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1. Rxh7+ Nxh7 2. Qxc8+ Re8 3. Qxe8+ Nf8 4. Qxf8#.
1. Qc8+ probably works just as well. 1…Re8 2. Rxh7+ Nxh7 3. Qxe8+ Nf8 Qxf8#
1…Ne8 2. Rxh7+ Kg8 3. Rag7#
1.Rxh7+ Kg8 2.Qg3+ Rg5 3.Qxg5+ Kf8 4.Rh8+ Ng8 5.Qxg8#
1. Rxh7+ Kg8 (1…Nxh7 2. Qc8+ mates) 2. Qg3/g2+ followed by Rh8+ or Qg7+ mates. If 2…Ng4 3. Qxg4 Rg5, clearing the a1-h8 diagonal, 3. Qc8+ mates.
@8:27
This won’t work if Black does not take h7.
@10:51,
1. Qc8+ Ne8 2. Rxh7+ Kg8 3. Rag7 Kf8.
1. Rxh7+ Nxh7 (1.. Kg8 2. Qg3+ etc)
2. Qc8+ Re8
3. Qxe8+ Qg8
4. Qe5+ 1-0