Suppose to have 12 coins, one of which is counterfeit, and weights different from
the others. Suppose that you can compare the weights of sets of coins with a
balance.

It is possible to find which is the counterfeit coin and whether it weights more
or less than the others, by three weightings.

Can you find the weighting strategy ?

Here is a solution.

What is the maximum number of coins, including a counterfeit coin, such that
you can find the counterfeit coin, and tel whether it weights more or less than
the others, with *n* weightings ?

*Conjecture*

With *n* weighting we can find the counterfeit coin, in a set of 4*3^{n-2}.

For *n*>2, we can also tell whether it weights more or less.

Marco Corvi - 2019