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Break it into a smaller problem. If there was only one blue face and you saw all non blue faces you would know that your's was blue. Similarly, if there were only two and you saw one and he didn't die the first night then you both know you have blue faces the second day. Extrapolate this up to ten days you and you get the present situation. It often helps to take a simpler version of a complicated problem and see if you can solve that first and go from there. I hope this made sense...the key that the foreigner added was that there was at least one blue face which changes everything.
But the people know that there is at least one blue face because they can see the other 9 people who have blue faces.
that actually doesn't matter. if you go back to only one blue face, he wouldn't know that his was blue just because he sees all non blue unless he knows that there's at least one blue. no one else would expect him to commit suicide since there's no way for him to know his face is blue. therefore even if you also had a blue face, you wouldn't assume yours is blue just because he didn't commit suicide the first night. once you know that there's a blue face, you'd have to assume that the blue face guy you see would have killed himself and therefore your's is also blue. The same thing works if you see 9 people. I'm not sure if this helps at all...
1) Why is day i related to person i with a blue face? 2) Why would you assume that your face is blue if you see another blue faced guy who killed himself?
One of the questions was from phi's pdf.
you only assume if he doesn't kill himself...i gotta go teach my class right now but maybe i can add more later
I'll be back in about 1 hour and 45 minutes if you'll be here then.
I still don't get how knowing that there is at least 2 blue faces changes anything because we, the readers, know that there are 10 people with blue faces meaning that they know there are 9 but there could be 10.
(the tenth being themselves).
It all starts with looking at just one blue face. If you see all non blue faces there's no reason for you to kill yourself unless you know there's at least one blue face. If you know there's at least one and you see all non blue you would have to know that yours is blue and thus kill yourself. once you've established this idea, the rest follows the logic already explained. Without knowing the existence of blue faces, there's no need for the first guy to die and thus the whole thing falls apart and it doesn't matter if you see blue faces or not cuz there's no reason to work through all the things already mentioned. at this point I think I'm going to keep repeating myself so hopefully the lightbulb moment comes soon.
How about this twist. The stranger is in a conspiracy with the blue faces. There are 10 blue faces on the island, but on the tenth day they do *nothing*. On the eleventh day everybody (but the blue faces) commit suicide.