Counterfeit Coin Revisited

Some time ago we posed the problem of The Counterfeit Coin. Remember? If you don't, you may want to refresh your memory.

Well, once again you're working in the Puzzlanian treasury. And, once again, on impulse you pocket a counterfeit Puzzlanian "dollar". And, once again, you accidentally drop it into a pile of real Puzzlanian dollars. Boy, you just don't learn, do you?

Well, since you didn't learn from history, you're doomed to repeat it. You must identify the counterfeit coin from the real one in just three weighings. Simple, right? Just go back to the old puzzle and look up the solution!

Except this time you had the misfortune of not dropping your counterfeit into a batch of just seven real coins. This time it's not eight, not nine, not ten, but eleven other coins. In just three balancings, how can you pick out the counterfeit coin out of a total of twelve? Remember, apart from weight, counterfeits look just like the real thing. And counterfeits may be either lighter or heavier.