Puzzles
Twelve coins, one fake, three weighings
You have 12 coins that look identical, but one is counterfeit and weighs slightly differently — you don't know if it's heavier or lighter. Using a balance scale only three times, how do you find the fake coin and determine whether it's heavy or light?
Reveal the answer
Divide the coins into three groups of four and weigh two groups against each other; the result narrows which group holds the fake, and two further carefully chosen weighings pin down both the culprit coin and whether it's heavy or light. The puzzle became a classic through Martin Gardner's 'Mathematical Games' column, and generalises neatly to any number of coins using the same information-theoretic logic.