Problem:
Determine whether it is possible to tile a standard chessboard with -tiles and -tile of the shapes below:
(Each tile covers four squares of the chessboard. The tiles can be flipped and rotated at will.)
Berkeley Math Circle Monthly Contest 8
Solution
Solution:
Let the squares of the chessboard be colored black and white in the usual way. Note that the -tile always covers two squares of each color, while the -tile covers either black and white or black and white squares. Since the chessboard has equal numbers of black and white squares, it is impossible to cover it with these tiles.
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