Remote island with a happy tribe
In a hypothetical scenario there exists an island with some number of inhabitants among which everyone knows everyone. If an inhabitant learns he/she has blue eyes, then he/she will flee at midnight; however none of the inhabitants will tell the other what color their eyes are, nor are there any mirrors for an inhabitant to learn the color of his/her eyes.
One day everyone on the island is told by an outsider at the same time that there are only two colors of eyes among the island's population: blue and brown.
43 days later many of the inhabitants flee at midnight.
How many have fled and why?
I don't see how any of the inhabitants can deduce they have blue eyes given only the information that there are two types of colors unless the outsider who tells this is lying and everyone has in fact brown eyes -- then everyone would believe they were the one and only person with blue eyes since there is supposedly at least one person with blue eyes.
Although due to the way the problem text is stated it doesn't seem like it would allow for the possibility of the outsider to be lying. But even if the outsider were lying, why would 43 days be relevant?
Is there some other way to consider the problem? Is there some other way for the inhabitants to deduce the color of their eyes? Why is 43 days important?