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White to move · Win the pawn
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Check, or pin the pawn, until Black's king has to stand on .
Check, or pin the pawn, until Black's king has to stand on .
A queen beats a pawn on the seventh rank, even with your king far away, if it's a centre or knight pawn. Check the king, or pin the pawn, until the king has to stand in front of its pawn. Then the pawn can't move, and you have one free move: bring your king a step closer. Repeat until your king arrives and the pawn falls. Against a rook pawn or a bishop pawn the defender has stalemate tricks, so your king has to be close already.
Every move is checked with an endgame tablebase, which knows the exact result of every position with up to seven pieces. The computer defends perfectly, and if a move throws the result away, the trainer stops and shows you a better one.