The Twelve Pennies Puzzle

You are to investigate twelve pennies: eleven are the same but one is a different weight (lighter or heavier, you don't know which). You have some scales and are allowed only three tests to identify the unique penny. One test consists of one use of the scales to compare two stacks of one or more pennies. For example, if you divide the pennies into two stacks of six, use the scales to compare them, draw a conclusion and remove all the pennies in anticipation of another comparison, all that is one test.

This is truly a complex problem, and the written answer takes up quite a bit of space, so don't worry that you're on the wrong track if you don't have a simple solution.

One solution is here. If you want a hint, you can just peek at the first line or two and come back!