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.

Mom, Dad, and two kids have come to a river, and they find a boat. It is small and can only carry one adult or two kids at a time. Both kids are good rowers, but how can the whole family reach the other side of the river?

At the same time a block of iron and an equally heavy iron sphere are released from the top of a slope. Assume that the friction between the slope has a negligible effect on the velocity of the block and the sphere. Which of the two will be down first?