Isiskhan
Gnostic Misanthropy
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Posted - 2008.06.16 22:19:00 -
[1]
 Originally by: ReaperOfSly
Start with the case of there being 1 blue and 100 brown eyed people. After the oracle's announcement, the blue eyed person would see no blue eyed people, so conclude that he must be the blue eyed person the oracle spoke of. So he would leave the island on the first night. Now ask yourself what would happen if there were 2 blue and 100 brown eyed people, and build up from there.
With 2 blue eyes, the first night none of them would leave the first night as they still wouldn't know their eye colour (since they see another blue eyed), but on the second night each of the blue eyes would reason that since the previous night no one left they must have blue eyes, so they would both leave.
They both know they must have blue eyes, because if it were otherwise, the other would have left the first night seeing that there were no other people with blue eyes, so it must be him the oracle is referring to.
If we consider there are 3 blue eyed people, what we have is:
- on the first night no one leaves as they are unsure.
- on the second night no one leaves either: the blue eyed know there are 2 or 3 people with blue eyes (the latter meaning they have blue eyes themselves), and the fact that no one left the previous night could support either case, so they are still unsure.
- on the third night, they have the new piece information that no one left on the second life, so each of the 3 blue eyed reasons: I see 2 blue eyed people, but if there were only 2, they would have left the second night, following the original reasoning. Therefore there must be 3 people with blue eyes, and that third one is me. So they all leave.
As we increase the number of blue eyes, the process is the same, but increasing it with one more step: with X amount of blues, until the night X-1 no one leaves as they don't have enough information, but on the night X they realize that since they see X-1 blue eyes, and no one left on the night X-1, there must be X blue eyes - ie: they themselves have blue eyes. All blue eyed logicians apply the reasoning and they all leave at once.
The answer then is that on the 100th night all the blue eyes leave.
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