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[Leafsnail]

"Oh, put me at the back, would ya?  Maybe I'll just miscount the number of red hats by one..."

[Darvi]

Then the next guy will die, and the rest will catch on and lynch him :<

[Jreengus]

Ok another one:
http://xkcd.com/blue_eyes.html

[Darvi]

Now that's a nice one.

[Darvi]

So. 100 blue, 100 brown, 1 green(guru)

1 blue confirmed. Were it not for the fact that there are other 99 people with blue eyes, the blue eyed guy would leave. Alas, they are there, so they stay.

Hmmm...

And they're also perfect logicians, so they would probably definitely know that. Dunno if it actually helps, though.

[Darvi]

Bluh, just too many people. With two, they wouldn't leave the first day because they know there's another one with blue eyes, but then they realize that the other one's thinking exactly the same thing, meaning they both get to leave.

Wait.

Wait.

I think I'm onto something.

Well I'm sure now that the brown eyed people and the guru won't leave. So then the maximum of people to leave would be 100.

[Jreengus]

You are thinking on the right track. They know that if there were only one person he would leave. Expand on that.

Ninja'd. Getting there. If there were 2 what day would they leave on? Assuming the day she makes the announcement is day one?

EDIT: Lol reading failure. anyhow think about what would happen with 3 people now.

[Darvi]

Day two, as I said.

Now, they know that too...

Two people would leave on day 2. So if they don't leave, it means that there are more than two.

So on day three, assuming that there aren't any more people, the third person would leave with them together, because they know that they were the reason the others wouldn't leave.


Wait.



I GOT IT!


It goes on like this, right? All 100 of them leave at day 100?

No wait that seems dumb >_>

[Leafsnail]

Yeah.  I was staggered when I found the answer to that one too...

[Darvi]

Wait, really? I thought that this line of thought would rely on a single person being added every day or something.

[Darvi]

Here's something: notpron

Hint: when asked a password that's in french, use proper accents, or you'll have to clear your cache.

[Jreengus]

Yup 100 on day 100.

Randal provides a proof here:
http://xkcd.com/solution.html

I prefer to describe it thusly:

If we assume X people leave on day X then we know that if there are X+1 people they will leave on day X+1, since they will see X people wait until day X arrives realise none of the others left and thus realise they too have blue eyes.

We can prove this is true for x=1 as a single person will look around immediately see no-one else with blue eyes and leave and since we proved that it's true for x+1 if it's true for X we know it holds true for every positive value of X.

Then again I did stumble upon the puzzle originally whilst studying mathematical induction.

[Darvi]

If we assume X people leave on day X then we know that if there are X+1 people they will leave on day X+1, since they will see X people wait until day X arrives realise none of the others left and thus realise they too have blue eyes.

We can prove this is true for x=1 as a single person will look around immediately see no-one else with blue eyes and leave and since we proved that it's true for x+1 if it's true for X we know it holds true for every positive value of X.

Yeah I just thought about that.

Or for laymen, a person thinks "Ok, there are 99 of them. Unless I'm blue, they're gonna leave on day 99. Of coure, if I'm not blue, they're gonna think, "Ok, there's 98 of them...""  and so on. Everybody leaves one day later than the number of blue eyes they see.

[iceball3]

I made myself a riddle, and YEW guys gotta answer it, if ya feel up to it of course.

All points hit,
The site where only one may sit.
Led away from creation,
Torn down by mutilation.
Seen across the far side of mind,
Lives of many, all to one bind.
Seen apart from many others,
Lost in the masses of broken lovers.
Never seen, eaten, or found,
Consume, you lose, your mind in pounds.
Thrown against the wall of shameless fear,
Following, but not creating, the arrant trail of tears.
Foresaw the loss, in that many others gain,
Felt the reflection of many others pain.
Grows upon the alias of stone and wood,
A determined combatant of one who could.
Lost deep in between stagnation and refresh,
Not a single memory, which one can relish.
Caught in the indecisive claws of guilt,
From the ground, from where anew can be built.
Colliding with the intensity of hail and sleet,
Yet the only thing to follow, is with a retreat.
What am I?

[eerr]

Now see, theorems don't apply if the assumptions underneath them aren't true.

There are at least 99 people,
not 1 through 98