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(a) 1.Rxe5+ Kxe5 2.Re1+ Kf5 3.Qxd5+ Kg4 4.f3+ Kh3 5.Qe6+ Qg4 6.Qxg4#
(b) 1.Rxe5+ Kf7 2.Qxd5+ Kg7 3.Rxe7+ Kh8 ( 3. …Kf8?? 4..Qf7# ) 4.Qf7 Rg8 ( or 4. …Qxh2+ 5.Kxh2 Rg8 or c2 6.Qxh7# ) 5.Bf6+ Rg7 6.Re8# or Qf8#
(c) 1.Rxe5+ Kd7 2.Qxd5+ Kc7 ( or 2. …Ke8 3.Rxe7+ Kf8 4.Qf7# ) 3.Rxe7+ Kb8 4.Qxb7#
1. Rxe5+ Kf7 [1…Kxe5 2. Re1+ Kf5 3. Qf4#] 2. Qxd5+ Kf8 [2…e6 3. Qxe6+ Kg7 4. Qd7 and whichever square the Black King chooses he is mated in two by 5. Qxc8+ and 6. Re7#] 3. Rxe7 and White mates in at most 3 moves.
Well done!
Very good!