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UPSC Prelims 2026 CSAT, question 51

Topic: Arrangements and puzzles

Q51

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) 2Correct answer
  2. (b) 3
  3. (c) 4
  4. (d) 1

Solution.

Answer: (a) 2

  1. Weigh 3 cubes against 3, keeping 1 aside; if the pans balance, the cube aside is the light one.
  2. If one pan rises, weigh 1 against 1 from that lighter group: the lighter cube, or the third if they balance, is the odd one.
  3. One weighing cannot always decide among 7 cubes, so 2 is the minimum that is certain.