#6 The Mutilated Chess Board
The props for this problem are a chessboard and 32 dominoes. Each domino is of such size that it exactly covers two adjacent squares on the board. The 32 dominoes therefore can cover all 64 of the chessboard squares. But now suppose we cut off two squares at diagonally opposite corners of the board and discard one of the dominoes. Is it possible to place the 31 dominoes on the board so that all the remaining 62 squares are covered? If so, show how it can be done. If not, prove it impossible.
Alabama, Alaska, Arizona, Arkansas,
California, Colorado, Connecticut, and more.
Delaware, Georgia, Florida, Hawaii, Idaho,
Illinois, Indiana, Iowa, only 35 to go.
Kansas, Kentucky, Louisiana, Maine,
Maryland, Massachusetts, and Michigan,
Minnesota, Mississippi, Missouri, Montana,
Nebraska’s 27, #28’s Nevada.
New Hampshire, New Jersey, and way down, New Mexico,
New York, North Carolina, North Dakota, Ohio.
Oklahoma, Oregon, Pennsylvania, now let’s see:
Rhode Island, South Carolina, South Dakota, Tennessee.
There’s Texas, and there’s Utah, Vermont, I’m almost through,
Virginia, and there’s Washington, and West Virginia, too.
Could Wisconsin be the last one in the forty-nine?
No, Wyoming is the last one, in the fifty states that rhyme!
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