1987 AJHSME Problems/Problem 7

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Problem

The large cube shown is made up of $27$ identical sized smaller cubes. For each face of the large cube, the opposite face is shaded the same way. The total number of smaller cubes that must have at least one face shaded is

$\text{(A)}\ 10 \qquad \text{(B)}\ 16 \qquad \text{(C)}\ 20 \qquad \text{(D)}\ 22 \qquad \text{(E)}\ 24$

Solution

Clearly no cube has more than one face painted. Therefore, the number of cubes with at least one face painted is equal to the number of painted unit squares.

There are $10$ painted unit squares on the half of the cube shown, so there are $10\cdot 2=20$ cubes with at least one face painted.

$\boxed{\text{C}}$

1987 AJHSME (Problems • Resources)
Preceded by Problem 6	Followed by Problem 8
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1987 AJHSME Problems/Problem 7

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