Online since 2002. Over 3300 puzzles, 2600 worldwide members, and 270,000 messages.

TwistyPuzzles.com Forum

It is currently Wed Apr 23, 2014 1:42 pm

All times are UTC - 5 hours



Post new topic Reply to topic  [ 52 posts ]  Go to page 1, 2  Next
Author Message
 Post subject: Blue Eyes
PostPosted: Thu Oct 21, 2010 12:41 pm 
Offline
User avatar

Joined: Fri Feb 06, 2009 2:57 pm
Location: Pittsburgh
Blue Eyes is a logical riddle that's been posted online by the author of xkcd.

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?


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."

I've done my best to make the wording as precise and unambiguious as possible (after working through the explanation with many people), but if you're confused about anything, please let me know.

A word of warning: The answer is not simple. This is an exercise in serious logic, not a lateral thinking riddle. There is not a quick-and-easy answer, and really understanding it takes some effort.


There is a solution, that's all I'm going to give you.

_________________
3x3x3 PB: 00:48.10
"Study gravitation, it's a field with a lot of potential."
Image


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 12:20 am 
Offline
User avatar

Joined: Thu Nov 05, 2009 7:30 pm
Location: New York
Well...I have read it twice and I think I know what it is...
The 1st night all 100 people with blue eyes leave the island. The remaining people with brown eyes can leave the island the next night. That's if they can guess right.

_________________
8/22/2012
Image
My Collection
Youtube Channel


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 1:26 am 
Offline
User avatar

Joined: Fri Feb 06, 2009 2:57 pm
Location: Pittsburgh
Why do you think all 100 blue eyes would leave the first night?

Also, nobody knows their eye color, so even if they see 99 people with blue eyes and 100 with brown eyes, for all they know they have gray eyes.

_________________
3x3x3 PB: 00:48.10
"Study gravitation, it's a field with a lot of potential."
Image


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 5:24 am 
Offline
User avatar

Joined: Tue Mar 10, 2009 2:14 am
Location: Bucharest, Romania
I think I misunderstood something, cause my solution is quite dumb...

Everyone goes the first night at the ferry and says "I have blue eyes". The 100 blue-eyed persons will leave that night...the rest and the guru will stay on the island...forever probably.
But I think this solution is too easy and I don't see anything special nor any logic in it... But I don't see how it is not in accordance with the problem either. Please show me if I am wrong.

_________________
http://www.speedcubing.ro/


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 8:45 am 
Offline
User avatar

Joined: Wed May 13, 2009 4:58 pm
Location: Vancouver, Washington
pablobaluba wrote:
I think I misunderstood something, cause my solution is quite dumb...

Everyone goes the first night at the ferry and says "I have blue eyes". The 100 blue-eyed persons will leave that night...the rest and the guru will stay on the island...forever probably.
But I think this solution is too easy and I don't see anything special nor any logic in it... But I don't see how it is not in accordance with the problem either. Please show me if I am wrong.
theVDude wrote:
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.
They have to know their eye color, not guess it.

I cheated and looked up the answer. It took me a while to believe it. Here's a hint:
If there was 1 blue eyed person and 199 brown eyed people, who would leave and on what night?
If there was 2 blue eyed person and 198 brown eyed people, who would leave and on what night?

_________________
Real name: Landon Kryger


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 9:18 am 
Offline
User avatar

Joined: Thu May 20, 2010 1:22 am
Location: Sweden
are the islanders allowed to guess?

_________________
If you have fun wasting time is it not wasted time


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 9:23 am 
Offline
User avatar

Joined: Wed May 13, 2009 4:58 pm
Location: Vancouver, Washington
No. They can only leave when they know for absolute certainty what their eye color is.

_________________
Real name: Landon Kryger


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 9:29 am 
Offline
User avatar

Joined: Thu May 20, 2010 1:22 am
Location: Sweden
Quote:
"I can see someone who has blue eyes."

does it matter that she says so?

