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Fool's mate
Fool's mate is the fastest possible checkmate in chess, with Black mating White in two moves (1.f3 e5 2.g4 Qh4#) after White's pawn moves open the h4–e1 diagonal; named in chess literature from 1617.
Scholar's mate
Scholar's mate is chess's four-move checkmate: 1.e4 e5 2.Bc4 Nc6 3.Qh5 Nf6 4.Qxf7#, exploiting f7, the square only the king defends. Defenses are ...g6, ...Qe7, or ...Qf6.