Nine Coins, One Counterfeit
The problem
You have nine coins that look identical. Exactly one of them is heavier than the others; the other eight weigh the same. Using a balance scale with two pans, what is the fewest number of weighings that is guaranteed to identify the heavy coin, whatever the outcome?
- The scale only tells you which pan is heavier, or that they balance. It gives no weight reading.
- You must be certain of the answer, not merely likely.
Take a minute
Reveal hint 1
Each weighing has three possible outcomes, so weighings can distinguish at most situations.
Reveal hint 2
A weighing with coins per pan leaves suspects: the left pan, the right pan, or the three coins you held back.
Solution
Answer**Two weighings.**
Derivation
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Count the information needed.
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First weighing.
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If the pans balance.
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If the left pan sinks.
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If the right pan sinks.
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Why the tripling matters.