Thursday, February 9, 2012

Is it possible to fill a checkerboard with 32 dominoes so that 15 are vertical and 17 are horizontal? Why?

Please explain.Is it possible to fill a checkerboard with 32 dominoes so that 15 are vertical and 17 are horizontal? Why?
It is an impossible task to accomplish. Basically, the reason for this is that if you place a vertical domino on the board, the horizontal rows now have only 7 spaces. Placing horizontal dominoes will only decrease the number of spaces by 2 or 0, so you have to place another vertical domino to get back to an even number of spaces. Even though the position for these may be changed, this basic concept works always, and so you have to have an even number of dominoes going each way.

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