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(a) 1.Qh6 Qd8 2.Rf7 ( threatening checkmate with either 3.Qxh7# or 3.Rxh7# ) Rxg3+ 3.fxg3 Qg8 4.Rf8 Rb8 ( 4. …Qxf8?? 5.Qxf8# ) 5.Rcf1 c3 6.Rxb8!! Qxb8 7.Rf8+ Qxf8 8.Qxf8#
(b) 1.Qh6 Rg7 2.Rf8+ Rg8 3.Rf7 Rxg3+ 4.fxg3 Qd8 5.Qg7# or Qxh7#
1. Qh6 Rg7 (to prevent 2. Rf7) 2. Rf8+ Rg8 3. Rf7 and checkmate will soon follow.
Qd2 I think is the best move for white
1. Qh6 (threatening Rf7 and mate on h7) if Rg7 2. Rf8+ Rg8 3. Rf7 wins
Very good!
Actually, 1.Qh6 wins instantly.
Very good!
Very good!