2013 AMC 10A Problems/Problem 14
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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?
Solution
We can use Euler's polyhedron formula that says that . We know that there are originally faces on the cube, and each corner cube creates more. . In addition, each cube creates new
vertices while taking away the original , yielding vertices. Thus , so
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