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# Math riddle

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Aaah good old times.

Since it's pretty quiet on the forum, I thought I'd find us all a nice riddle.

I was cruising through the pile of easier ones when I found this one.

Still haven't found the answer

A warden meets with 23 prisoners. He tells them the following:

• Each prisoner will be placed into a room numbered 1-23. Each will be alone in the room, which will be soundproof, lightproof, etc. In other words, they will NOT be able to communicate with each other.
• They will be allowed one planning session before they are taken to their rooms.
• There is a special room, room 0. In this room are 2 switches, which can each be either UP or DOWN. They cannot be left in between, they are not linked in any way (so there are 4 possible states), and they are numbered 1 and 2. Their current positions are unknown.
• One at a time, a prisoner will be brought into room 0. The prisoner MUST change one and only one switch. The prisoner is then returned to his cell.
• At any time t, given some N>0, there exists a finite t_0 by which time every prisoner will have visited room 0 at least N times. (In other words, there is no fixed pattern to the order or frequency with which
prisoners visit room 0, but at any given time, every prisoner is guaranteed to visit room 0 again. If you’re still confused by this statement, ignore it, and you should be ok).
• At any time, any prisoner may declare that all 23 of them have been in room 0. If right, the prisoners go free. If wrong, they are all executed.

What initial strategy is 100% guaranteed to let all go free?

(originally from http://mathriddles.williams.edu/?p=146&cpage=1#comments )

Sep 10, 2014

#3
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Reinout-g.....good to see you back...seems like u were having a really extremely busy time!anyways,now atlast we can unwrap our lunchbox!i had been longing for it so much!

Sep 11, 2014

#1
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Real hard. Never expected one of these!

Sep 10, 2014
#2
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All right, I got very close to the answer, but was stuck with the condition that their positions were unknown. Was too impatient and googled it (shame on me). If you think you have the answer, pm me :). If you want to discuss the riddle, use this thread.

Sep 10, 2014
#3
+11912
+3

Reinout-g.....good to see you back...seems like u were having a really extremely busy time!anyways,now atlast we can unwrap our lunchbox!i had been longing for it so much!

rosala Sep 11, 2014
#4
+117762
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It is all too much for me I am sorry Reinout

Sep 13, 2014