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[Sowelu]

The XKCD thing is dumb and wrong.

The Guru doesn't introduce ANY new information.  The only thing she provides is a "starting gun".  If EVERYONE is perfectly logical, and they want to leave the island, why wouldn't everyone automatically agree "Well, we all see more than fifty people with blue eyes, why not start at day 50 instead?  Waiting here for months is boring".

The thing that makes it even more wrong is that there *is not* a way to logically intuit that the starting gun serves that specific purpose!  Once it's explained, it seems obvious, but it does. not. logically. follow. that you would start on day 1 after that.  What DOES follow is that everyoue agrees to get off the island as soon as possible.  "In 100 days" is exactly as arbitrary as "Wait 50 days then start counting down", but "the fastest possible" is unambiguous.

...I've just spent an hour puzzling over this, trying to figure out how far ahead you can jump.  I don't rightly know, but it may be obvious and I may be overthinking it.  You want to find a number that everyone can agree with that is guaranteed lower than the size of the smallest group.  90 is clearly safe.  97 is safe:  Someone with blue eyes sees 99 people with blue eyes, and says "If I have brown then they'll each think there are either 98 or 99 and if I have blue they'll each think there are either 99 or 100".  99 isn't safe.  Is 98?..  How do you identify a special number like that?

I was trying to establish a rule where "if both groups can agree that one group is bigger than the other, then it's the smaller group's duty to leave first, so apply rule set A; otherwise apply ruleset B" to simplify it...but it's proving very difficult to even just figure out when the groups agree!

I am CERTAIN that I can improve on the given solution.


Wow, ninja'd 18 times.  Okay.  To state succinctly:  Starting counting from n=1 is not logically defensible, because 1 is an arbitrary number.  The ONLY defensible position is to leave in a minimum number of days, which means starting with n=the highest number possible in the circumstances.

[Earthquake Damage]

The Guru doesn't introduce ANY new information.

The Guru does provide new information.  We're given a new premise:  Someone has blue eyes.  In general, given any arbitrary collection of islanders with arbitrary eye colors, this premise tells us something valuable.  In the particular case we've been given (100 blue + 100 brown + 1 green we don't care about), it tells us nothing.

I'm not sure about 3, but certainly if 4 or more people have blue eyes, we don't need that premise.  I guess the problem is the XKCD version gives us information then pretends we don't have it.  While each individual doesn't know there are precisely 100 blue and 100 brown, they know damned well that in the given situation there is at least 1 blue and 1 brown.

[G-Flex]

I was trying to establish a rule where "if both groups can agree that one group is bigger than the other, then it's the smaller group's duty to leave first, so apply rule set A; otherwise apply ruleset B" to simplify it...but it's proving very difficult to even just figure out when the groups agree!

Too bad the groups can't even communicate.

[Leafsnail]

It's easy enough to say "The guru provides no new information".  But the thing is... 100 blue eyed people together on the island are never going anywhere without the announcement.

[Sowelu]

I was trying to establish a rule where "if both groups can agree that one group is bigger than the other, then it's the smaller group's duty to leave first, so apply rule set A; otherwise apply ruleset B" to simplify it...but it's proving very difficult to even just figure out when the groups agree!

Too bad the groups can't even communicate.

They don't have to communicate.  If both groups observe that there's ~10 people with blue eyes and ~100 people with brown eyes, then they both agree.  If one person sees 99 of one and 100 of the other, they don't agree.  The problem is drawing the line.

To put my own problem more specifically:  We know that we can skip to n=90, and we know that we can skip to n=95.  But what if blue thinks it's logical to skip to 90 and brown thinks it's logical to skip to 95?  Then we're up a creek.  THAT is why we need a way to say "It's Brown's turn", so that we can select an appropriate starting value for n based on Brown's data, and Blue can (depending on the algorithm) either play along with Brown's selected value, or stay out of the way until Brown has left the island.

[G-Flex]

At any rate, good luck on your quest to prove a bunch of mathematicians and logic professors wrong before actually asking someone qualified to explain it to you. Have fun with your insatiable hubris!

[Sowelu]

At any rate, good luck on your quest to prove a bunch of mathematicians and logic professors wrong before actually asking someone qualified to explain it to you. Have fun with your insatiable hubris!

Dude, this problem has bothered me for YEARS.  Stop telling me not to have fun, insatiable hubris is what I do best.  It's never done me wrong.

[G-Flex]

Then find someone qualified to help you understand it instead of just stewing in your own confusion and posting about it on forums about videogames.

[Sowelu]

Then find someone qualified to help you understand it instead of just stewing in your own confusion and posting about it on forums about videogames.

How nice.  You're going after me specifically after what, 25 other posts on the subject?  Go read some thread you enjoy more.

[G-Flex]

I like this thread fine, but your attitude towards this problem is a little grating. It's like when people learn about thermodynamics, think of some case where they don't understand why a perpetual motion machine of some description wouldn't work, and assume that it would instead of actually asking a physics instructor.

[Burnt Pies]

Just a thought, if they're all on an island, why don't they all look at their reflection in the sea on a calm day?

I know it's not meant to be solved like that, but it seems like a valid solution.

[iceball3]

On the XKCD thing, isn't the water a reflecting surface?

[G-Flex]

Just a thought, if they're all on an island, why don't they all look at their reflection in the sea on a calm day?

I know it's not meant to be solved like that, but it seems like a valid solution.

Read the page again. He says that's not an option.

There are no mirrors or reflecting surfaces, nothing dumb.

Yeah, water would be a reflecting surface, but hell, for the purposes of this puzzle, just assume it's not.

[Earthquake Damage]

On the XKCD thing, isn't the water a reflecting surface?

That crossed my mind, then I figured we're not meant to think so creatively. 

So it's probably safe to assume that no suitable reflective surface is available.

I remember a "logic" puzzle I ran across many years ago with a "solution" like that.  Random solution comes out of fucking nowhere!  And the author insisted that was the logical conclusion.

There are no mirrors or reflecting surfaces, nothing dumb.

Didn't catch that.  I fail reading.

[Burnt Pies]

I read the top paragraph for the rules, completely forgot about reading the other paragraphs.

How embarrassing.