The prisoners brainteaser

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RobustKwid

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Can you guys help me with this brainteaser ?

One hundred prisoners are given the chance to be set free tomorrow. They are all told that each will be given a red or blue hat to wear. Each prisoner can see everyone else's hat but not his own. The hat colors are assigned randomly and once the hats are placed on top of each prisoner's head they cannot communicate with one another in any form, or else they are immediately executed. The prisoners will be called out in random order and the prisoner called out will guess the color of his hat. Each prisoner declares the color of his hat so that everyone else can hear it. If a prisoner guesses correctly the color of his hat, he is set free immediately; otherwise he is executed. They are given the night to come up with a strategy among themselves to save as many prisoners as possible. What is the best strategy they can adopt and how many prisoners can they guarantee to save?

If you have any insights to help with, I'll be happy to discuss, thank you very much !
 
RobustKwid said:
Can you guys help me with this brainteaser ?

One hundred prisoners are given the chance to be set free tomorrow. They are all told that each will be given a red or blue hat to wear. Each prisoner can see everyone else's hat but not his own. The hat colors are assigned randomly and once the hats are placed on top of each prisoner's head they cannot communicate with one another in any form, or else they are immediately executed. The prisoners will be called out in random order and the prisoner called out will guess the color of his hat. Each prisoner declares the color of his hat so that everyone else can hear it. If a prisoner guesses correctly the color of his hat, he is set free immediately; otherwise he is executed. They are given the night to come up with a strategy among themselves to save as many prisoners as possible. What is the best strategy they can adopt and how many prisoners can they guarantee to save?

If you have any insights to help with, I'll be happy to discuss, thank you very much !
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Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.
 
RobustKwid said:
Can you guys help me with this brainteaser ?

One hundred prisoners are given the chance to be set free tomorrow. They are all told that each will be given a red or blue hat to wear. Each prisoner can see everyone else's hat but not his own. The hat colors are assigned randomly and once the hats are placed on top of each prisoner's head they cannot communicate with one another in any form, or else they are immediately executed. The prisoners will be called out in random order and the prisoner called out will guess the color of his hat. Each prisoner declares the color of his hat so that everyone else can hear it. If a prisoner guesses correctly the color of his hat, he is set free immediately; otherwise he is executed. They are given the night to come up with a strategy among themselves to save as many prisoners as possible. What is the best strategy they can adopt and how many prisoners can they guarantee to save?

If you have any insights to help with, I'll be happy to discuss, thank you very much !
Click to expand...
You go first.

Do you have any ideas? That's what we'll want to discuss.
 
I should add that I do have a pretty simple idea that I think will save almost all of them. I'm holding onto it until you start a discussion, because it will be better if you come up with that or a similar idea and I can encourage you in the right direction. But my inspiration comes, in part, from the concept of checksums.
 
You can save exactly 99 of the prisoners 50% of the time and you can save all the prisoners 50% of the time. Use Parity ( same as checksums(?))
 
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