I've got it! This was a tricky one. At first you're fooled by the lack of material. You're discouraged from allowing Black to take White's bishop, because you know that usually, a knight and a king are not enough material to finish the job. But we get to use Black's pawns to his disadvantage, and that's exactly what we do here...
1. Nc5 Kxg6
2. Nd7 Kh6
3. Ne5 g6
4. Nf7#
RE: Chess puzzle #4