A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube. The number of small cubes with only one of the sides painted is:
Answer & explanation
Answer: (b) 24
Each edge of the big cube is cut into 4, so every face is a 4 × 4 grid of small cubes. Only the inner 2 × 2 on each face has exactly one painted side: 6 × 4 = 24.
- The big cube becomes 4 × 4 × 4 = 64 small cubes.
- On each face, the cubes painted on that face alone form the inner (4 − 2) × (4 − 2) = 4.
- Six faces: 6 × 4 = 24.
Remember · Cube cut into n per edge: one face painted = 6(n − 2)², two faces = 12(n − 2), three faces = 8.
Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·