A cube whose two adjacent faces are coloured, is cut into 64 identical small cubes. How many of these small cubes are not coloured at all?

36

Since the cube is divided into 64 identical cubes, thus the side faces are divided into 4 by 4 squares.

Now the adjacent faces are coloured, therefore coloured cubes will be on Face 1 that is 4×4 = 16 Cubes

on the adjacent face 4 edge cubes will be common, thus only 3×4 cubes will be coloured exclusively = 12 Cubes

Non-Coloured cubes=Total cubes - coloured cubes = 64-16-12 = 36

The correct answer is Option (2) → 36