The Puzzle of the Twelve Coins


You have 12 coins.  Eleven are made of gold; one is counterfeit.  You don’t know which one because they all look alike.  Also, you don’t know if the fake coin is heavier or lighter than a real gold coin.  All eleven gold coins weigh the same. 

You have a classic balance scale: two pans suspended from a pole with the center point balanced on a post.  The scale can compare the weight of an object or objects in the left pan (L) with an object or objects in the right pan (R ). The scale will tell you if pan L is equal, heavier or lighter than pan R.

You can use the scale only three times for weight measurements with the coins.  Can you determine not only which coin is fake, but if it is heavier or lighter than the real gold coins?  Or, is the task impossible with only three measurements?