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.

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?

Four smart gnomes are standing in line with all faces pointed in the same direction. They all carry a hat, but they do not know their color. They only know that there are two red and two green hats. The first gnome stands behind a wall and does not see the others. The second gnome is able to see the hats of the third and the fourth. The third only sees the hat of the fourth, and the fourth gnome does not see any hat at all. The gnomes would like to know which hat they wear without checking their own. When a gnome has figured out which hat he carries, he will immediately tell the others. Suppose that the first gnome wears a red hat, the second a green one, the third a red one and the fourth a green one. Which gnome will be the first to figure out?