Ok, I can sortof see the answer. I guess.

2/6/2011 4:48:30 PM

this needs to be embedded. now. preferably with auto-start.
http://www.youtube.com/watch?v=WXkkYvGK2R0&feature=related

[Edited on February 6, 2011 at 4:50 PM. Reason : .]

2/6/2011 4:50:13 PM

I'm really not sure why it is so hard for you guys to understand the solution.


Consider this:

You are the only person on the island who has blue eyes. Guru says "I see an asshole with blue eyes."

You see everyone else does not have blue eyes. You leave that night.


Two people:

Guru says "I see blue eyes." You see one guy with blue eyes. Night comes. He doesn't leave. You're all like "oh, wtf, that guy didn't leave, he doesn't KNOW that he has blue eyes, and he must see someone else with blue eyes, but I only see him..... OH SHIT I HAVE BLUE EYES"



Five people:


Guru does the blue eyes bit

You see 4 people with blue eyes.

Each night, no one leaves. Why? Because they think that they don't have blue eyes, but they know that there are at least 4 people hat have blue eyes.

What can they infer from that? People are who should be leaving are not leaving, because they believe that they do not have blue eyes. Any one of this group of 4 people has seen at least 3 other people with blue eyes, but none of them has left, and it is now the 4th day but that's not the breaking point.

The breaking point is during the 5th day, when you realize that they must see at least 4 people with blue eyes as well. Who is that 4th person they see, obviously not counting themselves, because they believe that they do not have blue eyes?

YOU are the 4th person.



It goes on like that forever and is pretty much infallible.

2/6/2011 4:52:21 PM

I think we're a little bit past the solution and I'm trying to explain the purpose of the guru and why the brown eyes can't leave

2/6/2011 4:55:31 PM

yes, but its not 5 blues, its 5 blues and 5 browns.

HOW DO I KNOW I DON'T HAVE BROWN EYES!?!?!?

2/6/2011 4:55:47 PM

because it's 4 blues to you, and 5 browns


after 4 nights and none of the blues leaving you can deduce that you too must have brown eyes. the brown really has nothing to do with it and is as large a red herring as they come



none of the blue people have left because they do not realize that they have blue eyes - but they do realize that there are at least 4 people on the island who do.

[Edited on February 6, 2011 at 5:00 PM. Reason : .]

2/6/2011 4:58:37 PM

Quote :

"maybe this is the sticking point. we're not considering what #2 actually thinks. we're considering what #1 thinks #2 is thinking. they're not the same."

Ok so you say that #1 thinks #2 thinks #3 thinks #4 thinks there's nobody with blue eyes.

But #1 KNOWS that #2 knows there are at least 2 blue eyed people, and #1 knows that nobody could possibly see fewer than 1.

When you get up towards 100 this becomes even more absurd.

2/6/2011 4:59:18 PM

not at all



all #1 thinks is that he sees 99 people who have blue eyes that haven't left yet. that means that all 99 of those people are under the impression that they do not have blue eyes, and that there are at least 98 other people on the island who do have blue eyes.

the incremental differentiator is the night count.

large scale or small scale it always comes down to the 2 man solution

[Edited on February 6, 2011 at 5:04 PM. Reason : seriously this is not hard.]

2/6/2011 5:03:18 PM

Look I'm not arguing the solution, I want to know what meaningful information the Guru gives.

2/6/2011 5:07:21 PM

I think everyone talking about leaving on multiple nights is missing this important point:

Quote :

"The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:"

2/6/2011 5:10:16 PM

the guru is just a catalyst, it doesn't matter what the guru says beyond giving a color

2/6/2011 5:10:33 PM

Still think everyone except the Guru gets off on day 100, blue and brown.

The Guru never leaves, sucks to be her.

2/6/2011 11:38:25 PM

Quote :

"just go look in the damn water"

what i was going to post

2/6/2011 11:52:06 PM

I have brown eyes, so I know I'm outta there first boat

2/6/2011 11:56:23 PM

For folks that are confused, I think it's best to think about it as blue and non-blue.

