1991 AJHSME Problems/Problem 24
Problem
A cube of edge cm 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
Solution
If none of the cubes have edge length , then all of the cubes have edge length , meaning they all are the same size, a contradiction.
It is clearly impossible to split a cube of edge into two or more cubes of edge with extra unit cubes, so there is one cube and unit cubes.
The total number of cubes, , is .
See Also
1991 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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