==> logic/weighing/balance.p <==
You are given 12 identical-looking coins, one of which is counterfeit
and weighs slightly more or less (you don't know which) than the
others.  You are given a balance scale which lets you put the same
number of coins on each side and observe which side (if either) is
heavier.  How can you identify the counterfeit and tell whether it
is heavy or light, in 3 weighings?

More generally, you are given N coins, one of which is heavy or light.