Question

A cube is taken, and painted black all sides. Now n, n - 1 and n - 2 cuts are made in X, Y and Z axis respectively (for n > 5). How many small pieces have no black faces on them?
1. (n - 2)³
2. (n - 2) × (n - 3) × (n - 4)
3. (n - 3)³
4. (n - 1) × (n - 2) × (n - 3)

Answer 1

Correct Answer - Option 2 : (n - 2) × (n - 3) × (n - 4)

All the pieces that are on the outside, have black faces. Each axis has 2 sides on the outside. So every side is reduced by 2 for them to have no black faces.

So (n - 2), (n - 3) and (n - 4) are number of pieces on X, Y and Z axis respectively to have nocoloron them.

So the total number of pieces is (n - 2) × (n - 3) × (n - 4).

Hence, (n - 2) × (n - 3) × (n - 4) is the right answer.