Once upon a time there was a mighty and wise wizard who was
looking for a new student. Because he didn't like the idea
to tell someone stupid the secrets of magic he created the
following test. He took 12 coins which looked all the same.
One of these coins had a slightly different weight. The
student's job was to find out which one was different and to
state if its weight is lighter or heavier than the weight of
the other coins. Therefore the wizard created a magic pair
of scales. The scales could be used three times. After that
the scales disappeared in a blinding flash of light. Using
the scales once means to put the same amount of coins on both
sides, to check the equilibrium and to remove all coins.
Find out how to pass the test without guessing! The complete
solution needs a lot of explanation. To simplify the answer
just sum up the minimum number of coins to be placed on the
scales for the most complicated case, e.g. 5+5 / 3+3 / 2+2 = 20.
