VyralPandemic
(\/)_o_0_(\/) MMOLobster
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well put
OK, you win. That I can follow. Good explanation Sadge
Ok -- maybe this would help ...
A lot of people like to start their answer with "imagine there were 2 people with blue eyes". While that helps, I think it's better to start with 1 blue-eyed person.
Fact: We know that there is at least 1 blue-eyed person on the island (because the guru said so, and for this case we will assume the guru never lies).
Now, if there is only 1 blue-eyed person on the island, he immediately knows it's him, right? He cannot see another blue-eyed person among the 199 other people on the island (and it is 199 people -- the guru does not count for 2 reasons: the main one being that the guru (we assume) cannot see her own eye color). So in this case, the 1 blue-eyed person leaves that night.
Now let's go to 2 blue-eyed people. Person A (the first blue-eyed person) can see 1 other blue-eyed person (Person B). But remember that neither person A or B know that their own eyes are blue. So person A can assume that person B will leave the island that night if they do not see any other blue-eyed people (because of the first example), because person B would not be able to see any other blue-eyed people. But after the first night, person B does not leave because he knows that he sees person A with blue eyes (mathematically speaking, there can only be number of people seen with blue eyes+ the person looking ... or seen+1). Since person A did not leave the first night, person B knows that A cannot logically deduce how many people have blue eyes because he sees at least 1 other person with blue eyes. Since person B cannot see any more people with blue eyes, he must have blue eyes (person A reaches the same conclusion). So on the second night, both person A&B leave being the only 2 people with blue eyes.
You can follow that logic all the way up to 100 blue-eyed people. Each person can see that there are 99 other blue-eyed people. So he simply has to wait 99 days to see if they leave and if they don't, he can assume that he himself has blue eyes and leaves on the 100th day (and of course the other 99 people are reaching the same conclusion after 99 days).
I can go further if you want.
OK, you win. That I can follow. Good explanation Sadge