A cube has all its faces painted in different colors It is cut into smaller cubes of equal sizes suc...........

Quantitative Aptitude ( CCS) Geometry

A cube has all its faces painted in different colors. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube. The number of small cubes with none of the sides painted is:

Not even one

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Explanation:

Total number of cubes after cutting = n³=(4)³=64 (n = number of pieces)
Cube with 3-sides painted = 8 (for a proper cube number of the cube at corner is always 8)
Cube with 2-sides painted = 12(n-2)=12(4-2)=24
Cube with 1 side painted = 6(n-2)²=6(4-2)²=24
Cube with no side painted =[64-(8+24+24)]=8