Something does not have to change every time. And warmth of the light bulb is not a variable. The prisoners aren't allowed to feel the bulb, just the switch. Thaboss misunderstood the last part of your first post. Each person does not have to leave a mark every time.

Ah, my mistake. I didn't read into it enough.

They can't choose to do nothing, because they would never know who had gone and when. They can't leave the lightbulb on permanently because the same would apply. If they alternate (one turns it on, one turns it off), they will lose the pattern the instant someone is used twice.

They must find a way to each leave an individual mark/clue, so that twenty marks will show that they have gone twenty times. If a prisoner is selected twice, he would do nothing because he has seen his mark.

OH! After reading this I nearly have it.

If one person is chooses to always turn the light on when he goes in, everytime he sees the light off he can add one to the number.

But how to tell other people to turn on the light, I don't know. And that would mean he had to get picked 99 times.

Better off just waiting 3 years and reporting the jail to the government for disrupting mental health.

Leo is correct with his idea of choosing one special person. But he's off with the method.

And there is no time limit. Another hint. This takes a LOOONG time.

Sorry, *chosen

It was killing me.

Also, is there an interaction with other prisoners?

How could you possibly know that 19 people had gone ahead of you when the only clue you have is "on" and "off?" You get chosen, you get chosen again, someone else gets chosen, you get chosen again. You see "on" or "off." What possible pattern could exist?

You would...have to leave a clue...for yourself. Something specific would have to be different.

But it would only work if you got chosen again! The 19th person doesn't know that they are #19. If everyone went once, in a straight line, there is no possible way that #19 could show #20 that he was the last to go.

They are allowed to discuss their plan beforehand but that is all.No interaction after that.

Maybe that person can leave some sign on lever

The key is the special person. There's one special person, called the counter. He's the one who will eventually say that all prisoners have been in the room.

MattEmAngel, it's not that. It's this idea of the one counter.

Ok, well I think I have it then.

Leo is an awesome guy, so he gets chosen to be the leader because he was the first person to go inside. He tells everyone else that when they go in they must turn the light off if it was on when they entered. Once you turn the light off if you are chosen to go again you must not touch anything. If you come into the room and find the light off you do not touch anything. Every time this awesome guy that happen to be called Leo walks in he turns the switch on. He keeps count of  every time he does this and when he gets to 99 he wins.

I still stick with suing the government for trauma and distress.