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"what they don't know (until the 2nd) day) is that all the other blue-eyed islanders know that all the other blue-eyed islanders know that there are 99 other bl
by voyou 13y ago
"what they don't know (until the 2nd) day) is that all the other blue-eyed islanders know that all the other blue-eyed islanders know that there are 99 other blue-eyed islanders."
I don't see how they know that on the second day, either, though. Before the foreigner's statement, every blue-eyes islanders knows a) that there are at least 99 blue-eyed islanders b) that all the blue-eyed islanders know that there are at least 98 blue-eyed islanders. I don't see what the foreigner's statement adds to this knowledge.
- lisper 13y agoYou're right, my explanation is actually wrong. The idea is right, but the recursive knowledge is not gained incrementally the way I described but rather all at once at the end when they wake up on the nth day and see that everyone is still alive. Each one reasons (recursively) that if their eyes are brown then, given that common knowledge of the existence of blue-eyed people has been established, the remaining n-1 blue-eyed people will realize their eyes are blue (and kill themselves) on the n-1'th day. Since this doesn't happen, their eyes must be blue.