Prisoner, warden, and a light switch riddle.?

Turn a switch on and leave it for about 5 minutes.

Then turn it off, and turn a second switch on.

Now walk in :

If the bulb is on, then switch 2 works it

If the bulb is off but hot, then switch 1 works it

If the bulb is off and cold, then switch 3 works it

Freedom!

@Josh: sorry i missed that detail about prisoners not being able to hear each other. ***************edit 2: Brian, i was thinking about this riddle riding my bike earlier and I'm amazed at how close i was to the solution. I was actually thinking of equivalence classes of sequences and was gonna suggest that it might need the axiom of choice and something like vitali sets! Then i clicked on your link. Oh well... Great Riddle btw! ***************edit 1: Riddle 1: I don't know how to save all but a finite number of them. The best I can do so far is to save a fraction of the prisoners that can be made to approach 1 arbitrarily fast. The prisoners agree on a strictly (and preferably a very rapidly) increasing sequence (a.n) of natural numbers with a.1 = 1. For each n, they designate the a.n-th prisoner to take one for the team. They agree that red = 1 and blue = 0.¹ When it's the a.n-th prisoner's turn, he calls out the the mod 2 sum S of colors over the block of prisoners (a.n + 1), ...., (a.(n+1)-1).² If he's lucky, his hat is the same color. But meanwhile, each prisoner in that block now knows hisr own color, which equals (S - the sum of all other colors in that block) mod 2. Since the blocks get bigger and bigger, the survival rate tends to 1. _______________ ¹ The scheme generalizes to any number k of colors – just make all calculations mod k. ² The prisoners agree not to extend the blocks to a.(n+1) to spare the poor chap the agony of knowing he'll be shot and the temptation to call out his own color. ****************edit 0: Riddle 2: For the first 999 visits the rules are If it's off and you're a returning visitor, turn it on. Otherwise do nothing. For the 1000th visitor the rules are If it's off, go tell the warden everyone's been to the room. Otherwise turn it off and you become the counter. Set the count at 1. After the 1st 1000 visits the rules are If you're the counter and the light is on, turn it off and add 1 to the count and if the count is now 1000, go to the warden; otherwise do nothing. If you're not the counter and the light is off, turn it on; otherwise do nothing.

Nice one. Will watch for your answer.