Q1. A cube is coloured green on all its faces. It is cut into 64 smaller cubes of equal size. How many smaller cubes have exactly one face coloured?
A 20
B 22
C 24 Correct
D 26
Explanation
Since 64 smaller cubes are formed, the original cube is divided as 4 by 4 by 4. A smaller cube with exactly one coloured face must lie in the centre area of a face, not on an edge or a corner. On each large face, the count is (4 - 2) by (4 - 2), so 4 such cubes. There are 6 faces, giving 6 x 4 = 24. The counts 20, 22, and 26 do not follow the face-centre formula and either undercount or overcount these cubes.