# A coin-weighing puzzle with 80 coins

In 80 coins one coin is counterfeit. What is minimum number of  weighings to find out counterfeit coin?

PS: The counterfeit coin can be heavy or lighter.

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It can't be done with weighings at all. No self-respecting counterfeiter would commit the rookie mistake of getting the mass wrong. –  Henning Makholm Oct 20 '12 at 14:26
Please specify if you know whether the coin is heavy or light. That changes the process a bit. –  Ross Millikan Oct 20 '12 at 14:38
@Ross The question doesn't state that the counterfeit coin has a different weight from the others. My guess is that the real coins are made of gold and the counterfeit one, although it weights the same, is made of brass, and can be distinguished from the real coins with no weighings at all. –  MJD Oct 20 '12 at 15:36
@MJD: Good point. I can't imagine how to do it with less than zero weighings. –  Ross Millikan Oct 20 '12 at 15:38

Hint: Consider weighing one third of the coins on each side. What will this tell you?

In fact, it can be shown that the process, the definition of which you will be led to by this hint, is optimal. Try to think of why this is the case, and to classify how many weighings you need with $n$ coins.

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