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1.Bxh6 1-0
1 Bh6? No. I think Rxg7+ is even better: 1…Kxg7 Qxh6+ and then mate with the pawn and queen. Black is not obliged to take the bishop after Bh6, and can just take the queen.
Rxg7
Rxh7+.
if Kxh7, then 2. Qxh6+, Kg8, 3. Qh7+, Kf8, 4. Qf7# looks simple enough. greets, jan
Rxg7
1. Rxg7+ Kxg7
2. Qxh6+ Kf6
3. Ng4+ Ke7
4. Bg5+ Kd7
5. Nf6+ winning the Q
1. Rxg7+ Kxg7 2. Qxh6+ Kg8 3. Qh7+ Kf8 4. g7+ Ke7 5. g8=Q+ Kd6 6. Qgf7
or
1. Rxg7+ Kxg7 2. Qxh6+ Kf6 3. Ng4+ Kf5 4. Qh5+ Ke4 5. Nf6#
or
1. Rxg7+ Kxg7 2. Qxh6+ Kf6 3. Ng4+ Ke7 4. Qh7+ Kd6 5. Bxd3 Qxd3 6. Bf4+ Kc5 7. Qh5+ Kc6 8. Ne5+
or 1. Rxg7+ Kxg7 2. Qxh6+ Kf6 3. Ng4+ Kf5 4. Ne3+
Anon @4:22pm I think you mean 1/2-1/2 and maybe 0-1