_________________
If you have fun wasting time is it not wasted time


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 9:30 am 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
GuiltyBystander wrote:
I cheated and looked up the answer. It took me a while to believe it. Here's a hint:
If there was 1 blue eyed person and 199 brown eyed people, who would leave and on what night?
If there was 2 blue eyed person and 198 brown eyed people, who would leave and on what night?

I tried to simplify even further by asking myself this:

If there was only one blue eyed person and one brown eyed person, who would leave and on what night?

But I get stuck as soon as there are more than one person with blue eyes. :oops:

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 9:45 am 
Offline
User avatar

Joined: Mon Mar 03, 2008 5:30 pm
Location: NYC
Highlight below this to see my answer
Based on GuiltyBystander's hint, I think I've got it. If only one person on the island has blue eyes, he will look around and see all brown. However, the guru has said there is someone with blue eyes, so he knows that it must be him. He leaves the first night.

If there are two people with blue eyes, they'll each see everybody else with brown and the one other blue guy. He knows he either has blue or he doesn't have blue eyes, so he can wait for the other blue guy's reaction. This thought process is going through both blue eyed guys' heads at the same time. Each knows that if they don't have blue eyes themselves, then the guy with blue eyes that they do see is the only one, and he should leave the first night. If he doesn't leave on the frst night, it's because of the same uncertainty that they're going through. Therefore, they know by the 2nd day that they both have blue eyes. In summary, if two people on the island have blue eyes, then they will leave on the second night.

I will take the examples one step further for clarity, but you probably see a pattern building here.

If there are three people on the island with blue eyes, each one sees only two others with blue eyes. Each one waits two nights to see what the other two do. Each one should be able to deduce that if, after two nights, the two guys with blue eyes that they see haven't left (because of the explanation in the previous paragraph) it's because they themselves must have blue eyes too! So, if there are three people with blue eyes, then those three people leave on the 3rd night.

This explanation ca be taken all the way up to the 100 blue and 100 brown case posed in the riddle, I think. With 100 blue, if after 99 nights, nobody has left, then they know that 100 people have blue eyes and they all leave on the 100th night.

_________________
No matter how long I've been into this stuff, I always learn new things. That's why it's impossible to get tired of it.


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 9:56 am 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
That's brilliant, well done! :shock: (and very well explained too!) :D

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Last edited by KelvinS on Fri Oct 22, 2010 9:59 am, edited 1 time in total.

Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 10:02 am 
Offline
User avatar

Joined: Thu Oct 08, 2009 4:46 pm
After reading the answer, I must agree with the logic. However, what is the purpose of the Guru telling all the islanders that at least one person has blue eyes? I understand that with only 1 person having blue eyes then the knowledge that among them at least one of them has blue eyes is necessary. However, after the number of people with blue eyes increases to 2+ people, then the knowledge is trivial.

I'd hate to give hints so I've left my logic in white.
If there are 2 people with blue eyes. Each one can clearly see that the other has blue eyes, and no one else. Therefore, with each knowing that there is only 1 person with blue eyes or the other person and themselves, the second day they are there they would leave. The Guru's information has become redundant and useless.

If someone could tell me where my logic went wry I would be much obliged.


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 10:06 am 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
Simplexity4 wrote:
After reading the answer, I must agree with the logic. However, what is the purpose of the Guru telling all the islanders that at least one person has blue eyes? I understand that with only 1 person having blue eyes then the knowledge that among them at least one of them has blue eyes is necessary. However, after the number of people with blue eyes increases to 2+ people, then the knowledge is trivial.

Explanation below in white:

Because they wouldn't be able to *start* the "logic cascade" explained by dannyb above.

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 10:09 am 
Offline
User avatar

Joined: Mon Mar 03, 2008 5:30 pm
Location: NYC
More hidden arguments:
You may be right. If she says "I see someone with blue eyes", and there is more than one person with blue eyes, then everybody on the island can say "So what, i can see someone with blue eyes too!"

They would be able to start that logic cascade even without the guru's information. Just start with the case of 2 people with blue eyes. They could figure it out just fine without her saying what she said.

