Problem:
A cube of edge is cut into smaller cubes, not all the same size. If the edge of each of the smaller cubes is a whole number of centimeters, then
Answer Choices:
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Solution:
Since the edge of each smaller cube must be a whole number, the smaller cubes must be or cubes. There can be only one smaller cube of edge , so the rest of the smaller cubes have edge . Since the volume of the original cube was cubic , and the volume of the cube of edge is cubic , then there must be cubes of edge (volume cubic ). There are a total of cubes so .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions