The reason for the traveler in the blue eyes/ brown eyes problem

[borisp]

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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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In the case that there are 3 islanders with blue eyes, the statement "Everyone knows that everyone knows that everyone knows that someone has blue eyes" is not known to any of the 3 that have blue eyes. Without this knowledge, they cannot draw a conclusion upon seeing the other two people with blue eyes awake on the third morning. And so on.

[Max Raker]

Ok I think I get it now. Thanks. This seems pretty deep to me. The traveler doesn't give me any new info and I know that he hasn't given any info to anybosy else yet it is needed.

[PairTheBoard]

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Ok I think I get it now. Thanks. This seems pretty deep to me. The traveler doesn't give me any new info and I know that he hasn't given any info to anybosy else yet it is needed.

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If I am one of the 3 Blue Eyed, the traveler has given me new information as to what the other 2 Blue Eyed monks must be thinking under the assumption that I don't have blue eyes.

PairTheBoard