The Tetris Proof

7 types of tetrominoes

Suppose a standard 8×8 chessboard has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2×1 so as to cover all of these squares?

Square, L, and skew tetrominoes will always have equal number of black and white squares
The “T” tetromino can have either 3 black or 3 white squares.

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