White to move and Draw.At first sight, this seems an impossible task: if White tries to chase after Black's pawn he can never catch it (1. Kh7 h4 2.Kh6 h3 etc. is clearly hopeless), while it is clear that Black will simply take White's pawn if he tries to promote it.
White can draw , by taking advantage of the fact that the king can move in two directions at once: towards Black's pawn and towards White's own.
This is the solution: