Problem:
A solid cube of side length is removed from each corner of a solid cube of side length . How many edges does the remaining solid have?
Answer Choices:
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Solution:
The large cube has edges, and a portion of each edge remains after the small cubes are removed. All of the edges of each small cube are also edges of the new solid, except for the edges that meet at a vertex of the large cube. Thus the new solid has a total of edges.
The problems on this page are the property of the MAA's American Mathematics Competitions