Helpmate in 2 (3 Solutions)

White’s minor pieces control the light squares in the black king’s field. If the queen were to join the party, mates with it on e5, e7, or c3 could very well be on the cards. Delivering mate with, say, Qc3 requires meeting three conditions: (a) unpinning the queen, (b) removing the black rook from the fourth rank, and (c) creating a self-block on d6. The only sequence accomplishing this within the stipulated moves is 1.Rxg2+ Kxg2 2.Qd6 Qc3# — and that's one solution.

The other two solutions echo the same strategy. To enable mate with WQ on e5, Black sacrifices the bishop on f2 — which also opens the e-file — and then self-blocks b4 with the rook: 1.Bxf2+ Kxf2 2.Rb4 Qe5#. Lastly, to pave way for Qe7#, Black gives up the queen on h2 and follows up with a self-block on d4 by the bishop: 1.Qxh2+ Kxh2 2.Bd4 Qe7 — a model mate.