Ha az előbbi feladatban azt is tudni akarjuk, hogy a hamis pénz könnyebb-e, vagy nehezebb a többinél, hány pénzdarab a legtöbb, amennyi közül még három mérés elegendő ennek a kérdésnek az eldöntéséhez?

If in the previous task we also want to know whether the counterfeit coin is lighter or heavier than the others, how many coins is the maximum number from which three measurements are still sufficient to determine the answer to this question?
In this measurement procedure, the counterfeit coin only did not end up in the pan in one case: if we found balance in every measurement. In all other cases, we always knew whether the counterfeit coin was lighter or heavier than the others. Thus, with three measurements, we can always obtain this more precise answer from 12 coins.

It would be more tedious to show that with 13 coins (not only with the above but with any other measurement procedure), there can always be cases where it is not possible to answer this more precise question. We are afraid you might get bored. If anyone is still curious about this, ask, and we will write it down for them.

There were those who did not find the most efficient procedures, solving the problem with 4 to 7 measurements, or with 11 to 5 coins (depending on how incompetent they were).