### 12 apparently identical coins and a scale that can be used 3 times only

You are given 12 seemingly identical coins and are told that one of them is a counterfeit which is lighter *or* heaver than each of the others (i.e., 11 of them really do weigh the same). Given a balance scale and only 3 weighings allowed, how do you determine which of the coins is the counterfeit, **and** whether it is lighter or heavier?

SOLUTION

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