Among 11 coins of the same denomination, 1 is know to be counterfeit. Using a simple 2-pan scale or balance, how would you determine in 2 weighings if the fake coin is heavier or lighter than a real coin?

Take the 2 heaviest, and then weigh them. Take the two lightest, and then weigh them. After this you'll know which one is fake.

Not quite.

Put 5 coins in each pan.. (in theory) they should balance out.
Replace any coin in either pan with 11th coin and scale should once again balance out. If not.. fake coin is of diff weight.

Very good idea but it still doesn't determine if the fake coin is heavier or lighter.

I guess I didn't read the question well enough.

Facts: Eleven coins are in front of me. One of the coins is a counterfeit. I don't know which coin is the counterfeit coin, but I do know that the counterfeit coin is of a different weight.

Question: Using a simple 2-pan scale or balance, how would I determine in 2 weighings if the fake coin is heavier or lighter than a real coin?

Answer:

I'll put 5 coins in each pan.

scenario 1: The pans will balance out because all the 10 coins in the pans are real. Therefore, the 11th coin is the fake coin. I'll take all the coins out of the pans and weigh the fake coin against one of the real coins and I will know if the fake coin weights more or less than a real coin.

scenario 2: One of the pans will weigh more than the other. Therefore I will know that the 11th coin is a real coin. Selecting to continue my process of elimination with the heavier pan, I'll take the five coins in the lighter pan and set them aside. I'll take the 11th coin and the 5 coins in the heavier pan (6 coins in total) and put three in each pan.

scenario 2.1: The pans do not balance out, letting me know that the fake coin must be in this heavier group of coins and therefore is HEAVIER than a real coin.

scenario 2.2: The pans balance out. Therefore I will know that the fake coin must be in the lighter group (the 5 I set aside). So the counterfeit is LIGHTER than a real coin.


So the real question is... From scenario 2.2, in exactly two more weighings, how can you tell exactly which coin is the counterfeit coin?

my brain hurts 

First determine which is the fake coin. Then weigh the fake coin against one real coin and you'll get your answer.