Logic puzzle

[Sterling]

This is interesting, I think:

Imagine a small remote island. The following things are true about the island:

Every inhabitant has either blue or brown eyes
Everyone knows the colour of everyone else's eyes, but nobody knows their own eye colour (there are no mirrors on the island)
The tradition on the island is that if you ever discover the colour of your own eyes, you must kill yourself in 24 hours
Everyone on the island follows the tradition
Everyone on the island is an excellent logician
Everyone on the island knows all the above facts

Once every thousand years, a goddess appears on hill on the island and everybody gathers to hear her speak. The goddess always speaks the truth, and everybody knows this. The goddess says:

"I see someone with blue eyes"

What happens?

[Sterling]

Oh, one more rule (in case it wasn't clear): news travels fast, so if someone dies, everyone else finds out about it almost immediately.

[whitecrow]

I know the answer!

Should I post it or PM it?

[Sterling]

PM if you like and I'll confirm.

[Sterling]

Whitecrow has it more or less right.

The interesting thing is that, in general, the goddess doesn't say anything that people don't already know. And yet...

[Sterling]

Anyone else want to take a stab at it?

[Diva]

I am trying to think of something. The only thing that I can think of is that the villigers look at those around with blue eyes. Those people in turn kill themselves.

Yeah, I know... I suck. :whome:

[Sterling]

You're almost there. In short, everybody dies eventually. If there are N people with blue eyes, then they all die N days later. Then the people with brown eyes die the day after that.

Imagine there is only one person with blue eyes. He looks around and nobody else has blue eyes, so he knows it must be him, and hence he kills himself.

Now suppose there are two people with blue eyes. Each can see one other person with blue eyes. After a day has passed, each can deduce that there must be at least one other person with blue eyes, otherwise the other would have already died. Since they can only see one such person, they can conclude that they must have blue eyes too, and hence they kill themselves.

In general, after N days without a suicide, you can conclude that there must be at least N people with blue eyes. However, if you have blue eyes yourself, then you can only see N-1 people, and hence deduce that you must have blue eyes yourself.

[Boozer]

Aw, man, I gotta put up with this stuff in Algebra, do I have to do it here, too? LOL

[Sterling]

It's not algebra, just logic.

Isn't it weird, though? I mean, everybody already knows that somebody has blue eyes, so the goddess isn't really telling anyone anything new. And yet it's enough to enable everyone to figure out their own eye colour and hence kill themselves.