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This is a study I made. Enjoy. Scroll down for solution.
1...Nb3! 2.d4 Nc5+! 3. dxc5 d5+!! 4.Kxd5 Bc6#
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See if this works.
Yeah, it works!
Question: What happens if white instead plays 2.Qh1+?
2.Qh1+ does delay the checkmate, but after 2...Kc2 (threatening Nxd2 mate as well as Nc5 mate) White's best move is 3.Qb1+, which leads back to the original problem minus one white queen. The only attempt white can make to exploit the king's place on b1 rather than d1 is Kd3, but this allows Nc1+ Ke4 Bc6#. There are other ways to give away the queen but they all lead to similar checkmates.