You’re the realm’s greatest mathematician, but ever since you criticized the Emperor’s tax laws, you’ve been locked in the dungeon. Luckily for you, one of the Emperor’s governors has been convicted of paying his taxes with a counterfeit coin, which has made its way into the treasury. Can you earn your freedom by finding the fake? Jennifer Lu shows how.

[Ted Ed]

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There is an easier way of doing this. Basically your first step is to divide the group,in half and set the heavier set aside entirely as they are real coins. Then take the remaining 6 and divide them into pairs. Weigh 2 of the pairs. The heavier pair has 2 real coins. If they wiegh the exact same then the pair left out has the counterfiet. Then you wiegh either the pair that was lighter or the pair that was left out depending on the results of the second wieghing.

The difficulty lies in the fact that you do not know if the counterfeit coin is lighter or heavier.

The flaw is the assumption that a) there actually is a counterfeit coin (the setup just says he was convicted), and b) that there would only be one counterfeit coin.