You have N apparently identical coins, one of which may be a forgery.
Forged coins are either too light or too heavy. You have a balance, on
which you may place any of the coins you like and determine whether
the coins in one pan are together lighter, heavier or the same weight
as those in the other. Using the balance you wish to detect whether
there is a forgery and, if so, which coin it is and whether it is
lighter or heavier. Prove that at least log_3 (2N + 1)
{to the base 3} weighings are required.
* Show that for N =3D 12 three weighings su=EF=AC=83ce.
