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Old 06-17-2010, 10:34 AM   #44
pdurrant
The Grand Mouse
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Quote:
Originally Posted by dsvick View Post
OMK has a point - and not on top of his head either
In the set up you said that the prisoners were all told they were marked with either Green or Blue. So actually, as soon as there were at least 2 prisoners with each color, they should have been able to figure it out in X number of days, where X is the number of people marked with the least represented color.
Do the thought experiment - pretend you're the first prisoner to arrive, and you're given a green mark (although you don't know it's green). Subsequently one more green and two blue prisoners arrive. Every prisoner can now see at least one prisoner of each colour. So every prisoner knows that the prison contains prisoners of both colours. Can any of them conclude anything about their own colour from this? I think you will see that they cannot, especially if you try to consider the situation from the viewpoint of any one of the prisoners.

Spoiler:
And yet if the governor gathers all four prisoners together and gives his speech to them, I think you'll find that there is a now a difference, even though he appears to have only told them something that they all already know. In fact, he's told them something else as well. Work out what that is, and you'll probably be able to see the answer.
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