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Old 06-17-2010, 02:21 PM   #46
dsvick
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Quote:
Originally Posted by pdurrant View Post
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.
You're right, the governor is letting them know that everyone now knows there are two colors represented. But I think it only works when you have 2 of each color.

Spoiler:
If there are four of them sitting around, 2 blue and 2 green. Each of the four knows that both colors are represented. Regardless of what color I have I'll see 2 of one color and 1 of another. If the person that I see that is the single color does not leave then he must see both colors also, which means I've got the same color as him. But it only works if I know that he knows that both colors are represented, if he didn't know that then he would also have to consider that he had the same color as everyone else.


As soon as you have 3 of each color, you can be assured that everyone can see at least one of each color.

Spoiler:
I can then know that everyone else see's at least two of each. More importantly, I know that there are two people who see 3 of one color and at least one of the other. If neither of them leaves on the second day I have to assume they see the same color on me, making it at least two that they see.


Of course I could be way wrong
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