A cuboid 6 cubes long, 5 cubes deep and 4 cubes high is painted on all its faces and broken up into the small cubes. How many small cubes have paint on exactly two faces?

Question

Accepted Answer

36. Two painted faces: edge cubes that are not corners. A cuboid has 4 edges of each length. Non-corner cubes per edge: 6-2=4, 5-2=3 and 4-2=2. Total 4×(4+3+2)=36. (60 forgets to remove the corners: 4×(6+5+4).)

A cuboid 6 cubes long, 5 cubes deep and 4 cubes high is painted on all its faces and broken up into the small cubes. How many small cubes have paint on exactly two faces?

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