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I have a rook, a queen and my king while my opponent has only 2 pawns and king left. The situation is complicated because they cannot move anything, except for a single pawn move. But if they move that pawn their king is checked by my queen. Is this situation stalemate or checkmate?

       8/8/8/6rk/8/5qPK/7P/8 w - - 0 1
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If the situation is as in the diagram below, it is stalemate. You correctly noticed that white has no legal moves: any potential move would put the white king into check, which is not allowed. Furthermore in the position the white king is not attacked, so it is stalemate (not mate).

       8/8/8/6rk/8/5qPK/7P/8 w - - 0 1

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