Is it not a possible move to just move the king to g3, then capture the rook with the knight and the knight with the king?
Bug: Solo Chess
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This came up in Solo Chess. Per the rules, every move must capture a piece and the king must be the last piece on the board. With the puzzle below, that's impossible. The only way for there to be one remaining piece on the board here is for the knight to capture twice which would mean the knight would have to capture the king.