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I've attached a screen shot of my game. It is Black’s turn to move. Their king was under check, but not checkmate, as the website didn't show mate.

enter image description here

After awhile, Black had to resign due to not being able to make any valid move. Analyzing the game with a computer results in the move 41. gxh3 being suggested.

How is that possible?

17

As White's previous move was pawn on h2 to h4 then pawn g4xh3 is a legal en passant capture.

For more info - see Rule 3.7.d of the laws of chess

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