Difference between revisions of "Checkerboard and dominoes"

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==Puzzle==
 
==Puzzle==
  

Revision as of 00:52, 24 November 2010



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Puzzle

A regular checker board has 64 squares (arranged in an 8 by 8 square). You happen to have a set of dominoes, each of which can cover exactly 2 squares on the checker board. Suppose you cut out one square from opposite corners. Is it possible to cover this mutilated board with non-overlapping dominoes? That is, is there a way to pair up the remaining 62 squares so that the two squares in each pair are adjacent? Prove your answer.