Petals Around the Rose: Fraternity Register

It took me about an hour and a half to figure this out, but I think I was hindered by reading the background story first. Knowing Bill Gates and other 'smart' folk were scratching their heads at this puzzle gives you a preconcieved notion of the solution. I think if I had simply seen the puzzle and tried cracking the pattern, it would have occured to me sooner. But, maybe that's an intrigal part of the puzzle...the backstory.