Brain Teaser 3

Brain Teaser 3 - exactly 1 black and 1 white , it will not...

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Group 2-Peep Pulverizers Brain Teaser #3
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On an 8x8 Checkerboard, there are 64 squares, which means that there are 32 black squares and 32 white squares . Each domino can only cover 1 black square and 1 white square because they can only go horizontally or vertically. (As shown below) On the modified checkerboard, 2 corners are missing (squares that are of the same color) With 2 corners missing, that means that instead of a total of 64 boxes, there are a total of 62 boxes .
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Since 2 white corners were taken off, there are a total of 32 Black boxes and 30 White boxes. Because 1 domino can only cover
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Unformatted text preview: exactly 1 black and 1 white , it will not cover the entire checkerboard because there are sufficient Black boxes, but insufficient White boxes because there are 2 less whites than blacks. The ratio between Black and White boxes must be equal to (1:1). As long as the ratio between black white boxes are equal, no matter how many you take out, you will always be able to completely cover the checkerboard. Etc etc. Therefore, when the two corners are taken off, the covering is not possible because the ratio between black and white boxes are not equal....
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This note was uploaded on 11/09/2010 for the course ISE 234 taught by Professor Scze during the Spring '10 term at NJIT.

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Brain Teaser 3 - exactly 1 black and 1 white , it will not...

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