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Given that this position is legal, and could be reached in a legal game of chess, what were the two last half-movess, or one move for White and one for Black?

[FEN "5K2/8/6Pk/8/5Q1R/8/8/8 w - - 0 1"]

P.S.: I don't know the source. If someone knows the author, please say so and I will make an edit.

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The Black king is in check from both the White rook and queen, so it's impossible that either piece moved to give a check, it must have been a discovered check on the last move, which makes the White pawn on g6 the likely piece that was last moved.

White's last move must have been hxg6 en-passant. Which makes Black's previous move g7-g5 to block the check from the White queen.

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    In this constellation, it's impossible. It would be possible if the white queen were on e.g. e3 (Rf4-h4++). – xehpuk Dec 14 '20 at 16:26

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