In the 17th century, there were more than 800, 000 inhabitants of Paris. At the time, it was believed that no one had more than 200, 000 hairs on her/his head. Assuming these numbers are correct and that everyone has at least one hair on her/his head (that is, no one is completely bald), please use the pigeonhole principle to show, as the French writer Pierre Nicole did, that there had to be two Parisians with the same number of hairs on their heads. Then please use the generalized pigeonhole principle to show that there had to be at least five Parisians at that time with the same number of hairs on their heads