Petals Around the Rose: Fraternity Register

It's about time I figured this thing out. Granted, I cheated and read a teacher's story as to how she introduced the game to her class, but it didn't contain the secret, merely the rules and the effect it had on her students. It's so glaringly simple that it's not surprising that the smarter you are, the longer it takes you to solve it; us college students tend to overcomplicate things a bit too much.