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Question
A large cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fifth the side of the large cube. The number of small cubes with at least two colours on its body is:
A large cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fifth the side of the large cube. The number of small cubes with at least two colours on its body is:
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Solution
The correct option is B 44
Total number of small cubes = 5*5*5 = 125
In the diagram above, we need all the unshaded cubes (all the shaded cubes have only 1 face painted).
Number of cubes with 2 painted faces (edge cubes) = 12*(n-2) = 12*3 = 36
Number of cubes with 3 painted faces (corner cubes) = 8
Number of cubes with at least 2 painted faces = 36 + 8 = 44
Total number of small cubes = 5*5*5 = 125
In the diagram above, we need all the unshaded cubes (all the shaded cubes have only 1 face painted).
Number of cubes with 2 painted faces (edge cubes) = 12*(n-2) = 12*3 = 36
Number of cubes with 3 painted faces (corner cubes) = 8
Number of cubes with at least 2 painted faces = 36 + 8 = 44
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