Calculating the minimum number of cuts required to divide a cube

To minimize cuts for a specified number of pieces P, represent P as the product of three variables along the axes: x × y × z = 64. Minimizing total cuts requires choosing integers x, y, z as close to each other as possible.

For 64, the closest factor distribution is a perfect cube: 4 × 4 × 4 = 64.

The cuts needed along each dimension are (x-1), (y-1), and (z-1). Total cuts = (4 - 1) + (4 - 1) + (4 - 1) = 3 + 3 + 3 = 9.

Answer: (b).