One miserable day, a group of people with assorted eye color are marooned on an island inhabited only by an immortal Guru who always tells the truth. As they emerge onto the island, the Guru informs them that:
She always speaks the truth and all believe what she says.
No one knows the color of one's own eyes. (Perhaps trauma from the event that marooned them or the magic that keeps the Guru alive... but it's irrelevant.)
At the end of every day, a ferry stops (instantaneously) at the island.
If anyone has figured out the color of their own eyes, they [can and must] leave with the next ferry.
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.
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.
On one day, in all her endless years on the island, at midday, within communication range with all the islanders, the Guru says the following statement:
"I can see someone who has blue eyes."
Who leaves the island, and on what night? Make sure to account for all that leave and define your timeline.
There are no mirrors or reflecting surfaces, nothing dumb. The answer is logical. It doesn't depend on anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics.
And lastly, the answer is not "no one leaves."
I've done my best to make the wording as precise and unambiguous as possible, 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.
Please, when submitting guesses/answers, use the spoiler functionality from the side panel or simple type the BB Code (after removing the space from the "spo iler"s) with the appropriate substitutions:
[spo iler=visible text] hidden text [/spo iler]
This can actually be expanded to include any (whole) number of people in any (natural) number of eye color category.