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?

Four little gnomes are on one side of a scary wood. They have to travel through the wood to the other side. They can only do this safely if they have some light. Together they carry only one small candle. Unfortunately this candle only gives enough light for two gnomes. Some of the gnomes can walk faster than others. One of them can at fastest walk to the other side in 1 minute, one in 2 minutes, one in 5 minutes and the slow one in 10 minutes. If two gnomes are on the other side of the wood, one of course has to go back to bring the candle. If the gnomes go to the other side as quickly as possible, how much time does it take them in total?

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?