White to move
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1. Rg6 Rxg6 2. Qxg6+ Kh8 3. Qxe8+ Kg7 4. Qf7+ (Kh6 Rg6#) Kh8 5. Qh5+ Kg7 6. Rf7+ Kg8 7. Qg6+ Kh8 8. Rf8#
1. Rg6 Kh8 2. Rxg7 Kxg7 3. Qf7+ (Kh6 Rg6#) Kh8 4. Qxe8+ Kg7 and mate as above.
1. Rg6 R(8)e7 2. Rxg5 Rxg5 3. Qf8+ Kh7 4. Qxe7+ Kh6 5. Qf8+ Kh7 6. Rf7+ Kg6 7. Rg7+ Kh5 8. Rh7+ Kg4 9. Qc8+ Kf4 10. Rh4+ Kf3 11. Rh3+ Kf2 12. Qf8+ Ke2 13. Rxc3 +-
Yes, this indeed wins, but White played 1.Rf7. Still, well done 🙂