The queen usually stops a pawn easily, but with a rook's pawn (on the a- or h-file) on the seventh rank there is a famous exception. When the stronger side checks the king into the corner in front of the pawn, the defender is stalemated - and the king has to be released, losing the tempo.
Here White has the king on f7 and a pawn on h7; Black has the king on c1 and the queen on d4. White to move, and it is a draw (per the tablebases): Black's king is too far away, and the stalemate mechanism in the h8 corner denies the queen the tempo she needs to bring him up.
The lesson: with a rook's or a bishop's pawn on the seventh, the queen only wins with the king close by. Knowing this exception helps attacker and defender alike.
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The weaker side uses stalemate: the king hides in the corner, and any check leaves it with no moves. So your own king is needed.
Use checks to force the king onto the square in front of the pawn, and spend the tempi so gained on walking your own king right up.
Against central and knight's pawns the queen wins almost always; the trouble comes with rook's and bishop's pawns.
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