Quote:
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Originally Posted by Fortunate
From the anthropologist's remark that some villagers had blue eyes and all the rest had brown eyes, the villagers learned that if there had been only one blue-eyed person he would now be able to realize on the first day that he had blue eyes.
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There is more specific information than that conveyed, involving what people know about what other people know. See montebianco's resolution.
Quote:
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Originally Posted by Fortunate
If the anthropolgist had subsequently kept his mouth shut, the five blue-eyed people would have committed suicide on the fifth day. When the anthropologist then remarked that everyone had already been able to see that the tribe contained both blue-eyed and brown-eyed members anyway, he expedited the process because now if there had been exactly two blue-eyed people they would have realized that on the first day (since the remark insures that there are at least two blue-eyed people, it would allow a person seeing only one blue-eyed person to conclude that he, himself, had blue eyes). Hence, the five blue-eyed people would now expire on the fourth day.
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Excellent! I had not even intended this subtle alteration to the solution to (1), but you are right. The full solution to (1), counting the second remark by the anthropologist, dooms the tribe a day earlier. Once again you have found an unintended subtlety in my logic problems, cut it out! For the purposes of continued analysis of what the tribe can do to save itself, let's pretend the second statement never occured, or occured in confidence, since this day-faster clock is a complication we don't want. Very clever indeed, Fortunate.