There are eight coins, one of which weighs a slightly different amount from the rest. You have an old-fashioned balance like this one that you can use to compare the weights of whichever sets of coins you would like. Find the special coin in only three weighings. Bonus points if you can also determine whether the special coin is heavier or lighter than the rest without any additional weighings.
UPDATE: Try the problem with twelve coins instead of eight, although eight coins could still be a good warm-up.
UPDATE: Feel free to share solutions to the eight coin version too!