100 Prisoners

Prashanth_p@cchi · 2012-05-25T07:18:47+00:00

There is a prison with 100 prisoners, each in separate cells, which are sealed off, soundproof and windowless. There is a lobby in the prison with a lightbulb in it. Each day, the warden will pick one of the prisoners at random (even if they have been picked before) and take them out to the lobby. The prisoner will have the choice to flip the lightbulb switch if they want. The lightbulb starts in the "off" position. When a prisoner is brought out to the lobby, he also has the option of saying "Every other prisoner has been brought out to the lobby." If a prisoner chooses to say this and it is true, all the prisoners will go free. However, if a prisoner chooses to say this and it's wrong, all the prisoners will be executed. So a prisoner should only say this if he knows it is true for sure. Before the first day of this process begins, all the prisoners are allowed to get together to discuss a strategy to eventually save themselves. What strategy could they use to ensure their eventual salvation?

100 Prisoners

Prashanth_p@cchi
@prashanth-p-at-cchi-rg0z63

Updated: Oct 26, 2024

Views: 813

There is a prison with 100 prisoners, each in separate cells, which are sealed off, soundproof and windowless. There is a lobby in the prison with a lightbulb in it. Each day, the warden will pick one of the prisoners at random (even if they have been picked before) and take them out to the lobby. The prisoner will have the choice to flip the lightbulb switch if they want. The lightbulb starts in the "off" position.

When a prisoner is brought out to the lobby, he also has the option of saying "Every other prisoner has been brought out to the lobby." If a prisoner chooses to say this and it is true, all the prisoners will go free. However, if a prisoner chooses to say this and it's wrong, all the prisoners will be executed. So a prisoner should only say this if he knows it is true for sure.

Before the first day of this process begins, all the prisoners are allowed to get together to discuss a strategy to eventually save themselves.

What strategy could they use to ensure their eventual salvation?

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Prashanth_p@cchi

Member • May 28, 2012

No answers yet????

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Ramani Aswath

Member • May 28, 2012

It is presumed that the prisoners can see that the lobby light is on. Each prisoner will flip the switch once if he is brought out the first time or twice if he is being repeated. Everyone keeps count of the number of single switchings. When this reaches hundred every one has been out. Actually 99 counts may be enough for the hundredth man to say 'all have been out'.

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akash.kasina

Member • May 28, 2012

when a prisoner is brought to the lobby,he'll flip the switch only if he's already picked,so when the total number of unflipped days is 100,next prisoner can say that all have flipped the switch,problem solved,i presume👍

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Prashanth_p@cchi

Member • May 29, 2012

bioramani
It is presumed that the prisoners can see that the lobby light is on. Each prisoner will flip the switch once if he is brought out the first time or twice if he is being repeated. Everyone keeps count of the number of single switchings. When this reaches hundred every one has been out. Actually 99 counts may be enough for the hundredth man to say 'all have been out'.
They cannot see whether the lobby light is on or not, nor count the flips..... If that were the case then you have given a very good answer. Give it another try!

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Prashanth_p@cchi

Member • May 29, 2012

akash.kasina
when a prisoner is brought to the lobby,he'll flip the switch only if he's already picked,so when the total number of unflipped days is 100,next prisoner can say that all have flipped the switch,problem solved,i presume👍
who would have a count of that(unflipped count). They cannot communicate in between.

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Prashanth_p@cchi

Member • May 29, 2012

It may so happen that all 100 might not end up coming to the lobby, but lets be optimistic.... There is way.... Think what would they would have discussed during the discussion time...... I need that, as the answer.... Bioramani, I appreciate ur great effort. That is a great answer anyways.....

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Ankita Katdare

Administrator • May 29, 2012

Let us make one prisoner the head. He will have the right to turn the light off. (Nobody else will do it.)
Every time a prisoners (other than the head) is taken to the lobby, if the light is off, he/she will turn it on, but only if they've never turned it on before.
So, every prisoner turns it ON only ONCE.
At the same time, if the head is taken to the lobby, if the light is on, he will turn it off & he will count the number of times he has turned the light off.
Once the head turns off the light for 99 times, he may say, "Every other prisoner has been brought out to the lobby."

Please tell me if there are any loopholes in this answer.

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Prashanth_p@cchi

Member • May 29, 2012

AbraKaDabra
Let us make one prisoner the head. He will have the right to turn the light off. (Nobody else will do it.)
Every time a prisoners (other than the head) is taken to the lobby, if the light is off, he/she will turn it on, but only if they've never turned it on before.
So, every prisoner turns it ON only ONCE.
At the same time, if the head is taken to the lobby, if the light is on, he will turn it off & he will count the number of times he has turned the light off.
Once the head turns off the light for 99 times, he may say, "Every other prisoner has been brought out to the lobby."

Please tell me if there are any loopholes in this answer.
No loop holes AKD. It's absolutely perfect......... It would be great if you provide an answer to that "da" and "ja" puzzle..... 😀

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Prashanth_p@cchi

Member • May 29, 2012

@ AKD: In fact, the person who goes first to the lobby (1st day) can be the head. The rest 99 will know that some other is the head and not himself/herself. This will reduce the attempts. In your case the head can be called at last too...... Anyways, with, random being the criteria, ur answer too is good. Nice!

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akash.kasina

Member • May 29, 2012

s
Prashanth_p@cchi
They cannot see whether the lobby light is on or not, nor count the flips..... If that were the case then you have given a very good answer. Give it another try!
orry!!!did'nt think of that!!😀

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