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What is the number of cubes with no face painted?

Correct Answer: 24

Explanation:

For least number of cuts 120 = 4 x 5 x 6 i.e number of cuts must be 3, 4 and 5 in three planes in this case number of cubes on a face is either 6 x 5 = 30 or 6 x 4 = 24 or 4 x 5 = 20 cubes . And number of cuboids on an edge is 4 or 5 or 6
Number of cuboids with no face painted is (4 - 2)(5 - 2)(6 - 2) = 2 x 3 x 4 = 24


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