Question

How many cubes have none of their sides painted?

• A. 1
• B. 4
• C. 0
• D. 5
• E. None of these

Answer 1

The correct option is A 1

Here n = 3.
Therefore, number of cubes with 3 sides painted red = Number of corner cubes = 8.
Number of cubes with 2 faces painted = $(n-2)\times 12=(3-2)\times 12=12$.
Number of cubes with 1 face painted = $(n-2{)}^2\times 6=(3-2{)}^2\times 6=6$.
Number of cubes with no face painted = $(n-2{)}^3=(3-2{)}^3=1$