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A Prisoner Problem


Best Answer DeGe, 11 October 2013 - 03:07 PM

Spoiler for Possibile strategy

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#1 BMAD

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Posted 10 October 2013 - 05:39 PM

100 prisoners are imprisoned in solitary cells. Each cell is windowless and soundproof. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb from his or her own cell. Each day, the warden picks a prisoner equally at random, and that prisoner visits the central living room; at the end of the day the prisoner is returned to his cell. While in the living room, the prisoner can toggle the bulb if he or she wishes. Also, the prisoner has the option of asserting the claim that all 100 prisoners have been to the living room. If this assertion is false (that is, some prisoners still haven't been to the living room), all 100 prisoners will be shot for their stupidity. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world can always use more smart people. Thus, the assertion should only be made if the prisoner is 100% certain of its validity.
 
Before this whole procedure begins, the prisoners are allowed to get together in the courtyard to discuss a plan. What is the optimal plan they can agree on, so that eventually, someone will make a correct assertion?

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#2 phil1882

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Posted 10 October 2013 - 06:51 PM

Spoiler for

Edited by phil1882, 10 October 2013 - 06:51 PM.

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#3 ThunderCloud

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Posted 10 October 2013 - 11:14 PM

I had a solution here, but found a flaw in it... *REMOVED*


Edited by ThunderCloud, 10 October 2013 - 11:16 PM.

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#4 DeGe

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Posted 11 October 2013 - 03:07 PM   Best Answer

Spoiler for Possibile strategy


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#5 BMAD

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Posted 14 October 2013 - 01:58 AM

Spoiler for Possibile strategy

There is a flaw in this strategy.  Since the prisoners are chosen at random, the first person can visit the room all 99 times and toggle the switch off and not have 100 of the other prisoners still make it.  Resulting in the death of the group.  But your answer is closer to mine.  Just need a little revision.


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#6 dgreening

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Posted 14 October 2013 - 05:43 AM

I think DeGe's strategy is sound.

 

The term "toggle" may be adding confusion.

 

Prisoner 1 always turns the light OFF [or leaves it off]

 

Every other prisoner is allowed to turn the light ON only once [after they turn it on once, the leave it unchanged]. Other prisoners are not allowed to ever turn the light off.

 

after day 1 prisoner 1 counts the times he turns it off and after 99 he can safely assume that all have been in the room


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#7 DeGe

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Posted 14 October 2013 - 10:51 AM

 

I think DeGe's strategy is sound.

 

The term "toggle" may be adding confusion.

 

Prisoner 1 always turns the light OFF [or leaves it off]

 

Every other prisoner is allowed to turn the light ON only once [after they turn it on once, the leave it unchanged]. Other prisoners are not allowed to ever turn the light off.

 

after day 1 prisoner 1 counts the times he turns it off and after 99 he can safely assume that all have been in the room

Thanx for making it clear.


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#8 BMAD

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Posted 14 October 2013 - 04:30 PM

Thank you for clarifying
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#9 dawne

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Posted 14 October 2013 - 05:14 PM

What do I do?
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#10 phaze

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Posted 16 October 2013 - 05:32 AM

What do I do?

Don't turn the light off I'm counting


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