MathDB

At a dinner party there are

N

hosts and

N

guests, seated around a circular table, where

N\geq 4

. A pair of two guests will chat with one another if either there is at most one person seated between them or if there are exactly two people between them, at least one of whom is a host. Prove that no matter how the

2N

people are seated at the dinner party, at least

N

pairs of guests will chat with one another.

Problem Statement