Problem:

You have 12 coins and a balance scale. One coin is counterfeit and either heavier or lighter than the rest. You can use the scale three times to determine the counterfeit coin. How do you find the counterfeit coin and determine if it is heavier or lighter?

Scroll to the bottom of the page for the answer

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Solution:

Divide the coins into three groups of four. Weigh two groups. If they balance, the counterfeit is in the third group; if not, you know which group has the counterfeit and whether it's heavy or light. Use the second and third weightings to narrow down to one coin and its weight.