First “If A knows B then B knows A”.
Second “A knows at most other people at the party".
This problem is equivalent to the theorem: In a simple graph at two vertices have the same degree.
For the pigeonholes, there of them: .
Anyone at the party can know from to other people.
Suppose that none of those pigeonholes has more than one person in it.
Convince yourself that the hole would be empty.
Think about what that means.