Chess Pairing

You are hosting a chess tournament with $2N$ people. Exactly $X$ of them are *rated* players, and the remaining $2N - X$ are *unrated* players. Your job is to distribute the players into $N$ pairs, where every player plays against the person paired up with them. Since you want the rated players to have an advantage, you want to pair them with unrated players. Thus, you want to **minimize** the n