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that's a cutie. I first tried 1Qxh6 thinking if 1...gxh6 2Nf6+ Kh8 3 Rh7++ and if black declines the queen, white threatens 2Nf6+ gxf6 3Qh7++
I think white wins in all combinations with 1Qxh6, but the "correct" answer is the quickest mate.
One of the classics.
It doesn't have to be a mate in 3 to be a puzzle. The idea is most important. And you made the wrong moves. With your variation its mate in 4.
wrong, you can block with biship 4.... e7, mate in 5 just another variation.
And in a puzzle the opponet always plays the best move, and to give up to an early mate is bananas.
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