Petals Around the Rose: Fraternity Register

I was getting frustrated. I started out doing a math intensive solution but then noticed the Potentate giving the answers immediately. Now, I couldn't trust this person when they claimed to be dumb and terrible at math but I had to take them on their word. So with that I started thinking about other things, and considered the rules set out before the game.

Then it took me another 30 mins to get it.