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nice puzzle! 1. Qf6 +, this forces 1 .. Q x f6 2. g5 x f6+ Kg8 3. Rc8#
This sequence is forced because the black king’s escape route is limited by the threat, Rxh4.
I think this is also a repeat. I am not sure.
1.Qf6+ Qxf6
2.exf6+ Kh7
(2….. Kf8 3.Rc8#0
(2…. Kg8 3.Rc8+ transposes to main line)
3.Rxh4+ Nh5
4.Rxh5+ this is where B at b1 is useful.
4…… Kg8
5.Rc8#