White to play and win. You have to find the only sequence of moves that is guaranteed to produce a win, and you have to ensure that you find Black's best defence (a stalemate threat), and the way white can overcome this defence.
Rushing ahead with the h-pawn doesn't work, as Black replies axb5, and queen's his own pawn too.
The neat idea is: 1. b6+ to force Black to promote on the a1 square, instead of b1 - but then Black gas a cunning defence: 1. ... Kb8, so that after 2. h4 a5 3. h5 a4 4. h6 a3 5. h7 a2 6. h8=Q a1=Q and white cannot take the queen due to stalemate ... but he can still win!
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