# Q. Which is the least possible number of cuts required to cut a cube into 64 identical pieces?

a) 8

b) 9

c) 12

d) 16

Correct answer: b) 9

#### Question from UPSC Prelims 2024 CSAT

**Explanation : **

## Least possible number of cuts

Let’s approach this step-by-step:

1) We need to divide the cube into 64 identical pieces. This means we need to divide each dimension of the cube into 4 equal parts (4 x 4 x 4 = 64).

2) For each dimension, we need 3 cuts to divide it into 4 equal parts.

3) So, we need:

– 3 cuts parallel to the xy-plane

– 3 cuts parallel to the yz-plane

– 3 cuts parallel to the xz-plane

4) In total, this gives us 3 + 3 + 3 = 9 cuts.

Therefore, the least possible number of cuts required to cut a cube into 64 identical pieces is 9.

The correct answer is b) 9