Etaoin, how is the counting known to the isolated prisoners?

well, I asked if I had missed anything!

however, I'm going to go from this line:
given enough time

if they each keep track of how many times the switches have been reversed(as per my first concept), then the first person to reach 23 can reliably say that they have all visited the switch room. I can't quite get this to jibe with the "as many times as everyone else" thang, but... then, I can't count to infinity either. or even to .9999...




formerly known as etaoin...