1991 AJHSME Problems/Problem 5

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Problem

A "domino" is made up of two small squares: Which of the "checkerboards" illustrated below CANNOT be covered exactly and completely by a whole number of non-overlapping dominoes?

$\text{(A)}\ 3\times 4 \qquad \text{(B)}\ 3\times 5 \qquad \text{(C)}\ 4\times 4 \qquad \text{(D)}\ 4\times 5 \qquad \text{(E)...$

Solution

For a bunch of dominoes to completely tile a board, the board must have an even number of squares. The $3\times 5$ board clearly does not, so $\boxed{\text{B}}$ cannot be tiled completely.

1991 AJHSME (Problems • Resources)
Preceded by Problem 4	Followed by Problem 6
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1991 AJHSME Problems/Problem 5

From AoPSWiki

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