chess

Here's a brilliantly manic composition - a series help-mate in 36 (Black makes 36 consecutive moves to reach a position in which White can give mate) by Michel Caillaud. It is easy to see that the mating move must be cxb7, which leads to the conclusion that b8 and c7 must both be occupied by black bishops. Yet it seems impossible to promote two pawns on black squares. Here's how the magic works:

1.Kc7, 2.Kd6, 3.Kd5, 4.Ke4, 5.Kf3, 6.Kg3, 7.Nf3, 8.Rd5, 9.Nf5, 10.N5xd4, 11.Nb5, 12.Qc5, 13.g1=B, 14.Be3, 15.Bxd2, 16.Ba5, 17.d2, 18.d1=Q, 19.Qh1, 20.Qxh6, 21.Qh3, 22.Kh4!!

Half of those moves look utterly pointless, but the idea is now revealed: a position has been reached in which, had it been in a real game, White's previous move could only have been advancing the pawn from g2 to g4. Black may therefore capture en passant! So the solution continues 23.fxg3! 24.g2, 25.g1=B, 26.Bh2, 27.Bb8, 28.Bac7, 29.Kxg5, 30.Kf6, 31.Ke7, 32.Kd8, 33.Kc8, 34.Rd8, 35.Qd7, 36.Bb7+ when White mates with cxb7.

And why did Black wait until move 29 before playing Kg5? Because any earlier would have left White with no possible previous move. The game would be a draw by retro-stalemate.