Ignorance fought I believe it for 3 so I know it’s true But I still can’t implement it that easily for 100. But it’s just like everyone said it’s tough going any deeper takes even more work than with 3 hehe THANKS Frylock.
btw. let me know if i’m wrong hehe
I THINK SO TOO!!! 
Well, you did say one strange thing at the end about “if Bob in fact didn’t have the green”–but of course you (Emoticorpse) know he does."
I was going to go through an additional set of questions with a new circumstance, that the loudspeaker demands self-card-identifications only at particular intervals. (To simulate the boat thing from the puzzle.) Strictly speaking, you do need some kind of timing mechanism like this (so everone can actually see the others specifically not identifying their own colors). But from what you wrote here it looks like you went through all three of the iterations of reasoning without needing to mention an explicit timing mechanism. The only thing that worried me was that very last bit about Bob’s color that I mentioned above.
I have to go for the moment but if you want to go ahead and go through the rest of the reasoning process with a timing mechanism added to the scenario, here’s what I’d say and ask next. (If you are pretty sure you don’t need to do this part, though, please feel free to say so. I am pretty sure you now have the basic idea at least, whereas you didn’t before. If you do decide to answer, though, I’ll respond back as soon as I can.)
The loudspeaker comes back online. "Every five minutes, you will hear a beep. Whenever you hear a beep, if you know your own card color, speak up. Otherwise, remain silent.)
There is a beep–and no one speaks up. Now, some reasoning, followed by a question:
If you have a yellow card, then from Bob’s point of view, if Carl had thought that Carl himself was the only person with a green card, Carl should have spoken up. But Carl didn’t speak up. So apparently, Carl does not think that he’s the only person with a green card. So, do you agree that if you have a yellow card, then Bob must now believe himself to have a green card? (And a secondary question: Did you follow the reasoning I just laid out in this paragraph?)
That was if the scenario was when emoticorpse could see the other 2 cards. If Bob didn’t have a green then Emoticorpse would see Carl confused and if Bob didn’t have a green card then Emoticorpse himself could be the only one confusing Carl.
I will try that one in a little while my head is overheating from this exercise but thanks! I will keep thinking about this and hopefully want something more complicated 
Frylock, I accept the basic logic, and have worked it out so that the first 99 layers of he knows that he knows that… (etc), but I think that’s where it ends. I don’t believe that with 100 blue eyed islanders any new information is added when the guru speaks. Could you please draw me a diagram showing that this is possible?
/joke
I sort of figured.
(Well, I fervently hoped… :D)
I’ve heard similar puzzles before, and I do understand the concept of the induction. However, I have to agree that if 100 people have blue eyes, then the information that at least one of them does isn’t news to anyone. At the time the blue-eyed people started their induction, couldn’t the brown-eyed people deduce what was happening and start their own induction?
Do you think that if only three had had blue eyes, then the information that at least one of them does wouldn’t have been news to anyone?
If so, do you think, nevertheless, that in the three-blue-eyed-people scenario, they would have reasoned their way to leaving on the third day?
If not, please go back in the thread to the start of my conversation with Emoticorpse and follow the reasoning that we illustrate together and tell me what you think.
I think that the whole complicated part is in the “perfect logicians” part of this thing. These are perfect logicians we’re talking about here some of us aren’t perfect logicians.
I think that the “now he knows that he knows the knows that he knows…” is confusing. That to me just seems like something is passed from one to the other to the other to the other.
I’d present it as like this…
Every one is trying to figure out the color the color of their own eyes.
*once you know the color of your your own eyes you can catch the ferry no matter what color they are.
If you don’t know what color your eyes are you don’t know what colors they can possibly be (maybe blue? maybe colorless?, maybe you don’t have eyes? 
).
*you can guess anything you can guess nothing, you’re not boarding the ferry at this point since you don’t know.
at one point somebody reveals to ALL islanders at the same time that they are looking at at LEAST 1 blue eyed person.
*since somebody said that and every islander heard it it is now general knowledge
general knowledge is basically : information that is known to all
*don’t trip over the term general knowledge it’s just what you think it is universal information, something that everyone is aware of
so at this point the only thing that has changed is that every single person on the island knows that there is at least one blue eyed person (general knowledge).
*every one wants off the island but they have to know what their own eye color is nobody knows what their own eye color can possibly be they only know for sure what everyone else’s eye color is.
*once someone claims to see the eye color blue that means they can POSSIBLY see you and it may be your eyes they’re looking at. so you’re gonna try and figure out if you’re the one they’re talking about (everyone else is gonna too at the same time if they want off the island)… … this is where it gets complicated.
*in order to solve this logical puzzle you must think like a perfect logician as every islander is. Any islander who is not a perfect logician is disregarded from the puzzle because the puzzle clearly states that anyone involved is a perfect logician.
So if you can’t figure it out it’s because you’re not thinking like these islander are and don’t feel bad a lot of us aren’t real life perfect logicians (that’s why we’re on the straightdope fighting ignorance).
YOU MUST COME UP WITH THE LOGIC at this point with this information.
… I will continue I’m trying to make this part as SIMPLE AS POSSIBLE but it will take a while
BTW someone let me know if I’m wrong up til now
No, I already thought of that too, and ruled it out, see post 252.
The brown eyed people can try and will try…
but until you understand the logic behind this you will not know why they fail…
Of course they can, and in fact must. It’s not like they can say “well, I have brown eyes, so I don’t need to bother to reason this out”, because the whole point is they don’t know.
Very Important*******
it’s not the fact that the guru spoke out loud that gave the islanders hope or a reason to search.
it’s not the fact that the guru was looking at a set of blue eyes that gave the islanders hope or a reason to search
it’s the fact that each islanders realized WOW!!! she might be looking at me.
is that right?
every brown eyed person will begin the deduction independently
but because of the logic behind it they happen to reailze that they aren’t blue eyed
and even until a certain point every blue eyed person believes he’s brown eyed (that part is necessary in order to solve the puzzle)
I think that’s right…
Here’s another way to formulate the blue-eyed islanders’ reasoning which I am not sure has been typed into the thread yet.
Once the guru speaks, a blue-eyed islander on the 100th day will reason as follows:
And he would leave on the 100th day.
All the B-islanders are in the same boat, so to speak, as far as knowing anything about their own eye color. So all of them would follow the above reasoning, and all of them would leave on the 100th day.
Not really.
The essential value of the Guru’s proclamation is this knowledge it gives to everyone: “No one can now believe that there might be zero blue-eyed islanders.”
oh well i tried i seriously hope to get as smart as the other people on this site. I just started though joined straightdope like a week ago
That’s a tricky one. How could anyone believe there were zero blue-eyed islanders even before the Guru’s pronouncement?
Not really.
The additional information is: Everyone now knows that everyone now knows that there’s at least one blue-eyed islander.
They couldn’t.
But BEI-1 could believe it’s possible for BEI-2 to believe it’s possible for BEI-3 to believe … it’s possible for BEI-100 to believe there are zero blue-eyed islanders.
After the Guru’s announcement, everyone knows the final step is no longer possible, and that everyone else now knows this. And that is vital knowledge.