Finding a Counterfeit Coin

Source

I got this problem from Rustan Leino, who got it from Ernie Cohen. He'd also heard it from a student who got it from Ernie at Marktoberdorf.

I solved it and wrote up my solution.

Problem    

You have 12 coins, 11 of which are the same weight and one counterfeit coin which has a different weight from the others. You have a balance that in each weighing tells you whether the two sides are of equal weight, or which side weighs more. How many weighings do you need to determine: which is the counterfeit coin, and whether it weighs more or less than the other coins. How?

Solution     Reveal