Cause if the guru don't say nothin bout brown eyes, then those perfectly logical, non-communicating, brown-eyed folks are never leaving. They will logically never be able to guess brown and leave...so their eye color is only meaningful to us in that it is not blue.

[Edited on February 7, 2011 at 12:26 AM. Reason : ]

2/7/2011 12:20:22 AM

Why not? They can make the same judgements about other brown eyed people as blue eyed people can about other blue eyed people.

Now, if only the blue eyed people got to leave, then they would try to wait one more day (since they would be hoping they were blue eyed and leave on day 101) and they would be to late. But since on day 100, the 99 other brown eyed people haven't left yet, they know they have brown eyes, and all the blue eyed people know they have blue eyes, so 200 people leave the same night.


The guru is waiting for day 101 for either group, and it will never come.

2/7/2011 12:26:08 AM

The guru leaves after getting voted off the island for giving a clue so shitty that it makes everyone sit around for over three months before they can do a damn thing.

2/7/2011 12:36:01 AM

if no one knows the color of their own eyes then why do they assume everyone else knows the color of their own eyes

[Edited on February 7, 2011 at 12:41 AM. Reason : nevermind, I get it]

2/7/2011 12:39:33 AM

^^^There could be green, purple, red, yellow, hazel, etc...eyes...

Sure, you may observe 100 people with blue eyes, 1 person (guru) with green eyes, and 99 people with brown eyes...but that doesn't mean you have brown eyes. You still may have green, purple, hazel, etc... If they knew the proportions and color (100 blue, 100 brown, 1 green), they'd all leave immediately. If they knew just the colors (brown/blue, 1 green), then the blues would be gone on the 100th day after the guru's information, and the browns would be gone on the 101st day.

But they don't know that stuff. Until the guru gives the info, they're basically solving a logic puzzle in real life with lots of information about other people's eye colors but without the key piece (the guru's info)--the piece that takes the place of their ability to communicate.

See? They're all perfect logicians who will make instant deductions, but without the guru's catalyst, they can't begin deducing...all 200 of them will just be walking around with one of two sets of information (100 blue/99 brown/1 green or 99 blue/100 brown/1 green), but that gives them no information about their own eye color (which in their minds could be anything). They need a key piece to collectively get the real life logic puzzle ball rolling (in the form of observing when/how many people leave the island). And if the guru doesn't mention brown eyes, they can't roll that ball (since they can't communicate). It's just a 100 brown-eyed people sitting around, observing 99 other brown-eyed people while thinking their own eyes could be any color.

[Edited on February 7, 2011 at 1:10 AM. Reason : It's all about the fact that they're perfect logicians or whatever.]

2/7/2011 12:59:02 AM

The guru's info is knowledge they already have.

For the same reason that after 100 days the blue eyed person knows he has blue eyes because the 99 others haven't left yet, so too do the brown eyed people know they have brown eyes because the 99 other brown eyed people haven't left yet.

Why would the blue eyed people know their own eyes are blue after the 100th day, but not the brown eyed people?

Before that 100th day they could assume their eyes are any color, but the same goes for the blue eyed people.

[Edited on February 7, 2011 at 1:09 AM. Reason : ]

2/7/2011 1:09:00 AM

That guy's answer is wrong.

Come the next midnight as they see that no one is getting on the ferry, they will all assume they have blue eyes since they'll all assume everyone else isn't leaving because they see someone with blue eyes who isn't leaving and they'll think the blue eyed people must not be leaving because of them. Everyone will attempt to leave, the 100 people who have blue eyes will think they have blue eyes and think the brown eyed people somehow figured out they have brown eyes. The brown eyed people will all think they are blue eyed people. Either no one will be able to leave the island since they can't communicate whether or not they actually know their eye color and the ferryman will not let them board the ferry, or all 200 will leave the island since the ferry man cannot tell whether or not they know.

