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MathNet 2024-part-05 — 168 problems (EN–VI) Question 33

Math Olympiad Vault · MathNet 2024-part-05 — 168 problems (EN–VI)

Question 33

A cube of side length $n$ is made up of $n^3$ smaller unit cubes. Some of the six faces of the large cube are fully painted. When the large cube is taken apart, 245 smaller cubes do not have any paint on them.
Determine the value(s) of $n$ and how many faces of the large cube were painted.