must play three singles matches against her parents. If she wins two matches in a row she gets the yacht. Her mother is a better player than her father. Should she play mother-father-mother or father-mother-father?

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The Last Ball

An urn contains 75 white balls and 150 black ones. A pile of black ones is also available.

The following two-step operation occurs repeatedly. First we withdraw two balls at random from the urn, then:

  • If both are black, we put one of them back in the urn and throw the other away.
  • If one is black and the other white, we put the white one back and throw the black one away.
  • If both are white, we throw both away and put a black ball from the pile into the urn.

Because the urn loses a ball at each step, eventually it will contain a single ball. What color is that ball?

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