Two guests with the same number of friends
A party has guests (with ). Friendship is mutual: if Ana is friends with Ben, then Ben is friends with Ana, and nobody is their own friend. For each guest, count how many of the other people present are their friends.
Prove that at least two guests have the exact same friend-count, no matter who is friends with whom.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.