There are
n
n people living in a small village. Their main pass time is forming various clubs, which is starting to threaten the economy of the village. In order to limit the number of clubs, the mayor has decided to decree the following rules:
Each club has to have an odd number of members.
Every two clubs must have an even number of members in common.
Prove the following theorem, making sure that you explain your reasoning.
Theorem. Under these rules, it is impossible to form more clubs than
n
n, the number of people in the village.
Mathbot Says...
I wasn't able to parse your question, but the HE.NET team is hard at work making me smarter.