Re: The reason for the traveler in the blue eyes/ brown eyes problem
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The only case where you need a visitor is when their is exactly one guy with a horn right? If there is more than one person with a horn his statement does not give new information to ANY person so it would play out the same way. (If the number of days passed is greater than the horns you count you gotta go) Am i missing something?
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Consider the case with two blue eyed islanders. All of the islanders know that someone has blue eyes. But the two islanders that have blue eyes don't know that the other blue eyed inhabitant knows that someone has blue eyes. After the traveler comes, they now know this.
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But now if the number of blue eyes is greater than 2 everyobdy knows that everybody knows that some people have blue eyes. So I don't see a need for the traveler.
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