You have nine coins, one of them being false, made of lighter metal than the good coins. If you have a balance, how can you identify the false coin using two weightings at the most?

1. The first weighing:

Three coins are put on each plate. If the scales are in equilibrium, it results that the false coin is in the last group of three coins. In this case we return to them for the second weighing (case A).

If the scales aren't in equilibrium it results that the false coin is in the lighter group; we'll deal with these three coins (case B) at the second weighing.

2. The second weighing:

At the first weighing we identified a group of three coins (A or B) lighter than the other two groups. We take two coins at random and put them on the scales. If the scales are in equilibrium that means that the false coin is the third one. If the scales don't remain in equilibrium that means that the false coin is on the higher plate.