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How to checkmate with king and rook

Rook and king mate · You are White · checkmate within 50 moves

♚♖♔

White to move. FEN: 8/8/8/4k3/8/8/8/R3K3 w - - 0 1

The idea

The rook cuts the king off along a rank or file; your king walks up to stand opposite it; then the rook checks along the edge. If the king attacks your rook, move the rook far away along the same line, keeping the cut.

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Every position's result, and every move the text recommends, was checked against the Lichess 7-piece tablebase. Part of Chess Path, a free chess course.