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White to play and mate in 3

1.bxa8=N !!

Taking a Q or a B would obviously draw the game instantly by stalemate. But why a Knight? It is too far away to possibly have influence on the mate, right? And if a knight works, then surely a rook would work too? Read on...

...Kxg2 (only move)

2.Nb6!!

The mate is coming on the long diagonal, so it's necessary for the knight to block b6 (otherwise Bxa7 ruins everything.) That's why 1.bxa8=R? doesn't work, because it can't protect the queening pawn.

2...any

That includes 2...Kf3, 2...Kh1, and six bishop moves.

3.a8=B#

Yes, you can promote to a queen there, but I think to finish it this way is more in the spirit of the problem. I especially like the final position when Black tries 2...Kf3, the lonely king is surrounded by all those empty squares yet he has no luft.

First, it's clear that both the White queen and knight must continue to exist in order for the Black king to be mated (i.e., no sacrifices). Second, the only first move White has which checks the king without permitting the checking piece to be captured, is Qh8: from there, it is easy to see that the king has only one flight square.

Obviously then, White must find a way to check the king without moving the queen off the 5th rank (since that would allow Black to move the king to a safer location). The only other safe spots (for White's queen) on the 5th rank are a5 and g5, but g5 does not permit a subsequent check which also covers the flight square: so, White's first move must be Qa5.

Note that moves which severely restrict the degrees of freedom of a puzzle -- especially those which permit only a single possible response -- are frequently indicative of being on the path to solution, in these types of puzzle. Hence, when I saw that the king has a single flight square, I concentrated on a method of checking which also eliminated that flight square.

Kriegspiel

Sam Loyd's "Cyclopedia of Puzzles" is available for download. The main page is here: http://www.mathpuzzle.com/loyd/

<The "Mirror of American Sports" published a four-move problem in their Solving Tourney in 1885, with the motto "Little Footsteps." They explained that the problem had been submitted to them for publication, in a letter which read as follows:

Plainfield, N. J. Dec. 1885

Chess Editor, Mirror:
My children are all fond of playing chess, and the youngest boy is particularly interested in answering the problems which appear in your paper. He asks me to send you the following little problem to take part in your prize competition, if found worthy. The author's name and solution will be found in the envelope, which he hopes you will not open until you have solved.

Most respectfully,
Mrs. --------------