Guaranteed acquaintances at a party
Trivia
A classic result in combinatorics shows that among any group of $6$ people, there must exist either $3$ people who all know each other or $3$ people who are all mutual strangers. This is the smallest case of what general theorem, which guarantees that sufficiently large structures must contain some kind of order?
ARamsey's Theorem
BPigeonhole Principle
CHall's Marriage Theorem
DSylvester-Gallai Theorem