Insight · ★★★★☆ · ~9 min
The 12 Coins
One fake coin among 12 — heavier or lighter, you don't know. Find it in 3 weighings.
by MindYourPuzzle
A classic deduction puzzle — simple to state, deviously tight on information.
You have 12 identical-looking coins. Exactly one is counterfeit: it weighs slightly different from the rest — but you don't know whether it's heavier or lighter.
Your only tool is a balance scale (it tells you which side is heavier, or that the two sides are equal). You get 3 weighings.
What is the maximum number of coins for which 3 weighings can ALWAYS identify the fake (and say whether it's heavy or light)?
(Answer with the number of coins.)
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