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Imagine a 8x8 cell board that is missing two cells at the opposite corners, a domino takes up exactly two cells. How can you fill the board with dominoes so that none overlap or hang off the edge?

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seeker
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KevinBui
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    Color it as a chessboard and count the number of white and black squares to see that it is impossible. – t.b. Aug 23 '11 at 07:27
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    Before you ask "How can you fill the chessboard?" you should ask "Can you fill the chessboard?" – Aaron Aug 23 '11 at 07:29

1 Answers1

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This is a well-known problem - it even has its own wikipedia article: Mutilated chessboard problem.

Here you can find a few similar but more challenging problems for trominos.

Problems like this are usually solved using some type of coloring argument, as explained in Theo's comment and the above links.

Martin Sleziak
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