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Pawns: Pawns can only move forward. On their first move, they can move one or two squares. Afterwards, they can move only one square at a time. They can capture an enemy piece by moving one square forward diagonally. They can only move diagonally when capturing an enemy piece.
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Bishops: Bishops can move any number of squares diagonally.
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Knights: Knights can move only in an L-shape, one square up and two over, or two squares over and one down, or any such combination of one-two or two-one movements in any direction.
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Rooks: Rooks can move any number of squares, up and down and side to side.
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Queens: Queens can move any number of squares along ranks, files and diagonals.
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Kings: Kings can move one square at a time in any direction.