Question 40
Let $n$ be a positive integer. $2n$ persons are sitting around a round table. Let $a \ge n$ be an integer. We call two persons *friends* if and only if there are exactly $a$ persons between them on one of the two arcs joining them. For each positive integer $n$ find all possible values of $a$ for which we can choose $n$ persons, no two of them antipodal, such that there are exactly $n$ friendly relations between them.