You have an empty wine bottle with a cork that has been secured at the top in a normal way. There is a metal ring inside the bottle that is suspended by a string.
How can you make the metal ring drop to the bottom if you are not allowed to touch anything - not the bottle, not the cork, not the thread and not the ring?
Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.
How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?
How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?