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UPSC CSE 2026 · PYQ · Logical Reasoning / Weighing Puzzle · medium

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?

  1. A.2✓ Correct
  2. B.3
  3. C.4
  4. D.1

Explanation

Divide the 7 cubes into three groups: 3, 3, and 1. Attempt 1: Weigh the two groups of 3 cubes against each other. If they balance, the odd (lighter) cube is the one left out. If one side is lighter, the odd cube is in that lighter group of 3. Attempt 2: From the group of 3 known to contain the lighter cube, pick any two and weigh them against each other. If they balance, the third (unweighed) cube is the odd one; if not, the lighter pan contains the odd cube. So 2 attempts suffice with certainty.
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