Solve the really challenging riddle?

Question

Blue Eyes

A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.

On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.

The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:

"I can see someone who has blue eyes."

Who leaves the island, and on what night?

There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."

And lastly, the answer is not "no one leaves."

I've done my best to make the wording as precise and unambiguious as possible (after working through the explanation with many people), but if you're confused about anything, please let me know. A word of warning: The answer is not simple. This is an exercise in serious logic, not a lateral thinking riddle. There is not a quick-and-easy answer, and really understanding it takes some effort.

Answer 1

Standing before the islanders, she says the following:

"I can see someone who has blue eyes."

She isn't necessarily standing before ALL of the islanders. For arguments sake, she's standing before only two. A brown eyed islander, and a blue eyed islander. The blue eyed islander, seeing the others brown eyes, then realizes that he has blue eyes, and he's on the next boat home at midnight.

EDIT: Thinking more into it, here's how I see it now.

Scale it down:

If there are two men, one blue eyed and one brown, then the situation above would happen. If there are three men, two with blue eyes, and one with brown, then when they three hear that she sees one man with blue eyes, the brown eyed man will see two sets, and both blue eyed will see another blue eyed man, so they think that the other is the one she's talking about. When the night comes, neither blue eyed man, nor the brown eyed one will leave, because they think the others to be the one she was talking about. Upon seeing that no one has left in the morning, both blue eyed men will realize that the other is seeing their blue eyes, and thinking the same thing that they themselves were thinking: 'The other person is the only one with blue eyes'. So, the two blue eyed men leave on the second night.

The same thing will happen if there are three blue eyed men, and it'll happen on the same night as the number of blue eyed men there are.

For 100 blue eyed men, they (all the blue eyed men) will all leave on the 100th night.

Are any of us right? =P

Answer 2

The guru, the night after she speaks,

She knows her eye color- "I count at least one blue-eyed person on this island WHO ISN'T ME."

This was actually the first thing i thought of, but, i didn't put here becuase i thought it was too easy...

The guru and the last person on the island (blue-eyed) leave the night that the guru talks

The guru knows her eye color and the last person knows becuase he is the last one there....only he could have the blue eyes....

Answer 3

Why would saying "I see blue eyes" matter?  There would be 100 blue eyed people anyway.  Everyone would be able to see blue eyes.

How many people does the Guru talk to at once?  Are we supposed to assume she talks to everyone at once?  Or are we supposed to assume there is a rare chance that only 1 brown eye and one blue eye show up, which creates a chain reaction that might have never started unless of that freak chance?

And catluvr's explanation makes no sense at all.