_________________
No matter how long I've been into this stuff, I always learn new things. That's why it's impossible to get tired of it.


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 10:14 am 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
The implications of this are blowing my mind. :shock: :shock: :shock:

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Last edited by KelvinS on Fri Oct 22, 2010 10:14 am, edited 1 time in total.

Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 10:14 am 
Offline
User avatar

Joined: Thu Oct 08, 2009 4:46 pm
Kelvin Stott, I believe DannyB's explanation is correct.

We can also rephrase it in a different way.

What does the Guru's explanation add? It merely tells everyone on the island at least one person has blue eyes. Is that not information that everyone on the island knows? Because everyone on the island can see at least 99 people with blue eyes.


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 10:16 am 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
I agree, that's why it's blowing my mind. The implication is that nobody needs to say anything, yet suddenly everyone knows their own eye colour.

It's kind of like mind reading, but completely based on logic ... and VERY spooky! :shock:

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Last edited by KelvinS on Fri Oct 22, 2010 10:18 am, edited 1 time in total.

Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 10:17 am 
Offline
User avatar

Joined: Mon Mar 03, 2008 5:30 pm
Location: NYC
I guess that's why it was important to explain at the beginning that everybody on the island is a perfect logician :lol: :lol:

_________________
No matter how long I've been into this stuff, I always learn new things. That's why it's impossible to get tired of it.


Last edited by dannyb21892 on Fri Oct 22, 2010 10:19 am, edited 1 time in total.

Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 10:19 am 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
This is the most incredible problem/riddle I've ever heard. Wow.

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 10:20 am 
Offline
User avatar

Joined: Tue Feb 16, 2010 12:15 pm
Location: Sandnes, Norway
dannyb21892: I believe your answer is correct. A few weeks ago one of my math classes discussed this, but with hats, not eye colors. And the solution my professor gave us at the end of the lecture is identical to yours. It's quite tricky, but once you first get it, it all makes perfect sense.

Also, my professor also specified that everybody in the room (his version of the riddle) were perfect logicians.


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 10:21 am 
Offline
User avatar

Joined: Thu Oct 08, 2009 4:46 pm
So while the logic used to solve the riddle is infallible and unchanging, the riddle itself isn't as perfect as it can be? ;)


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 10:49 am 
Offline
User avatar

Joined: Tue Mar 10, 2009 2:14 am
Location: Bucharest, Romania
Ok. So this problem has indeed an interesting solution and something not quite obvious at first sight. Then I won't read any hints and I'll try to figure it out myself. I think it's worth. You don't encounter too often problems like this.
I've only read Kelvin's "That's brilliant... " :).

_________________
http://www.speedcubing.ro/


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 11:37 am 
Offline
User avatar

Joined: Mon Mar 03, 2008 5:30 pm
Location: NYC
I think we might have been mistaken. The guru's words are necessary. Two scenarious in the case with 2 people with blue eyes:


Scenario 1
The guru has told us she sees someone with blue eyes. I see one person with blue eyes. If he's the only one with blue eyes, he knows he must have blue eyes because he sees only other color people, but the guru told him there was someone with blue. So he should leave after the frst night. If he doesn't it must be because there's someone else with blue eyes making him uncertain. I see nobody else with blue eyes, so it must be me. We both leave on the second night with the knowledge that we both have blue eyes.

Scenario 2
The guru has told us nothing. I see one person wth blue eyes. If he's the only person with blue eyes, he doesn't know anything because he sees only other color people and for all he knows, he's another color too. Therefore he won't leave on the first night. I know nothing of my own eye color.

SUMMARY
The knowledge that the guru sees someone with blue eyes is trivial to everyone who can see a blue eyed person. However, if only one person has blue eyes, the knowledge is NOT trivial to him because it tells him he's the one with blue eyes since he sees no one else. This case of the single blue eyed person is the base for everything that follows. If this knowledge isn't given at the start, the entire mountain of logic that piles up later is invalidated.

Kelvin Stott, you were right. Sorry :]

_________________
No matter how long I've been into this stuff, I always learn new things. That's why it's impossible to get tired of it.


