Alrighty then.

It's quite simple. You have to start with a situation of 2 blue and 100 brown. This will happen:

Blue guy 1: Hey, I see 100 brown eyed people and 1 blue. Damn, then I can't be sure about my own eye color. I can't leave.

Blue guy 2: Hey, Blue guy 1 doesn't leave. That means he can't be sure about his own eye color. All the others have brown eyes so that must mean I have blue eyes, whoohoo!

And Blue Guy 2 leaves.

Blue Guy one however, can't know at this point what color his eyes are, since the blue guy who just left, may have been the only blue eyes person on the island. He'll have to wait for the Guru's announcement the next day. If she sees a blue eyes person again he can be sure it is him and he can leave. So 2 people leave after 2 days.

Same goes for 3 people.

Blue Guy 1 and 2: Hey, that guy over there has blue eyes but doesn't leave. That must mean at least one of us has blue eyes too!

Blue Guy 1: Damn, the other guy has blue eyes too, now I can't be sure about mine.

Blue Guy 2: Hey, the other guy doesn't know it either! That means I have blue eyes, yay!

And Blue Guy 2 leaves.

Blue Guy 1 and 3 both can't be sure about their own color now, and the next day the situation for 2 people follows.

After 3 days 3 people will have left.

Etc.. up to 100 people who will have left on the 100th day.

After that, it depends on what the Guru will say.

Twii Light wrote:

That's not the riddle you posted originally...

That explicitly states that she speaks exactly once in all their time on the island. Now, I agree with some of what you've said. Because blue guy 1 sees that blue guy 2 is still there after night 1, he knows that he has blue eyes. But, BG2 sees that BG1 doesn't leave, and he knows thus that he has blue eyes. This pattern will continue infinitely; for any number x of blue eyed people, all will leave on the xth night, all based on one proclamation.

So, as I stated, all 100 people will leave on the 100th day, and none before then.

You didn't explain at all why the brown eyed people would leave, since the Guru only speaks once, and that relates directly to blue eyes. After night x, all non-blue eyed people know only that they are not blue eyed. Thus, they are under no obligation to leave.

What are you talking about? The Guru only NEEDS to talk once in order for them to to get off the island.

...He'll have to wait for the Guru's announcement the next day.