Solve the 12-coin balance puzzle
Overview
This question evaluates understanding of combinatorial reasoning, information theory, and decision-tree construction for identifying a single counterfeit coin and whether it is heavier or lighter using constrained balance-scale observations.
Coinbase
Oct 13, 2025, 9:49 PM
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12-Coin Counterfeit Problem (3 Weighings)
Setup
- You have 12 visually identical coins.
- Exactly one coin is counterfeit; it is either heavier or lighter (unknown which).
- You have a balance scale and no additional reference weights.
Task
Design a weighing strategy that uses exactly three weighings and always identifies:
- which specific coin is counterfeit, and
- whether it is heavier or lighter.
Provide the complete decision tree: for each weighing, specify which coins go on each pan, and for each possible outcome (left pan heavy, right pan heavy, or balance), indicate the next step and final identification where applicable.
Finally, prove the correctness of your strategy and that three weighings are minimal (i.e., two weighings cannot always suffice).
Solution
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