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Author Topic: Blue eyes
Ashitaka

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Icon 11 posted February 16, 2009 04:54      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
I ran across this at xkcd, I cheated and looked up the answer anfter about an hour. This puzzle is cool becuase you may not even believe teh answer, and if you do I have a few questions for you.

[Geek]
quote:
The Hardest Logic Puzzle
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?


There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."

And lastly, the answer is not "no one leaves."



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"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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TheMoMan
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Icon 1 posted February 16, 2009 05:23      Profile for TheMoMan         Edit/Delete Post   Reply With Quote 
__________________ TheMoMan __ Tis simple, after the meeting, they all walk past each other, If all you see are brown eyes, then you must be blue eyed. If you see a blue eyed person you may or may not have blue eyes.

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Those who would give up essential liberty to purchase a little temporary safety deserve neither liberty nor safety.


Benjamin Franklin,

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Ashitaka

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Icon 1 posted February 16, 2009 06:02      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by TheMoMan:
__________________ TheMoMan __ Tis simple, after the meeting, they all walk past each other, If all you see are brown eyes, then you must be blue eyed.

True, but they don't they see many people with blue eyes as there are 100 people on the island with blue eyes. They already knwo many many people have pblue eyes. The guru saying " I see someone with blue eyses" doesn't give them any information about eye colour they don't already have. The also see people with blue eyes, but thiers could be brown, yellow or red.

--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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TheMoMan
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Icon 1 posted February 16, 2009 09:56      Profile for TheMoMan         Edit/Delete Post   Reply With Quote 
_______________ TheMoMan __ Of the people at the town square The Guru said "I see some one with Blue Eyes." Then if you meet every one else at the town square and THEY ALL HAVE BROWN EYES the only conclusion is I must have Blue EYES.

--------------------
Those who would give up essential liberty to purchase a little temporary safety deserve neither liberty nor safety.


Benjamin Franklin,

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GrumpySteen

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Icon 1 posted February 16, 2009 10:16      Profile for GrumpySteen     Send New Private Message       Edit/Delete Post   Reply With Quote 
There two answers and not quite enough information to determine which one is correct.

I know how many people leave first and what night but more that that will leave if the boat comes back again after it takes the first people away.

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The Famous Druid

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Icon 1 posted February 16, 2009 10:53      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
Ok, I cheated and looked at the solution.

I've got some questions too.

I don't want to spoil peoples fun, so Ive created a a new thread to discuss the solution.

--------------------
If you watch 'The History Of NASA' backwards, it's about a space agency that has no manned spaceflight capability, then does low-orbit flights, then lands on the Moon.

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Ashitaka

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Icon 1 posted February 16, 2009 11:52      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by TheMoMan:
_______________ TheMoMan __ Of the people at the town square The Guru said "I see some one with Blue Eyes." Then if you meet every one else at the town square and THEY ALL HAVE BROWN EYES the only conclusion is I must have Blue EYES.

yes, but you know that they all DON'T have brown eyes.

--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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Ashitaka

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Icon 1 posted February 16, 2009 11:53      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by GrumpySteen:
There two answers and not quite enough information to determine which one is correct.

I know how many people leave first and what night but more that that will leave if the boat comes back again after it takes the first people away.

I would read this sentance again.
quote:
Or 100 brown, 99 blue, and he could have red eyes.



--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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DoctorWho

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Icon 1 posted February 17, 2009 18:48      Profile for DoctorWho     Send New Private Message       Edit/Delete Post   Reply With Quote 
Well I think if only one person would have blue eyes, he would see that everyone else had brown eyes and then realize that he must have blue eyes and leave the island that night on the ferry.

Everyone else would see the one guy with blue eyes, think he has blue eyes and expect him to be gone by the next day.

Now what happens when there are more blue-eyed people?

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Laughter is like changing a baby's diapers. It doesn't solve anything but it sure improves the situation. Leo F. Buscaglia

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GrumpySteen

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Icon 1 posted February 17, 2009 19:31      Profile for GrumpySteen     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by Ashitaka:
quote:
Originally posted by GrumpySteen:
There two answers and not quite enough information to determine which one is correct.

I know how many people leave first and what night but more that that will leave if the boat comes back again after it takes the first people away.

I would read this sentance again.
quote:
Or 100 brown, 99 blue, and he could have red eyes.


Umm... you do realize that what you quoted has nothing to do with whether the ferry comes back, right?

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Ashitaka

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Icon 1 posted February 18, 2009 00:14      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by GrumpySteen:
quote:
Originally posted by Ashitaka:
quote:
Originally posted by GrumpySteen:
There two answers and not quite enough information to determine which one is correct.

I know how many people leave first and what night but more that that will leave if the boat comes back again after it takes the first people away.

I would read this sentance again.
quote:
Or 100 brown, 99 blue, and he could have red eyes.


Umm... you do realize that what you quoted has nothing to do with whether the ferry comes back, right?
You can assume the ferry comes every night at midnight regardless.

