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(a) 1.Rg7+ Bxg7 2.Rf7+
(a1) 2. …Kd8 3.Qg5+ Bf6 ( or 3. …Ke8 4.Qe7# ) 4.Qxf6+ Ke8 5.Qe7#
(a2) 2. …Ke8 3.Rxg7+ Kd8 ( or 3. …Kf8 4.Qf7# ) 4.Qg5+ Ke8 5.Qe7#
(b) 1.Rg7+ Kxf6 2.Qg5+ Ke6 3.Qf5#
(c) 1.Rg7+ Kd8 2.Rxf8+ Rxf8 ( 2. …Be8?? 3.Qxe8# ) 3.Qg5+ Rf6 ( or 3. …Ke8 4.Qe7# ) 4.Qxf6+ Ke8 5.Qe7#
Since Black threatens mate, no time for hesitation! 1. Rg7+ Bxg7 [1…Kd8 2. Rxf8+ Rxf8 3. Qg5+ Rf6 4. Qxf6+ Ke8 5. Qe7#] 2. Rf7+ Kd8 [2…Ke6 3. Qd5# or 2…Ke8 3. Rxg7+ Kd8 4. Qg5+ Ke8 5. Qe7#] 3. Qg5+ Bf6 4. Qxf6+ Ke8 5. Qe7#
Very good!
Well done!