Twelve weights

A classic weighing problem, much harder than the similar Nine weights puzzle.

Puzzle

Each year at the Fairytale Fair, a contest is held to see which goose can lay a golden egg. Unfortunately, almost everyone who enters just takes a standard silver egg and paints it gold. This year, there are exactly one dozen eggs submitted. The wizard in charge of the contest has a vision, in which it is revealed that all but one egg is a fake. Each fake egg weighs exactly the same, but the real egg weighs either more or less than all the fake eggs. This being a Fairytale Fair, the only measuring instruments are standard two side balance scales. How can you determine which egg is the real one using only the balance scale, and using it only three times?

See also

Nine weights - an easier version (you know that the different weight is heavier). Six weights - Find the three heavier weights among three sets of two weights each.