What is the least possible number of cuts required to cut a cube into 64 identical pieces?
Answer & explanation
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). ·