--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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TheMoMan
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Icon 1 posted February 18, 2009 01:52      Profile for TheMoMan         Edit/Delete Post   Reply With Quote 
___________________ I don't know why I did not think of this earlier. Person A goes to the ferry and declares that I have Blue Eyes. The ferry operator: one, lets that person board or two, does not allow passage. Person A now does now his/her eye color.

--------------------
Those who would give up essential liberty to purchase a little temporary safety deserve neither liberty nor safety.


Benjamin Franklin,

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The Famous Druid

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Icon 1 posted February 18, 2009 03:11      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by TheMoMan:
___________________ I don't know why I did not think of this earlier. Person A goes to the ferry and declares that I have Blue Eyes. The ferry operator: one, lets that person board or two, does not allow passage. Person A now does now his/her eye color.

That's a far more elegant solution than the 'official' one. [Applause] [Applause] [Applause] [Applause] [Applause]

Sadly, it violates one of the rules...
quote:
It doesn't depend on tricky wording or anyone lying or guessing


--------------------
If you watch 'The History Of NASA' backwards, it's about a space agency that has no manned spaceflight capability, then does low-orbit flights, then lands on the Moon.

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TheMoMan
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Icon 1 posted February 18, 2009 03:23      Profile for TheMoMan         Edit/Delete Post   Reply With Quote 
_______________________ TFD __ If I state I have blue eyes, as a belief then it is not a lie. Next day if I state I have brown eyes, as a belief then that is not a lie.

--------------------
Those who would give up essential liberty to purchase a little temporary safety deserve neither liberty nor safety.


Benjamin Franklin,

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Ashitaka

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Icon 1 posted February 18, 2009 03:56      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by TheMoMan:
_______________________ TFD __ If I state I have blue eyes, as a belief then it is not a lie. Next day if I state I have brown eyes, as a belief then that is not a lie.

The puzlle doesn't ay anything about that there is a ferry operator, or that one must Say what colour thier eyes are. It simply states that if you know your eye colour at midnight, you leave. No choice¨!

--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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deathweaver
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Icon 1 posted February 18, 2009 07:29      Profile for deathweaver     Send New Private Message       Edit/Delete Post   Reply With Quote 
OK, I haven't read the answer yet, but my guess is that all the blue-eyed people leave on the first night. Reason being is that there are 201 people on the island, including the Guru. Everyone can see the Guru and know that her eyes aren't blue, and there's no way for the Guru to know her eye color. As these people are logicians, they'll be able to count 201 people on the island, 100 of which have brown eyes, and 99 that have blue eyes. In order to keep an even count, the person looking will know that they have blue eyes as well and leave. And now I'm going to look at the answer...

Edit: Damn, I was wrong...

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DoctorWho

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Icon 1 posted February 18, 2009 16:54      Profile for DoctorWho     Send New Private Message       Edit/Delete Post   Reply With Quote 
Okay,

I have pondered this off and on all day. If two people had blue eyes each one would think this other guy has blue eyes and no one else does. Therefore he should be gone tomorrow. However both would still be there. Since everyone else has brown eyes they would each deduce that they also had blue eyes and leave on the ferry on the second night.

Meanwhile all the brown-eyed people would see two blue-eyed people and think. These two people with blue eyes will wait and see if the other one leaves, both will realize the next day that he has blue eyes and leave on the second night. And by some chance if they don't leave then I must have blue eyes too and must leave the island on the third night.

Based on this I have written my answer in rot13 so that I don't spoil it for anyone else. Would someone who knows the answer please verify it for me so I don't spoil myself and can try again if I am wrong.

---------------www.rot13.com---------------
Gurersber nyy bar uhaqerq oyhr-rlrq crbcyr jbhyq yrnir ba gur uhaqerqgu avtug.

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Laughter is like changing a baby's diapers. It doesn't solve anything but it sure improves the situation. Leo F. Buscaglia

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GrumpySteen

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Icon 1 posted February 18, 2009 17:52      Profile for GrumpySteen     Send New Private Message       Edit/Delete Post   Reply With Quote 
DoctorWho:
Gurersber nyy bar uhaqerq oyhr-rlrq crbcyr jbhyq yrnir ba gur uhaqerqgu avtug.

Yup.

--------------------
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Zwilnik

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Icon 1 posted February 18, 2009 18:06      Profile for Zwilnik   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
the solution is rather cool, but I've got one that will take the islanders a little longer but would be more fun.

Male/Female Islanders pair off and have sex with one another, if the resulting baby is blue eyed, then both know they have blue eyes. If not then they know one of them has brown eyes, so they split and pair up with other partners who may or may not have brown eyes.

After a few iterations and binary chops some years later you should end up with couples who know they both have blue eyes and a population problem.

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The Universe is entirely made up of elements.
The most important of which is the element of surprise.

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The Famous Druid

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Icon 1 posted February 18, 2009 18:06      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
I disagree with the official solution, details on the spoiler thread.

--------------------
If you watch 'The History Of NASA' backwards, it's about a space agency that has no manned spaceflight capability, then does low-orbit flights, then lands on the Moon.

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