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?

Answer