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Black Mate in 4

Qf3 Kh4 Rxg4 Kh5 (if instead pawn takes g4 then Qxg4 is mate) Rg6 Kh4 and finally Rxh6 is mate
1. ...Rxg4 2. hxg4 Qf3+ 3. Kh2 Nxg4+ 4. Kg1 Qf2#
1. ...Qf3+ 2. Kh4 Rxg4 3. Kh5 Qxf5+ 4. Qg5 Qxg5#

Questions:
1. Would I have found a mate in 4 moves, if I hadn't been told that there is a mate in 4 moves in this position ? Maybe, YES.
2. Would I have found both solutions, if I hadn't been told that there are 2 solutions ? I guess, NO.

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