2/7/2011 1:31:44 AM

^^ yeah i think the brown eyed people leave eventually too

[Edited on February 7, 2011 at 1:46 AM. Reason : ]

2/7/2011 1:42:14 AM

What's the hardest logic puzzle out of this world?

2/7/2011 1:55:30 AM

^^^ LOL yeah I think that's being handwaved away, but I also posted that on the first page.

Quote :

"After thinking about it, nobody ever leaves the island. Since they can't communicate, there's no way to indicate to the ferryman that they know their own eye color."

2/7/2011 2:01:11 AM

^^^Dang, I was going to assume that AndyMac was just trolling. But, moron, you're killing me here!

Very simple explanation...

What allows the blue-eyed people to figure out that they have blue eyes?

Two pieces of information: 1) the observations that they have made about everybody else's eye colors, and 2) the observations that they have made about who/how many people leave or do not leave each night.

How were they able to observe everybody else's eye colors?

By looking at them and recording them.

How were they able to observe who/how many people left each night?

By watching.

How were they able to use their observations about who/how many people left each night?

By using the guru's information to determine that blue-eyed people would begin trying to figure out their eye colors and leave.

They can't communicate with one another so the guru is basically the person that guides their individual deductions into collective ones. If the guru doesn't say anything about brown-eyed people, then they can't begin making observations about who/how many people leave each night (in terms of brown eyes)...so the brown-eyed people can never begin making deductions about whether or not they have brown eyes.

^^^^No, they wouldn't assume that because they are perfect logicians. They will follow the information to its deliberate end in order to be sure before trying to board the ferry. If they all just tried to jump on the boat immediately, then they wouldn't be very good at logic puzzles.



I think y'all definitely get it, but you're just picking at the dude's wording and solution. His solution is terrible since he frames their individual thinking in terms of blue and brown. But they don't actually know (the way that we know since we read the premise) that the only two possible colors are blue and brown. In their minds, they would actually be thinking blue and non-blue.

[Edited on February 7, 2011 at 2:16 AM. Reason : No more edits.]

2/7/2011 2:10:54 AM

Quote :

" What allows the blue-eyed people to figure out that they have blue eyes? Two pieces of information: 1) the observations that they have made about everybody else's eye colors, and 2) the observations that they have made about who/how many people leave or do not leave each night. How were they able to observe everybody else's eye colors? By looking at them and recording them."

Why can't the brown eyed people do the same thing?

Quote :

"If the guru doesn't say anything about brown-eyed people, then they can't begin making observations about who/how many people leave each night (in terms of brown eyes)...so the brown-eyed people can never begin making deductions about whether or not they have brown eyes."

Why, exactly?

They may not be able to communicate, but it doesn't mean they can't think.

2/7/2011 2:16:45 AM

I was trying to type out why I thought they would leave, then i realized i was wrong.

So, yeah the brown eyes stay. They only know they are not-blue, but they don’t know if they are red/yellow/green/whatever.

If there are 3 blue eyed and 3 brown eyed people and the guru, the 3 brown eyed people know after the blues leave that they are not blue. But they don’t know if they are green eyed or brown eyed or red eyed, etc.

[Edited on February 7, 2011 at 2:31 AM. Reason : ]

2/7/2011 2:29:23 AM

Quote :

"Why can't the brown eyed people do the same thing?"

The brown-eyed people cannot do the same thing because the second piece of information (who/how many people leave each night) is only valuable in terms of blue-eyed people. It is only valuable in terms of blue-eyed people because it was brought on by the guru's words about blue-eyed people.

Nothing has been said about brown-eyed people so when it comes to observations about who is leaving each night, they can't use that information to make deductions about brown-eyed people.

Quote :

"Why, exactly? They may not be able to communicate, but it doesn't mean they can't think."

Sure, and they can make all sorts of inductions. If all the blue-eyed people leave, and one guy is left with 99 brown-eyed people, then that guy can guess that he most likely has brown eyes, too. But he can't know that.

And since they can't communicate, they can't start individually/collectively working towards the brown-eyed piece of the puzzle. They can't assume, "Oh, now, we're doing brown eyes."


