A cube has its top, front and right faces painted red, and its bottom, back and left faces painted green. It is cut along the lines into 64 equal small cubes. How many small cubes have exactly one red face and one green face?

Question

Accepted Answer

12. A cube with exactly two painted faces sits on an edge, away from the corners: 4 - 2 = 2 cubes per edge. Red meets green on 6 of the 12 edges (top–left, top–back, front–left, front–bottom, right–back, right–bottom), so 6 × 2 = 12.

A cube has its top, front and right faces painted red, and its bottom, back and left faces painted green. It is cut along the lines into 64 equal small cubes. How many small cubes have exactly one red face and one green face?

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