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?
- (a) 2 ✓ UPSC's answer
- (b) 3
- (c) 4
- (d) 1
Why the answer is (a)
• Split the seven cubes into groups of 3, 3 and 1.
• Weighing 1: put 3 against 3. If they balance, the single cube left out is the light one.
• If one side rises, the light cube is among those 3. Weighing 2: put 1 against 1; the lighter pan shows it, and if they balance it is the third cube.
• Two weighings always suffice, and one cannot, since a single weighing can distinguish at most 3 cases: (a).
Why the other options are wrong
- (b) 3
- Three weighings are not needed; the 3–3–1 split finds the cube in two.
- (c) 4
- Four weighings are more than needed.
- (d) 1
- One weighing can separate at most 3 cases, not 7.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.