Pedalling Around the Rose

After disappointing myself by passing the Bill Gates mark (probably, I was not watching the clock) I set the problem aside for a couple days. When I returned I solved it in about six minutes. I can say that I was pretty much on the right track for a long time, and upon finishing it I was reminded of Shannon Selberg's tattoo, alluded to above.

I am not supposed to give hints, but I will say this: you don't need to learn Hexdecimal to solve the problem.