I have so far been only able to create examples where it is possible, and I am not sure how to create a formal proof using the difference between white and black squares. There are 32 white and 32 black squares, and after removing 12 dominoes, there will be 20 white and 20 black. I am not sure how to go from here.
2026-02-22 17:20:01.1771780801
12 1x2 dominoes are cut out of a chessboard. Is is true that one will always be able to cut a 1x3 rectangle from the remaning figure?
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No, place the dominoes in a grid pattern such that there are 3 dominoes in columns C and F and 3 dominoes in rows 3 and 6. The part not covered consists of nine 2x2 squares and four 1x1 squares, none of which fit a 3x1 domino.