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)
• There are 7 possible positions for the light cube, and one balance attempt gives only 3 outcomes: left pan lighter, right pan lighter, or balance.
• Since 3^1 = 3 < 7, one attempt cannot identify the odd cube with certainty.
• In two attempts, first weigh 3 cubes against 3 cubes, keeping 1 aside.
• If the pans balance, the cube kept aside is the light cube; if one pan is lighter, the light cube is among the 3 cubes on that pan.
• In the second attempt, weigh 1 of those 3 against another, keeping the third aside; balance means the third is light, and a lighter pan identifies the light cube on that pan.
• Hence the worst-case number of attempts is 2, so option (a) follows.
Why the other options are wrong
- (b) 3
- Three attempts are not minimum because the 3-versus-3 followed by 1-versus-1 strategy identifies the light cube in at most two attempts.
- (c) 4
- Four attempts are not minimum because two attempts suffice by first weighing 3 against 3 and then 1 against 1 from the lighter group.
- (d) 1
- One attempt is impossible because a single balance has only three outcomes, which cannot distinguish among seven possible light cubes.
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.