Suppose you have five bags filled with the same type of coins and a weigthing machine. One of this bags is completely filled with fake coins, the other bags contain only real ones. A real coin weights 10 gram and a fake one 11 gram. What is the minimal number of times you need to use the weighting machine in order to find the bag with the fake coins?

Nine billiard-balls are lying in front of you. Except for one they all have the same weight. The exception is a little bit heavier than the others. What is the minimal number of times you have to use a balance in order to find the wrong billiard ball?

A jeweller has three boxes: A, B and C. Each box contains three rings, which are either all made of pure gold, or all fake. The fake rings weight 1 gram less then the real ones. It is known that a least one of the boxes contains fake rings. The jeweller has a balance with three weights of exactly 1 gram. Is it possible that the jeweller finds out which box(es) contain the fake rings with weighing only once? And if so, how does she do it? (We define weighing only once that only once a situation is reached in which the balance is in equilibrium.)