OJ Board

This is quite a strange problem. I have been thinking about the algorithm for a long time. I tried to solve this problem using maximum flow with minimum cost, but at last, I didn't come up with the right solution. Also, I don't know whether a greedy algorithm exists.
So, can someone give some better ideas of this problem? Thanks!

Ok, finally, I understand why a judge can judge a segment of participants... A maximum flow with minimum cost algorithm can be used.