Not really that hard, but I found it interesting.

http://xkcd.com/blue_eyes.html

Quote :

"A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph. On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes. 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: "I can see someone who has blue eyes." Who leaves the island, and on what night?"

2/5/2011 11:39:48 AM

They all leave on the first night, since if they are all perfect logicians they would all figure it out instantly, even if I have no idea what this is supposed to be about.

2/5/2011 11:45:14 AM

I have blue eyes, so I would get to leave.

2/5/2011 11:45:38 AM

it'd take a few days, but everyone gets to leave. everyone guesses his eye color each night, and eventually, everyone guesses correctly.

alternately, someone finds a mirror.


[Edited on February 5, 2011 at 11:56 AM. Reason : you didn't quote the whole puzzle]

2/5/2011 11:54:24 AM

2/5/2011 11:54:40 AM

Quote :

"you didn't quote the whole puzzle"

certainly not. that's called tl;dr

2/5/2011 12:03:48 PM

it would only be tl;dr if you'd quoted the whole damn puzzle

2/5/2011 12:09:56 PM

common knowledge has weird properties

2/5/2011 12:11:02 PM

right, it took me longer to work out the implications than the solution

2/5/2011 12:13:28 PM

Just the implications hurt my head: I don't know what a perfect logician is!

So I looked up the solution. Very cool.

And now I know a little bit more bout logicians.

2/5/2011 7:34:16 PM

Is there a plane on the island? If so, it will take off from the treadmill.

2/6/2011 2:31:24 AM

Quote :

"100 brown-eyed"

hahahahha brown-eyed. They getting it in the dookie hole.

2/6/2011 2:41:20 AM

so, i read the answer, and i still don't get it.



*SPOILER MAYBE*





won't the brown eyed people also think that they're blue eyed? based on what i read, it seems like the brownies would be in the same boat as everybody else, but the answer doesn't make it sound that way. i'm also kinda drunk, so maybe i'm missing something

2/6/2011 3:30:26 AM

I like AndyMac's assessment

I'm going with that.

2/6/2011 4:13:11 AM

hum..interesting.

2/6/2011 9:16:44 AM

Remember that the person doesn't know what their own eye color is, but they know what yours is.

Remember that they cant communicate, but they can mentally mark every other person on the island.

The answer makes perfect sense.

Determining whether or not to leave on a personal level is just an iterative loop from that point.

2/6/2011 9:30:23 AM

I say that between the guru's proclamation and observing others, everyone guesses blue or brown and leaves within 2 days.

2/6/2011 9:50:04 AM

^nope

Quote :

"won't the brown eyed people also think that they're blue eyed? based on what i read, it seems like the brownies would be in the same boat as everybody else, but the answer doesn't make it sound that way. i'm also kinda drunk, so maybe i'm missing something"

no, there's a special case for why the brown eyed people can't leave. it's similar to why the guru can't leave.

2/6/2011 10:50:33 AM

just go look in the damn water

2/6/2011 10:53:31 AM

2/6/2011 10:57:56 AM

I've heard the answer to this before and the answer is complete bullshit

2/6/2011 10:59:55 AM

Looked up the answer, its deceptively simple and logical. Though I don't see why the guru would need to say anything, she presents arbitrary information

(yes I saw this on google too)

2/6/2011 11:24:30 AM

Quote :

"Though I don't see why the guru would need to say anything, she presents arbitrary information"

this is the probably the hardest part to understand. it helps to consider the case of just 2 blue eyed people (and no guru). would they leave the island?

2/6/2011 12:11:53 PM

But there are more than 2 blue eyed people. In the problem as given, what information is the guru adding?

2/6/2011 12:19:23 PM

I have blue eyes if that's what you're asking.

2/6/2011 12:26:02 PM

The guru is giving the common knowledge that there is at least one blue eyed person.

This is why I bring up the 2 blue eyed case. In that case, everyone sees at least 1 blue eyed person. A third party stating that seems redundant. But without that info, the 2 blue eyed people would never leave (and I hope it's obvious why).

She isn't giving new information about eye color, but she is giving information about what other people are now thinking. That's crucial to solving the puzzle.

[Edited on February 6, 2011 at 12:52 PM. Reason : asdfasdf]

2/6/2011 12:28:22 PM

How is it crucial?

Why can't common knowledge be inferred? Everyone knows there is a blue eyed person already, and everyone knows that everyone else knows there's a blue eyed person.

[Edited on February 6, 2011 at 12:41 PM. Reason : ]

2/6/2011 12:40:35 PM

The solution given is bullshit. And there's no reason my islanders wouldn't be gone in 2 days.

Actually, I can make it into one day. 200 people guess blue and leave, 1 guru and 1 ferry crew beaten to death.

