Question 12
Let $n \geq 1$ be an integer. A group of $2n$ people meets. Each of these people has at least $n$ friends in this group (in particular, if $A$ is a friend of $B$ then $B$ is a friend of $A$, and nobody is a friend of themselves). Prove that these $2n$ people can be arranged around a round table so that each of them sits between two of their friends.