A large painted cube is cut into equal small cubes, and 60 of the small cubes turn out to have paint on exactly two faces. How many small cubes have no paint at all?

Question

Accepted Answer

125. Two-face cubes sit on the 12 edges, n-2 per edge: 12(n-2)=60 gives n-2=5, so n=7. The unpainted core is 5^3=125. (343 is the total number of small cubes.)

A large painted cube is cut into equal small cubes, and 60 of the small cubes turn out to have paint on exactly two faces. How many small cubes have no paint at all?

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