A cuboid is built from unit cubes, painted all over and taken apart. It was 4 cubes long and 3 cubes deep, and exactly 2 of the cubes have no paint. How many unit cubes were there in all?

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Accepted Answer

36. The unpainted cubes form an inner block (4-2)×(3-2)×(h-2), where h is the height. So 2×1×(h-2)=2, giving h=3. The cuboid had 4×3×3=36 cubes. (24 takes the height as 2.)

A cuboid is built from unit cubes, painted all over and taken apart. It was 4 cubes long and 3 cubes deep, and exactly 2 of the cubes have no paint. How many unit cubes were there in all?

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