One of twelve coins is counterfeit: it is either heavier or lighter than the rest. Is it possible to identify the counterfeit coin in three weighings on a beam balance?

Classic puzzle that I first encountered in 1993-1994 time frame.

Several excellent expositions of various approaches:

1. Solution by Brian Bundy.
2. Solution by Jack Wert is especially pleasing.
3. McWorter's solution.
4. Dyson and Lyness solution.
5. Newman's solution.
6. Wilson's solution.