All of this interpreting is complicated, but take a look at this sentence and read it for what it is:
"But, given enough time, everyone will eventually visit the switch room as many times as everyone else.
1. We've commented here on "given enough time"
2. But everyone will visit the switch room as many times as everyone else?
3. That could take a helluva long time. The warden could save the last guy for last. He could let the others visit the switch room countless times, knowing full well that he's saving the last guy for the final count. Say, let the others each visit it three, four, even five times or more before introducing the last guy whom he fully intends to let visit the switch room many times in a row to reach his own 'equality' of number of visits. [Hang in here with me; I'm about to make a point.]
4. The catch is: At what point would the prisoners know the last guy (if that's the warden's plan) had gone his first time thereby being able to say all had visited, but not necessarily the equal number of times. Equality of visits was never a consideration, but multiple visits was.
I like the fingernail scratch idea someone proposed up there. I don't think the problem could be worked out mathematically given the fact that the warden could juggle around visits in any dadburned way he wanted to, always leaving at least one guy behind.
