Pawn Sideways Moves
No, pawns cannot move sideways. They can only move forwards. And pawns cannot ever move backwards. Pawns move one square at a time, directly forwards (vertically) into an empty square.
Capture moves are different: Pawns cannot capture directly forwards, they can only capture diagonally. And the pawn diagonal capture also must be forwards.
So pawns move forwards at every move, vertically for a normal move, and diagonally for a capture move. At the end of the pawn, a pawn can become a queen, called “queening a pawn” or “pawn promotion”.
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