Steadfast

steadfast chess problem

By W. Bone. White to move and mate in four.

The catch: He must mate with the queen — and she’s glued to the board.

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1. Nd3 Ka3 2. Nb1+ Ka2 3. Kf1 Ka1 4. Nc3# By W. Bone, collected in R.A. Brown, Chess Problems, 1844. (12/12/2008 Thanks to Jason for a three-move solution: 1.Nd3 Ka3 2.Nc4 Ka2 3.Nb4#)

September 4, 2008January 21, 2013 | Puzzles

Measuring the River

measuring the river

A traveler reaches a river at the point A and wishes to know the width across to B. As he has no means of crossing the river, what is the easiest way of finding its width?

From Henry Dudeney.

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“Measure any convenient distance along the bank from A. to C, say 40 yards. Then measure any distance perpendicularly to D, say 12 yards. Now sight along DB and find the point E. You can then measure the distance from A to E, which will here be 24 yards, and from E to C, which will be 16 yards. Now AB:DC = AE:EC, from which it is evident that AB, the width of the river, must be 18 yards.”

August 31, 2008January 21, 2013 | Puzzles

“Cryptic Addition”

cryptic addition

From Henry Ernest Dudeney. Can you prove that this sum is correct?

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“If you turn the page upside down you will find that one, nine, one, and eight added together correctly make nineteen.”

August 19, 2008January 21, 2013 | Puzzles

Fire Escape

You’re new to hell, and you’re given a choice: You can go directly to the fourth circle, or you can play simultaneous chess games against Alexander Alekhine and Aron Nimzowitsch. Alekhine always plays black and smokes a pipe of brimstone. Nimzowitsch plays white and wears cufflinks made of human teeth. Neither has ever lost.

If you can manage even a draw against either player, you’ll be set free. But if they both beat you, you’ll go to the eighth circle for eternity.

What should you do?

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Accept the challenge. Wait for Nimzowitsch’s first move, and then play that move on Alekhine’s board. When Alekhine responds, copy his move on Nimzowitsch’s board. In effect the two masters are playing against one another; you’re just transferring the moves between them. Since their game must end in a win or a draw, you’re guaranteed to escape hell. You don’t even have to know how to play chess!

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August 9, 2008January 21, 2013 | Puzzles

“Who Can Read Franklin’s Cipher?”

Benjamin Franklin wrote from Passy, in 1781, a letter to M. Dumas. He said:— ‘I have just received a 14, 5, 3, 10, 28, 2, 76, 203, 66, 11, 12, 273, 50, 14, joining 76, 5, 42, 45, 16, 15, 424, 235, 19, 20, 69, 580, 11, 150, 27, 56, 35, 104, 652, 20, 675, 85, 79, 50, 63, 44, 22, 219, 17, 60, 29, 147, 136, 41, but this is not likely to afford 202, 55, 580, 10, 227, 613, 176, 373, 309, 4, 108, 40, 19, 97, 309, 17, 35, 90, 201, 100, 677.’ This has never been deciphered. The state department at Washington has no key to it. I submit it for the consideration of the whole world.

— Elliott Sandford, New York World, cited in Henry Williams, A Book of Curious Facts, 1903

04/09/2014 Now solved!

12/30/2014 Oops, that link seems to have gone bad. Here’s another one. The numbers are keyed to the text of a book that Franklin’s correspondent Charles Dumas had sent to him. The message reads, “I have just received a neuu comiissjon joining me uuith m adams in negodiaions for peace but this is not likely to afford me much employ at present.”

July 23, 2008December 30, 2014 | Puzzles

Curry’s Paradox

curry's paradox

July 15, 2008September 24, 2010 | Puzzles

Two Many

How many people are in “two pairs of twins twice”?

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Eight. A twin is just one person.

July 12, 2008January 16, 2013 | Puzzles

The English Officer

Here’s a poser adapted from a 1923 intelligence test:

“I was so sorry to hear of Harold’s death, Mary.”

“Thank you, Mildred.”

“May I ask the circumstances?”

“Of course. He had fallen asleep in church during the sermon and was dreaming that an executioner was approaching to cut off his head. He had witnessed some rather gruesome things during the Boxer Rebellion in China some years ago, you know. Just as the sword was falling, I happened to touch him on the back of his neck with my fan, to awaken him. The shock was too great, and he fell forward dead.”

What’s wrong with this story?

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If Harold died in his sleep, how did Mary know of his dream?

July 8, 2008January 16, 2013 | Puzzles

King Walk

By J. Kling. White to mate in 64 moves, forcing the black king to occupy every square on the board:

1. Rb8+ Ka7 2. Qc7+ Ka6 3. Qb7+ Ka5 4. Qb6+ Ka4 5. Rc4+ Ka3 6. Qe3+ Ka2 7. Rc2+ Ka1 8. Ra8+ Kb1 9. Rcc8 Kb2 10. Qc1+ Kb3 11. Ra3+ Kb4 12. Qc3+ Kb5 13. Rc5+ Kb6 14. Qa5+ Kb7 15. Rd3 Kb8 16. Rb5+ Kc8 17. Qa8+ Kc7 18. Qb8+ Kc6 19. Rb6+ Kc5 20. Qd6+ Kc4 21. Rd4+ Kc3 22. Qb4+ Kc2 23. Re6 Kc1 24. Rc4+ Kd1 25. Qb1+ Kd2 26. Qc1+ Kd3 27. Rc3+ Kd4 28. Qe3+ Kd5 29. Re5+ Kd6 30. Qc5+ Kd7 31. Rf3 Kd8 32. Rd5+ Ke8 33. Qc8+ Ke7 34. Qd8+ Ke6 35. Rd6+ Ke5 36. Rf7 Ke4 37. Qf6 Ke3 38. Qd4+ Ke2 39. Rh6 Ke1 40. Re7+ Kf1 41. Qg7 Kf2 42. Rh1 Kf3 43. Qg1 Kf4 44. Qg2 Kf5 45. Qg3 Kf6 46. Qe5+ Kg6 47. Qe6+ Kg5 48. Qf7 Kg4 49. Rh5 Kg3 50. Qf5 Kg2 51. Qf4 Kg1 52. Rg5+ Kh1 53. Qe4+ Kh2 54. Kf7 Kh3 55. Qg2+ Kh4 56. Rg4+ Kh5 57. Re5+ Kh6 58. Qc6+ Kh7 59. Ke8 Kh8 60. Rh4+ Kg7 61. Kd8 Kg8 62. Rg5+ Kf7 63. Rh7+ Kf8 64. Qf6#

king walk solution

July 5, 2008September 24, 2010 | Puzzles

“A Cube Paradox”

dudeney cube puzzle

A puzzle from Henry Dudeney:

I had two solid cubes of lead, one very slightly larger than the other, just as shown in the illustration. Through one of them I cut a hole (without destroying the continuity of its four sides) so that the other cube could be passed right through it. On weighing them afterwards it was found that the larger cube was still the heavier of the two! How was this possible?

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It is a curious fact that a cube can be passed through another cube of smaller dimensions. Suppose a cube to be raised so that its diagonal AB is perpendicular to the plane on which it rests, as in Figure 1. Then the resulting projection will be a regular hexagon, as shown. In Figure 2 the square hole is cut for the passage of a cube of the same dimensions. But it will be seen that there is room for cutting a hole that would pass a cube of even larger dimensions. Therefore, the one through which I cut a hole was not, as the reader may have hastily supposed, the larger one, but the smaller! Consequently, the larger cube would obviously remain the heavier. This could not happen if the smaller were passed through the larger.

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June 23, 2008January 16, 2013 | Puzzles