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”.
Thanks to xkcd for this logic puzzle, I have never heard of it before. http://www.xkcd.com/blue_eyes.html
If anyone would like a hint… try using smaller numbers and see what would happen logically.
On day 100 – all people with blue eyes leave
On day 101 – guru and people with brown eyes leave
Your first statement is correct, but your second … isn’t. How would the guru and the brown eyed people ever know their own eye color?
solution was based on the fact that when the guru sees all the people preparing to leave it’s bound to know he has a different eye color
Answer you probably wanted:
On day 100 – all people with blue eyes leave
On day 101 – all people with brown eyes leave
On day 102 – guru leaves
Um, still no. The guru and the brown eyed people … how could they ever deduce their own eye color? How would the guru know that her eyes are green not purple?
1. Day, all blue-eyed people leave.
2. Day, all brown-eyed people leave.
3. Guru leaves when all other people are gone, because of the fact that she is a guru.
Still wrong.
THE BROWN EYED PEOPLE CAN NEVER LEAVE.
EVER.
If these are all logical people doing logical things, wouldn’t they just ask “What color is my eyes” and everybody leaves on Day 1?