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?

Suppose you have five matches. How can you form the number sixteen with them?