Breakthrough

Chess Endgames (1999) by Laszlo Polgar offers this position, attributed to Teed 1885, as problem number 2936.

White to move


The first move is easy.

1.Kf7

But White has a problem to solve when Black replies, 1...h5!

2.Kf6 leads to a draw. 2...hxg4 3.hxg4 Kh6 4.Kf5 Kh7 5.Kxg5 Kg7

White to move


This position would be a win if it were Black's move, but it is White's.

White must find the breakthrough idea.

2.h4!

Black to move


Play might proceed, as it did when I played against Houdini 1.5.

2...Kh6 3.Kf6 gxh4 4.g5+ Kh7 5.Kf7 h3 6.g6+ Kh6 7.g7