Checkerboard and dominoes

From Math Puzzle Wiki
Revision as of 13:38, 23 September 2010 by Oscarlevin (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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.