Q: You have eight coins. They all look identical, but one is a fake and is slightly lighter than the others. Explain how you can use a balance scale to determine which coin is fake in exactly two weightings.
A: Divide the coins 3,3,2.
Put the two groups of 3 in balance
If one side is lighter, divide the lighter group in 2 and 1, and place 1 of the 2 groups in each side of the balance if one is lighter it is the fake coin if not the 1 left out is the fake.
If the first weighing is equally balanced, divide the group of 2, one in each side of the balance. Whichever is the lighter is the fake.
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(also see: Seeking Mathematical Truth in Counterfeit Coin Puzzles | Quanta Magazine).
