white to move and win in 3 moves. It is quite possible to win in other ways, but as far as I saw there's only one solution in 3 moves:
The answer is the following sequence of moves:
1. Qb3, there's now only one legal move:
1. ... Rxb3
2. Ke2 (Bb2), promoting black's pawn to a bishop. Rook, queen and knight won't work. The point is that black now has again just one legal move:
2. ... Bd2
3. Rb3 mate.