King Kreso had decided that one of his daughters, princess Ikani had to marry the mean grave Gwenn. When Ikani did hear of this she started crying for days and she did not want to eat anything anymore. The king became a little bit uncomfortable with this situation, so he decided that she should take a small stone from a hat. If Ikani would take the white stone, she would have to marry grave Gwenn, if she takes the black one she would not have to. Some days later, grave Gwenn, King Kreso and Ikani are together on the lane to the castle which is paved with small black and with stones. The king asks grave Gwenn to take two stones and put it in his hat. Princess Ikani sees that the mean grave puts in two white stones. She thinks of saying this, but then most likely the procedure has to start over. Suddenly she gets a great idea. Some minutes later it is decided that princess Ikani does not have to marry grave Gwenn. What did princess Ikani do?

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?

You've got two jars, one of them fits exactly 5 litres, the other one fits exactly 3 litres. How could you get exactly 4 litres with these two jars? It is allowed to spoil some water.