Problem:
A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are only two ways to construct a solid from three cubes so that each cube shares a face with at least one other:
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and
Neither of these configurations has both the front and side views shown. The four-cube configuration has the required front and side views. Thus at least four cubes are necessary.
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Question: Is it possible to construct a five-cube configuration with these front and side views?
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions