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Everyone does know each other's eye colour, so they DO know how many people have blue eyes.

You were right about the one blue-eyed person case. He realizes it must be him, because everyone else has brown eyes, and kills himself.

What if there were two blue-eyed people?

@Nicky: I see "elevator" but I don't know why it's broken down that way

No they don't, because they don't know what colour their eyes are.

What could the sign be telling people

The elevator's broken?

@Nicky: Broken elevator? (damn, beaten)

@nickspoon: Well, they know how many OTHER people have blue eyes or brown eyes, and that's all they need to know.

Do the case for only 2 blue-eyed people and you should start to see what happens for the generalized case of N blue-eyed people

Yeah lol

Actually its worded ELEVATOR OUT OF ORDER
Hence the anagram

Well, OK. If two people have blue eyes, both of the blue-eyed people will not do anything, therefore alerting everyone of the fact that there are more people with blue eyes. Everyone will look around and either see one person with blue eyes or two with blue eyes depending on whether or not they have blue eyes. The people who only see one person with blue eyes will kill themselves. The the other person with blue eyes will.

Kind of.. when will the people who only see one blue-eyed person kill themselves?

CALMNESS, CANOPY, DEFT, FIRST, SIGHING, STUN

What is the common feature of these words

At midnight. But news of suicide spreads instantly, does it not?

@Nicky: caLMNess, caNOPy, DEFt, fiRST, siGHIng, STUn.

@nickspoon:

They won't kill themselves immediately at midnight. If there were ONE blue-eyed person, he would kill himself at midnight. There are two... and each sees one blue-eyed person.
What do the blue-eyed people expect the other blue-eyed person to do? When he doesn't, what new knowledge have they gained? And then what happens?
Assume you don't learn about the suicides until the next day, so that if there were one blue-eyed person, he'd kill himself at the end of day 1, and then the brown eyed people would all kill themselves at the end of day 2.

At the end of day 1, nobody dies. Day 2, 2 die. Day 3, Nobody sees anyone with blue eyes, but I can't think how the people with brown eyes kill themselves.

The blue eyed people would not have killed themselves if there were more blue eyed people

@nickspoon: yep.
@Nicky: yep

Now what if there are 3 blue-eyed people?
What if there are N blue-eyed people?

The number of days it takes for the blue eyed people to kill themselves is the number of blue eyed people there,