Plus, and this is important, there is no deliberate end to the brown-eyed piece of the puzzle. Even if the guru did come out and say, "I see brown eyes" after all the blue-eyed people left, the brown-eyed people still couldn't follow the same process that the blue-eyed people followed because the only people left are people with brown eyes. You need the other eye-colored people there to determine if you're the remaining one with the selected eye color. I mean, if you get two the 199th or 200th day (or whatever), and all the brown-eyed people are still sitting there, you still can't assume you have brown eyes...you need people with another color eyes to make the deductions. OMG I FIGURED IT OUT FOR REAL! AND ON MY OWN!

[Edited on February 7, 2011 at 2:50 AM. Reason : Or did I?]

2/7/2011 2:48:47 AM

^AHA, my paragraph with the bold is me betraying the point of the puzzle and being totally wrong.

Anyway, I think I get common knowledge now, but I suspect it's only in terms of this puzzle.

I'm trying to do this one now:

Quote :

"On a game show, two people are assigned whole, positive numbers. Secretly each is told his number and that the two numbers are consecutive. The point of the game is to guess the other number. Here are the rules of the game: –The two sit in a room which has a clock that strikes every minute on the minute –The players cannot communicate in any way –The two wait in the room until someone knows the other person’s number. At that point, the person waits until the next strike of the clock and can announce the numbers –The game continues indefinitely until someone makes a guess –The contestants win $1 million if correct, and nothing if they are wrong Can they win this game? If so, how?"

http://mindyourdecisions.com/blog/2010/04/20/guess-the-number-a-game-theory-puzzle/

2/7/2011 3:55:23 AM

that one is neat too! very similar setup and reasoning to this one

as far as blue eyes, a lot of ya'll are doubting the guru provides valuable information. she does. it's not just a kick in the ass to "start figuring it out."

2/7/2011 9:13:31 AM

That would be the most boring game show I've ever seen.

[Edited on February 7, 2011 at 9:21 AM. Reason : Sounds like he's got a 50% chance if he just guesses]

2/7/2011 9:19:49 AM

i'm done with this thread



this is why we cant advance as a society

2/7/2011 9:31:44 AM

Because we sit around making up and trying to solve pointless logic puzzles instead of working to advance society?

2/7/2011 9:47:51 AM

Quote :

"EuroTitToss: it's not just a kick in the ass to 'start figuring it out.'"

The guru makes it common knowledge. Everybody already knew that there were people with blue eyes, but now everybody knows that somebody else knows that there are people with blue eyes. And, as each day passes, they increase orders of knowledge.

It's interesting, but the blue-eyed people example sucks. The only way it's going to be compelling to me is if I see it work meaningfully in real life.

Can you explain it in a way that would make me care?

2/7/2011 3:01:41 PM

I thought I got it...and then I made the mistake of reading the whole thread. Now I'm more confused.

2/7/2011 4:40:24 PM

Quote :

"It's interesting, but the blue-eyed people example sucks. The only way it's going to be compelling to me is if I see it work meaningfully in real life. Can you explain it in a way that would make me care?"

It has implications for computer science which affects all of our lives.

2/7/2011 5:33:21 PM

Quote :

"Because we sit around making up and trying to solve pointless logic puzzles instead of working to advance society?"

no, it's because people don't understand basic logic, so they argue it with idiotic points and then piss off the reasonable people who do understand

2/7/2011 6:03:20 PM

^^Yeah, I read a little bit about that.

But I don't know computers or computer science. So an explanation that uses computer science is gonna need to be pretty darn good.

2/7/2011 8:31:22 PM

^^^Any interesting, simple explanations for what they are?

I'm trying to think of some real world applications, but can't. No matter. I actually find the puzzle interesting just because it's so mind boggling.

A similar problem I found neat:
http://en.wikipedia.org/wiki/Two_Generals'_Problem

And what the hell, while I'm at it:
http://en.wikipedia.org/wiki/Prisoner's_dilemma (iterated version is the best)

2/7/2011 9:09:11 PM