# If we remove two opposite corners of an 8×8 chessboard, is it possible to tile the resulting ﬁgure with 31 dominoes?

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If we remove two opposite corners of an 8×8 chessboard, is it possible to tile the resulting ﬁgure with 31 dominoes?
posted Jul 8, 2019

No

When removing 2 opposite corners we get 32x30 board by colors as the same colored squares removed..
A domino will cover one black and one white square of the board. 31 dominoes will cover 31x31.
However, the board has 32x30 opposite colored squares in all, so a tiling does not exist.

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