This article is from the Puzzles FAQ, by Chris Cole email@example.com and Matthew Daly firstname.lastname@example.org with numerous contributions by others.
You have 12 coins, one of which is counterfeit. The counterfeit is
indistinguishable from the rest except that it is either heavier or
lighter (but you don't know which). How can you determine which coin is
the counterfeit in 3 weighings on a balance scale?
One solution is to label the coins with the letters from FAKE MIND CLOT
and weigh the coins: MA DO -- LIKE, ME TO -- FIND, FAKE -- COIN. Logic
will now suffice to find the odd coin. For instance, if the results are
left down, balance, and left down, then coin "A" is heavy.