किसी घन (क्यूब) के सभी फलक विभिन्न रंगों से रंगे गए हैं। उसे समान आमाप के छोटे-छोटे घनों में इस प्रकार काटा गया कि छोटे घन की भुजा बड़े घने की एक चौथाई हो। केवल एक ही रंगे हुए फलक वाले छोटे घनों की संख्या संख्या कितनी होगी ?
Read this question in English
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:
(a) 32 · (b) 24 · (c) 16 · (d) 8
उत्तर और व्याख्या · explanation in English
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). ·