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AMO · 2027 · Grades 4-5 · SET 25 - Self-study Question 6

AMO

Question 6

A solid brick is formed by gluing together eighty $1\times1\times1$ cubes. The brick has as little surface area as possible. The two faces with the least area are painted blue. What is the number of square units in the area of one blue face?

Here “brick” means a completely filled rectangular prism with whole-number side lengths.

Enter only the whole-number answer, without units.