2/6/2011 12:49:44 PM

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.

2/6/2011 12:59:28 PM

Unless the ferryman has orders to take people off the island if they just show up at the dock with the right eye color

2/6/2011 1:01:58 PM

The people with brown eyes just say fuck it and get on a C-130 that takes off on a treadmill.

2/6/2011 1:05:32 PM

Quote :

"How is it crucial? Why can't common knowledge be inferred? Everyone knows there is a blue eyed person already, and everyone knows that everyone else knows there's a blue eyed person."

***REALLY LONG EXPLANATION AND SPOILERS***

I'm going to draw a diagram. Xs for blue. Os for brown. The numbers will be different from the puzzle for simplicity (but you can generalize). Let's say the island is comprised of 4 blue eyed, 4 brown eyed, and no guru. I happen to be #1.

12345678
XXXXOOOO

12345678
OXXXOOOO

12345678
OOXXOOOO

12345678
OOOXOOOO

12345678
OOOOOOOO

2/6/2011 1:26:26 PM

It seems to me that what the guru is providing is the start of a timer of a specific eye color.

Before the Guru speaks each individual person could be focusing on the blue color timer or the brown color timer, and so no one leaves. By the Guru indicating blue eyes, everyone focuses on the blue color timer, and so they are able to leave after 100 days. That could be completely wrong though.

The brown people don't leave because their timer would have them leave on the 101st day, since they see 100 other blue eyes. So all the blue people leave a day before the brown people would leave (thinking they had blue eyes).

2/6/2011 1:34:24 PM

We call that hand waving. Why wouldn't they just leave as soon as they got on the island? You know, any person at any given time could think they have purple eyes.

2/6/2011 1:38:33 PM

^ They only leave when they have certainty, not when they hypothesize that they may be different

2/6/2011 1:46:28 PM

nvm, I see what you were saying. it seemed like you throwing out this magical "timer" concept with no real explanation, but I agree after having reread it.

2/6/2011 1:51:05 PM

the numbers are cursed

2/6/2011 1:55:20 PM

They all leave because Snape kills Dumbledore.

2/6/2011 2:54:53 PM

2/6/2011 3:27:31 PM

is it just me, or does something look funny here?

2/6/2011 3:28:47 PM

people who don't understand basic logic getting mad ITT

2/6/2011 3:48:09 PM

^long explaination. Wait, you're saying that they NEED the Guru's statment to know there's any blue eyed people?

How can you possibly end up with OOOOOOOO, when everyone sees at least 3 blue eyed people, and being perfectly logical person #1 knows that even if he has brown eyes, the fewest blue eyed people that any other person would see is 2.

[Edited on February 6, 2011 at 3:53 PM. Reason : ]

2/6/2011 3:52:29 PM

i dont get it and am too lazy to figure it out

2/6/2011 4:18:31 PM

Also, wouldn't the brown eyed people leave the same day, since there are 100 of them also?

2/6/2011 4:31:31 PM

^^^ yes, you need the statement. Otherwise you can't use induction

2/6/2011 4:37:14 PM

^^no, for the reasons listed below

^^^^I explained it bro. #1 is thinking that #2 might be thinking this:

12345678
OOXXOOOO

2/6/2011 4:38:00 PM

I don't see how a perfectly logical person could assume that another person would see something you know is impossible.

Person 1 can deduce that every single person can see at least 2 blue eyed people using simple logic, which he's supposed to be perfect at.

EDIT: Yes, #2 might be thinking OOXXOOOO, but he knows that nobody can think OOOXOOOO because he knows there are too many blues. The closest to that would be someone is thinking XOOXOOOO.



[Edited on February 6, 2011 at 4:47 PM. Reason : ]

2/6/2011 4:42:58 PM

Wouldn't they just pick a color and if they don't leave that means they are wrong and they'll just go home on night number 2

[Edited on February 6, 2011 at 4:43 PM. Reason : didn't read the thread to see if anyone else said it]

2/6/2011 4:43:30 PM

I sort of understand the solution with respect to the blues, but it seems to ignore the how the browns know they are not blue.

disclaimer: i never had any formal logic classes, so this is more of a "common sense" exercise for me

2/6/2011 4:44:37 PM

^^^dude,you seem to be getting it. just generalize that. I don't want to have to bore everybody with each step in the chain.

Quote :

"EDIT: Yes, #2 might be thinking OOXXOOOO, but he knows that nobody can think OOOXOOOO because he knows there are too many blues."

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.


^that's what I was trying to explain in my hypothetical (well, no guru... which leaves them all in the same boat).

[Edited on February 6, 2011 at 4:52 PM. Reason : adsfsdf]

2/6/2011 4:46:15 PM