We have 12 coins and a balance. 11 coins are of the same weight, but one coin differs in weight (note that you do not know whether the coin with different weight is heavier or lighter!). You may perform three weighings to find out which coin has a different weight, and whether this coin is heavier or lighter.
How should you perform these three weighings to find out which coin has a different weight, and whether this coin is heavier or lighter?