I feel like I'm being led down a primrose path by the creator of this puzzle, but the careful wording below seems critical, but cryptic, wording to me...

"But, given enough time, everyone will eventually visit the switch room as many times as everyone else. At any time anyone of you may declare to me, 'We have all visited the switch room'. "

This seems to indicate that the total number of visits (or switches thrown) would have to be either 23, or a multiple of 23, that is, 46, 92, 184, etc. All even numbers, naturally, except 23.

Now say, for example, if the prisoners could distinguish between the two switches beforehand* and assign beforehand a separate meaning for the switch position of each...eh??? (odd/even)

Well, you see what I'm getting at.

And if you do will you please post it, because I sure as heck don't.


* (Post Edit: Of course they can, Milo-you-big-dummy, they are labeled A and B!)

Second Post Edit: Etaoin, how is the counting known to the isolated prisoners? But if, let's say, that if eleven prisoners have pre-agreed to always switch the A switch and the other twelve have agreed to switch the B ???
And remember the prisoners are selected at random (or whim, if you perfer,) and then their name, so to speak, goes back into the hat, which is the crux of the quiz: Randomness tamed by order.