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 ?
With n weighting we can find the counterfeit coin, in a set of 4*3n-2.
For n>2, we can also tell whether it weights more or less.
Marco Corvi - 2019