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Find the mate in 6 (white to move)

I found a mate in 7 with the line Qxf7+ Kd8 Qf8+ Kc7 Nb5+ Kb6 Qd6+ Ka5 b4+ Ka4 Nc3+ Ka3 b5#, which is a beautiful mate in it's own right, but after checking the engine there's a better move than Nb5+.

Nice puzzle!
Posting a bullet chess game just to show a puzzle . Are you serious?.We can solve puzzles everywhere

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