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Hats and alligators (Posted on 2006-07-15) Difficulty: 4 of 5
A group of prisoners is under sentence of death and the warder decides to give them a test to gain their freedom. He tells them, "I will place a red or blue hat on each of your heads and then I'm going to arrange you in random order in a row so that no prisoner will be able to see his own hat but each one will see all the hats in front of him. Starting with the guy at the back each of you in turn must loudly say what color hat you think you have. Correct answers will go free, incorrect ones will be thrown to the alligators in the moat. I will give you time for a brief meeting before we start, so you can plan your optimum strategy."

What strategy can the prisoners - there are N of them - adopt to improve their odds above 50:50?

Hint: They need to agree on a strategy which allows each person to identify his/her own hat while simultaneously providing as much information as possible for all those in front.

No Solution Yet Submitted by JayDeeKay    
Rating: 4.4000 (5 votes)

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Matter of Trust | Comment 12 of 19 |

Nice solutions list if everyone is helpful.  But these are people sentenced to death.  How well do you trust them to give you information to save your life?

So what is the probability that the first one told the Truth?  Could you no the fate of the second person in line who used the information?

What is the probability that person 2 stated the oposite because he did not trust person 1?

 


  Posted by Patrick on 2006-07-18 13:06:46
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