So, the full problem goes like this:
There are $25$ people at a party. Assuming that among any three people, at least two of them know each other, prove that there exists one person who must know at least twelve people.
I've been stuck on this problem for a while and haven't really figured out how to proceed. I'm pretty sure that there is an answer that can be found via the pigeonhole principle or some graph theory, but I'm not really sure how to get started. Any help would be appreciated.