Math Problem #3 (Logic) - Page 2

Let's look at this with some hypothetical cases

there are 999 people with brown eyes and 1 person with blue eyes:

After the foreigner said there were blue eyed people on the island, clearly the 1 blue eyed guy offs himself tomorrow.

there are 998 brown eyed, 2 blue eyed:

Each of the blue eyed people know that there is only 1 person on the island with blue eyes, aside from the possibility of themselves having blue eyes. Now if they didn't have blue eyes, the other person would've known that he was the only person with blue eyes and offed himself accordingly the next day at noon. When the next day at noon rolls around, and no one is suiciding, they realize that there must be a reason that the blue-eyed person didn't kill himself, which could only be because they too have blue eyes. And both blue-eyed people kill themselves at noon of the 2nd day.

and et cetera. If there are 997 brown eyed people and 3 blue eyed, when the 998 brown eyed, 2 blue eyed scenario doesn't take place, the 3 blue eyed people come to a similar realization as the 2 blue eyed people in the 998-2 combination after there are no suicides on day 2, and kill themselves day 3. So in the 900 brown eyed, 100 blue eyed case, they all will kill themselves on day 100 after the outsider came, not sooner.

The explanation SourCheeks posted is pretty much perfect, IMO