# A "friendly" combinatoric problem

There is a bunch of $n$ people. Everyone is friends with 3 other people in this bunch. They want to have breakfast seated around a round table, but, they are wanting to sit next to their friends. Then, for each pair of friends, the number of seating possibilities in which they sit next to each other, is an even number.

Let $G$ be a $3$-regular graph, and let $e$ be an edge of $G$; then the number of Hamilton cycles containing $e$ is even.