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(a) 1.Bf6 Bxf6 2.Qh7+ Kf8 3.Qxf7#
(b) 1.Bf6 Nh6 2.Qxh6 Bxh6 ( or 2. …Bxf6 3.Qh7+ Kf8 4.Qxf7# ) 3.Rxh6 ( threatening checkmate with 4.Rh8# ) Re1+ 4.Rxe1 and 5.Rh8#
(c) 1.Bf6 Kf8 2.Qh8+ Bxh8 3.Rxh8#
1. Qh7+ Kf8 2. Bf6 Nce7 [2…Bxf6 3. Qxf7#] 3. Ng5 Rd8 [3…Ng8 4. Qxg7+ Nxg7 5. Nh7#] 4. Qh8+ Bxh8 5. Rxh8+ Ng8 6. Nh7+ Ke8 7. Rxg8#
After getting all this worked out, chess engine points out that 1. Bf6! is much stronger. 🙂
Very good!
Yes, 1.Bf6 is indeed much stronger 🙂