Seven cubes are identical in shape. Out of these, the weight of each of the six cubes is equal and the weight of the remaining cube is less than the weight of any other cube. A balance is used to identify the lightest cube. What is the minimum number of attempts required to distinguish the odd cube with certainty?
Answer & explanation
Answer: (a) 2
Each weighing has three outcomes (left lighter, right lighter, balance), so split the cubes into three groups: 3, 3 and 1. One weighing narrows the light cube to a group of at most three, and a second weighing of one against one finds it.
- Weigh 3 cubes against 3. If they balance, the 7th cube is the light one.
- If one side rises, the light cube is among those 3.
- Weigh 1 against 1 from that group: the lighter pan shows it; if balanced, it is the third cube.
- So 2 weighings always suffice; 1 cannot, since one weighing separates at most 3 possibilities, not 7.
Remember · A balance gives three outcomes: with k weighings you can find one odd (known-lighter) item among up to 3ᵏ items.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·