What is the least possible number of cuts required to cut a cube into 64 identical pieces?

Correct Option: (b) 9

To cut a cube into N identical smaller pieces with the minimum number of cuts, the cuts must be distributed as equally as possible along the three mutually perpendicular axes (x, y, and z). Let the number of cuts along the three axes be x, y, and z. The total number of identical pieces obtained is given by (x + 1) × (y + 1) × (z + 1) = 64. To minimize the total cuts S = x + y + z, we should make the factors (x + 1), (y + 1), and (z + 1) equal. Since 64 = 4 × 4 × 4, we set (x + 1) = 4, (y + 1) = 4, and (z + 1) = 4. This gives x = 3, y = 3, and z = 3. Therefore, the minimum number of cuts required is x + y + z = 3 + 3 + 3 = 9. Thus, the correct option is (b).