Everyone who calls a [chess] problem "beautiful" is applauding mathematical beauty, even if it is beauty of a comparatively lowly kind. Chess problems are the hymn-tunes of mathematics.

—G. H. Hardy, A Mathematician's Apology

It has been my policy to avoid chess problems of the type "Mate in n moves" on the assumption (perhaps a mistaken one) that too few readers play chess and that, even among those who do, too few like chess problems. In this chapter, however, I shall consider a variety of what are called chess "task" problems. They have so little in common with actual play that they are of more interest to puzzle buffs than to serious chess players. True, a knowledge of chess rules is essential. But apart from that, even a tyro is as likely as a grandmaster to be able to solve such problems.

What is a chess task? It is a chess problem where a person seeks an objective in a way that maximizes or minimizes one or more parameters. Among chess players the best-known task question is: What is the shortest possible game? The answer, of course, is the "fool's mate." White opens with, say, P—KB4. Black replies P-K3. If White foolishly moves P-KN4, Black checkmates on his second move, Q—R5.

The shortest game ending in perpetual check was published in 1866 by one of the great pioneer chess problemists, Sam Loyd. It is

Black now has a perpetual check by moving his queen back and forth from the square it is on to Black's R3 square.

A much more difficult task was also posed in 1866 by Loyd. What is the shortest game ending in stalemate? Loyd's spectacular 10-move solution has never been surpassed:

 White Black 1. P-K3 1. P-QR4 2. Q-R5 2. R-R3 3. QxQRP 3. P-KR4 4. QxBP 4. QR-KR3 5. P-KR4 5. P-KB3 6. QxQP(ch) 6. K-B2 7. QxNP 7. Q-Q6 8. QxN 8. Q-KR2 9. QxB 9. K-N3 10. Q-K6 (stalemate)

The final position is shown in Figure 116, No. 1. In 1882 a search began for the shortest "no capture" stalemate that left all 32 men on the board. The present record, 12 moves, was found by C. H. Wheeler in 1887. It was forgotten, then redis covered independently by several men, including Loyd and Henry Ernest Dudeney (who gives it as Problem 349 in his Amusements in Mathematics). In January, 1906, Loyd published in Lasker's Chess Magazine a hilarious commentary on the game, pretending to explain the strategy behind each crazy move and calling attention to a five-move mate overlooked by Black when he made his final stalemating move. (Loyd's commentary can be found in Alain C. White's Sam Loyd and His Chess Problems, 1913, pages 128—129, currently available as a Dover reprint.)

Figure 116, No. 2 shows how 30 men, the largest number known, can be placed in a legal position—a position that can result in actual play—such that no move is possible by either side: a double stalemate. It was published in 1882 by G. R. Reichelm, who also showed how the position could be reached in 25 moves. Note the pattern's twofold symmetry.

Another remarkable task solved by Loyd is to play the shortest game ending with only the two kings on the board. Loyd's 17-move solution is given in Alain White's book as Problem 116. The two kings are left on their own pawn squares. Different 17-move solutions were later found by others, with the lti

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