ANSWER: The Warden, 100 Prisoners, and a Lightbulb

[AndyDeck]

I can't believe that no-one has posted a solution to this yet - have you all forgotten how to use Google?

Answer: The prisoners choose a controller, call him Adam.
The prisoners OTHER THAN Adam will follow this protocol with the light: If the light is on, take no action. If the light is off, turn it on - ONCE. If the light is off but you have already turned it on once, take no action.
Adam will follow this protocol: If the light is off, take no action. If the light is on, turn it off and remember how many times you have turned it off. Once Adam has turned off the light 99 times, he tells the Warden that everyone has visited the room.

Harder answer: I didn't see a definite solution to this version. Adam would now have to count to either 99 or 100, depending on the initial state.

Either way, this will take a LONG time as each prisoner's 'vote' doesn't get counted until Adam enters the room, which on average will be 1 in 100 times. Please let's not start a probability/odds discussion, though - if that interests you, Google for this puzzle and look at some real math on the problem.

[bhao]

andydeck said:

Either way, this will take a LONG time as each prisoner's 'vote' doesn't get counted until Adam enters the room, which on average will be 1 in 100 times. Please let's not start a probability/odds discussion, though - if that interests you, Google for this puzzle and look at some real math on the problem.

...and again with the problem of time. if 1 random person per day gets sent to that room, it will take on average over 27 years to get out.

[dodrudon]

Better than never getting out at all. It's an exercise of logic, not of... believability.

And the point of this isn't to practice your Googling skills! Otherwise I'd've posted the solution right under the puzzle.

[AndyDeck]

bhao said:

andydeck said:

Either way, this will take a LONG time as each prisoner's 'vote' doesn't get counted until Adam enters the room, which on average will be 1 in 100 times. Please let's not start a probability/odds discussion, though - if that interests you, Google for this puzzle and look at some real math on the problem.

...and again with the problem of time. if 1 random person per day gets sent to that room, it will take on average over 27 years to get out.

To fill in the blanks - I found this puzzle referenced on www.cut-the-knot.org/Probability/LightBulbs.shtml including an analysis of time required (see Stuart Anderson's comment) - the expected time does indeed seem to be 26.2 years with one visit per day. However, if I'm reading the probability calculations here correctly, the chances are better than 999,999 in a million that the count will reach 99 in 5 years.

Given the phrasing of this particular instance of the puzzle, the visits could be more or less frequent, which would obviously change the calculations. I don't see a different solution that would guarantee success faster, though.

[dodrudon]

I believe there are some, with multiple Adams, but have no idea how it would work.

[fromthyhell]

the prisoners would use a tactic like this.

they would designate one person to switch the light off.

then whenever a prisoner goes in if the light is off they turn it on.

then when the designated person goes in if the light is on they have to turn it off and keep count of how many times they have turned it off so far.

if a prisoner goes in the cell and the light is allready off they dont turn it on again.


EDIT: lol should have read the post above oh well mabye my version is a bit clearer

when the designated person has switched the light off 100 times he would know that all the prisoners had been in the cell and could get the gaurd to set them free.

the only problem with this is that it would take a really long time.

i hope i got it right

[dodrudon]

Yep! It's okay if it takes a long time, this is all theoretical.

In fact, we could even reduce it to 10 prisoners....

[illandous]

dodrudon said:

Yep! It's okay if it takes a long time, this is all theoretical.

In fact, we could even reduce it to 10 prisoners....

You could make it 2 prisoners also.