Imagine that you have a box which have 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?

Three times is the most common answer however that is incorrect.

The small cogwheel will turn around four times.

You might already have deciphered that while turning against each other, the small wheel will turn three times (3*8) as the big wheel turns once (24 teeth). Now what we require is the big wheel to stop and the small one to turn around the big one. In this process, the small one will make another full turn on the way around the big one. Thus in total, it will make four turns.