First divide the 12 balls into three groups, A, B, and C.
Then, weigh A, and B: 3 possible scenarios
A > B, A = B, or A < B
Then, randomly select three balls from each group, and do a circular switch. A to B, B to C and C to A
Second three scenarios appear.
If initially, A > B, and second scenaro:
- A > B: then, the ans is obvious
- A = B: then, a lighter ball is being switched to C, and we have localized a lighter ball in a group of three, the ans is easy when we have one more weighing left.
- A < B: then, a heavier ball is being transferred from A to B, and similarly, it can be determined with one more weighing.
Similar logics can be applied to other scenarios.
Thanks for playing.
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