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What is the fastest/shortest possible checkmate? What is the minimum amount of moves to checkmate a side?

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Two moves! And this has a name as well! It is called Fool's mate!

 [title "Fastest Mate"]
 [fen "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]

 1. f3? e5 2. g4?? Qh4++

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