With the solution you gave,
are you sure you set the story up right?
If there are more than 2 people, what is the point of using the outsider as some type of trigger to set off the event ?
The information would already be a given in the people’s head and the process of leaving would have already taken place, right?
That’s precisely why the answer is so counterintuitive. The outsider comes and doesn’t tell the islanders anything new, but the process of telling the islanders this in public does something. The case for n = 3 is no harder. By the reasoning I just gave, each of the 3 blue eyes, sees other two and reasons that they must leave the 2nd dawn after the announcement. After seeing that they don’t, all three come to the realization that they’re blue eyed
So If I’m thinking about this right, it’s about setting off an event / rule on knowing who must know - it’s not about the knowledge about the community - but what happens when the outsider actually sets off a chain by verbalizing?
Because you are asking what effect it will have, and nothing can be effected until something is said?
EDIT
Friedmanite, this is only valid for N=1 or N=2. Once N=3 or more, it changes the game. I am out of time right now, but will post a scenario later this evening…
1B|10G scenario:
Blue realizes he only sees green eyes and leaves on first night.
2B|10G scenario:
Blues individually realize that if they had green eyes, the other blue would have left on the first night. The blues leave on the second night.
3B|10G scenario:
Blues individually realize that if they had green eyes, the 2B|11G scenario would be the same as the 2B|10G scenario, and the blues would have left on the second night. The blues leave on the third night.
And it continues in this pattern, so the blues will leave on the ninetieth night.
Sat. 12/05/26 19:30 EDT
.post #155
Oh wait…I’m wrong. Assertion #2 in my previous post is wrong.
In the case of two (or more, or even one) blue-eyed islanders, it is not true that “every islander knows that every islander knows that there is at least one blue-eyed islander.”
Using the case of two blue-eyed islanders again, then there are two islanders, namely the blue-eyed ones, who don’t know that “every islander knows that there is at least one blue-eyed islander.”
One blue-eyed islander doesn’t know the other knows “that there is at least one blue-eyed islander.”
But, after the announcement, both know that the other knows. So, the announcement does add new information.
There’s more to this than I originally noticed. I’ll think about what you’ve said a bit more before I post again.
MMMark,
I think you misunderstand my problem/solution. The outsider comes and says in public,
“At least one of you has blue eyes.”
This is not the same as the outsider telling every person in private, “At least one of you has blue eyes.” The latter would have no effect at all (unless n = 1) as intuition would suggest.
Vive,
What’s the effect? The blue-eyed people leave.
More explanations on the puzzle: