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1. Rb8 Qxb8
2. Bxh6 Qxe5
3. Bg5#
1. Rb8?, as Aaron pointed out, will fail to 1…Qxb8 2. Bxh6 Qb1+ 3. Kh2 Qg6.
Instead, 1. Bxh6! gxh6 2. Rb8 should win. 2… Qg7 3. Rxg8+ Kxg8 (3…Qxg8 4. Rf6) 4. Rg3 +-
If 1.Rb8 Q:b8 2. B:h6 Qb1+ 3. Bc1 #
No it is not cos the white queen hold h7 🙁
1 Rf6 gxf
2 Bxf6+ Rg7
3 Qxh6+ Kg8
4 Rb8 Qxb8
5 Qxg7#
I think this is the better line unless somebody has a better first move for black than gxf.
Mark
1. Rf6 is good, but after 1…Kh7, White has to play 2. Rb8. This is stronger than the previous case, because after 2…Qxb8, 3. Rxh6+ is check and Black doesn’t have time to check on b1.