[dsvick]

I gave in and looked at OBS's answer. I had initially started in that direction but stopped, my problem with it was

Spoiler:

I got wrapped up in human nature and asked myself "what if one of the prisoners did not attempt to leave at the earliest possible time?" That would have thrown everything out of wack. I didn't make the assumption, and maybe I should have, that logic implied they would leave as soon as they could - anything else would be illogical.