You have eight pennies that look the same, but one is counterfeit. The counterfeit penny is known to be heavier than the others. How can you tell which one is counterfeit by using a balance scale only twice? (The balance scale has two pans but no weights; you can place any combination of pennies in either pan and then observe whether the pennies in each pan weigh the same, or if one collection is heavier than the other.)

The original question did not include the information that the counterfeit penny is heavier, but without that information not even the MathNerds could do it. Can you?

Hint 1

Start small. Try to solve this problem instead: You have 3 pennies, and one is counterfeit and heavier than the others. Find it in one weighing. (If this is too hard, start even smaller: suppose you only have 2 pennies; find the counterfeit in one weighing.)

Hint 2

With three pennies, the only reasonable thing you can do is pick any two of them and put one in each pan. There are three possibilities:

left pan is heavy
the pans balance
right pan is heavy

Explain how you can deduce the heavy coin in each case.

Click here if you need another hint.

Click here for the solution.