Outside

You may argue my conclusion was not scientific.

Of course not. There are in fact standard mathematical solutions to the question. (Interested visitors can search the Internet by these key words: prisoners light bulb puzzle.)

Nonetheless, my analysis of the question goes this way:

Assuming there is a mathematical way to determine reliably that all fellow prisoners have already been in Cell X at least once, their success depends on the reasonable chance of having each and every prisoner to stay in Cell X. If as few as one of them is never assigned to this very Cell, the whole plan would never bear fruit. Since the allocation of prisoner is conceivably done by the jail officer, who obviously has the conflict of interest and would not like to see his prisoners being released, the claim of random allocation is unlikely to be the truth, and, from the prisoners's side, therefore, unrealistic to plan their escape along this line.

Don't laugh. Doesn't McDonalds Monopoly - and thousands of other lottery games - use the same tactics?