Suppose you have an enormous long rope. You place this rope on the soil along the equator, such that the rope forms a circle around the earth. After you have finished this big job, you increase the length of the rope by one meter. How far from the soil do yo have to attach the rope to make again a circle around the equator? Assume that the earth is a perfect sphere, without mountains etc.

Make 24 by using the following numbers only once: 1, 3, 4 and 6. You are allowed to add, subtract, multiply, divide and to use curly brackets. Do the same excercise with 3, 3, 7 and 7.

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?