Suppose, you would like to divide the pie from the figure on the right-hand side into eight equal pieces. How often do you minimally have to cut? Every time you put the knife again in the pie counts as an additional cut.

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.)

At a nice sun shiny day, a man rowed with his boat to an island in the middle of a big lake. On the island he caught some fish. Then he decides to return with his rowing boat. After 10 meters of rowing he looks behind him, but to his big surprise there is no island anymore. What happend to the island?