GATE CS 2024 Set 2 Q9 — General Aptitude

To divide a cube into $8$ pieces of equal size and shape using straight, end-to-end cuts, we can make cuts along its three mutually perpendicular axes (length, width, and height).

Let $x$, $y$, and $z$ be the number of cuts made along the three dimensions. The total number of pieces $N$ obtained is given by the formula:

We are given that $N = 8$. To minimize the total number of cuts, $T = x + y + z$, we should distribute the factors of $8$ as evenly as possible among the three dimensions:

Comparing the terms:

• $x + 1 = 2 \implies x = 1$
• $y + 1 = 2 \implies y = 1$
• $z + 1 = 2 \implies z = 1$

Thus, the minimum number of cuts required is:

These $3$ mutually perpendicular cuts (one horizontal and two vertical) divide the cube into $8$ identical smaller cubes.