Prisoners and Lightbulbs

I've been chatting on IRC a little bit, after discovering that, yes, people still use IRC sometimes. I really had no idea. Anyone, someone there posted this problem called One Hundred Prisoners and a Lightbulb, and it was driving me insane trying to figure out the answer. Unfortunately, the paper they linked to also had the answer, so I looked after a little while. Still, a fun problem, and it might be interesting to derive the details of the solution just using the basic outline.