Problem:
A cube with -inch edges is to be constructed from smaller cubes with -inch edges. Twenty-one of the cubes are colored red and are colored white. If the -inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white?
Answer Choices:
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Solution:
The amount of white surface area is smallest when you place one white cube in the interior of the larger cube. Place each of the other white cubes at the center of a face so that white face and red faces are visible on that face. The total surface area of the larger cube is square inches, so the fraction of the surface area that is white is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions