A counterfeit coin - Math Central

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Question from Delian, a student:

Hi there,

I have a counterfeit penny problem - however this one is slightly more challenging. I have twelve pennies, and one of them is counterfeit. The only difference between the counterfeit coin and the real ones is that the counterfeit is EITHER heavier or lighter than the others (We don't know which). I need to be able to solve this in only three weightings, and I REALLY NEED HELP!!!

Hi Delian,

I can help you get started. Divide the 12 coins into three groups with 4 coins each. Call them the red group, he blue group and the green group. Balance the 4 red coins against the 4 blue coins. If they balance you know that the odd coin is one of the green coins. In this case balance one red and one green against 2 green coins.

Can you see how to proceed?
Penny

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