एक घन को 64 समरूप (आइडेंटिकल) टुकड़ों में काटने के लिए आवश्यक काटों की न्यूनतम संभावित संख्या क्या है?
Read this question in English
What is the least possible number of cuts required to cut a cube into 64 identical pieces?
(a) 8 · (b) 9 · (c) 12 · (d) 16
उत्तर और व्याख्या · explanation in English
Answer: (b) 9
64 identical pieces means a 4 × 4 × 4 arrangement. Each direction needs 3 cuts to make 4 slices, so the least number is 3 + 3 + 3 = 9.
- With a, b and c straight cuts in the three directions, the number of pieces is (a + 1)(b + 1)(c + 1).
- We need (a + 1)(b + 1)(c + 1) = 64 with a + b + c as small as possible; the total is least when the three factors are equal: 4 × 4 × 4.
- So a = b = c = 3, and the number of cuts = 3 + 3 + 3 = 9.
- Check: other splits cost more, e.g. 8 × 4 × 2 needs 7 + 3 + 1 = 11 cuts.
Remember · Pieces = (a + 1)(b + 1)(c + 1) for a, b, c cuts in three directions; cuts are fewest when the factors are equal.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·