It’s white turn to move. What is the minimum number of moves for white to win? Assume that white and black both play optimally.
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The winning move I found is: 1. g6 (meaning the pawn moves to g6) threatening Qh7#
If black captures the pawn: 1....fxg6 2. Qxg6+ Kh8 3. Rh5#
If black protects h7 with the knight: 1....Nf6 2. Rh5 and the queen mates on h8, h7 or g6 depending on black's response.
If black moves the rook on f6, white mates early: 2. gxf7#