Last edited by dannyb21892 on Fri Oct 22, 2010 11:45 am, edited 2 times in total.

Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 11:42 am 
Offline
User avatar

Joined: Fri Feb 06, 2009 2:57 pm
Location: Pittsburgh
Simplexity4 wrote:
Kelvin Stott, I believe DannyB's explanation is correct.

We can also rephrase it in a different way.

What does the Guru's explanation add? It merely tells everyone on the island at least one person has blue eyes. Is that not information that everyone on the island knows? Because everyone on the island can see at least 99 people with blue eyes.

Because they can't GUESS. They can see 99 other people with blue eyes, sure, but for all they know they have red eyes, or gray eyes, or any color eyes. The 'logical cascade' needs to be started. Basically this (highlight to read):What is the quantified piece of information that the Guru provides that each person did not already have?

Each person knows, from the beginning, that there are no less than 99 blue-eyed people on the island. Furthermore, everybody knows that everybody knows that there are at least 98 blues. And, everybody knows that everybody knows that everybody knows that there are at least 97 blueys....etc...etc...

But not everyone knew that everyone knew that last statement that can be inferred (involving the at least 1 person case) until the Guru spoke up.

_________________
3x3x3 PB: 00:48.10
"Study gravitation, it's a field with a lot of potential."
Image


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 11:51 am 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
dannyb/theVDude, I agree with your analysis that the Guru's information is critical. The problem is I also agree with Simplexity's earlier statement:
Simplexity4 wrote:
What does the Guru's explanation add? It merely tells everyone on the island at least one person has blue eyes. Is that not information that everyone on the island knows? Because everyone on the island can see at least 99 people with blue eyes.

So we seem to have a paradox that the Guru's information does/doesn't matter. How do we resolve this? :?

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 12:05 pm 
Offline
User avatar

Joined: Mon Mar 03, 2008 5:30 pm
Location: NYC
This may be the world's most interesting riddle.

_________________
No matter how long I've been into this stuff, I always learn new things. That's why it's impossible to get tired of it.


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 12:11 pm 
Offline
User avatar

Joined: Thu Oct 08, 2009 4:46 pm
Ahh I understand now, Thanks for resolving the matter DannyB.

Edit: Actually, I don't fully understand. Highlight below.

If we have 4 blue eyed people and a trivial amount of other colored eye people. Each blue eyed person can see 3 other blue eyed people. Each do not know their own color. Each one can infer that any of the other can see at least 2 blue eyed people. So each one is armed with the knowledge that everyone of the blue eyed people can see at least 2 blue eyed people.

Can someone explain to me, in layman's terms, how repeating that knowledge helps?


I'm clearly not thinking well today :/


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 1:04 pm 
Offline
User avatar

Joined: Mon Mar 03, 2008 5:30 pm
Location: NYC
You're thinking just fine. this riddle is just monstrously confusing when you really pick it apart. Trying to fully explain a case where 4 people have blue eyes: (highlight)

I'll explain from the point of view of one of the blue eyed people as I think that helps. When I write from this point of view, I will end up getting into other blue eyed-people's heads to think through my own solution. This may get really confusing. Take a deep breath...

The guru has just told us all she sees someone with blue eyes. I see 3 blue eyed people. I do not know whether my eyes are blue or some other color. I also know that if I have blue eyes, the other blue eyed people also see 3 blue eyed people total, including myself. If I do not have blue eyes, the other blue eyed people see only 2 blue eyed people each.
I'll assume for the moment I don't have blue eyes. The other 3 people do have blue eyes and they see that I don't. Each one sees 2 people that do have blue eyes and are unsure of their own color.
I assume that one of those 3 assumes that his own eye color is not blue. By that assumption, the two people with blue eyes can each see one person with blue eyes. If, after one night, one hasn't left (due to the guru's information), the other knows he has blue eyes and they would leave. If they don't leave it's because they saw someone extraneous with blue eyes. therefore, the third blue eyed person knows he has blue eyes and the three of them should leave on the third night. If they don't, it's because all three see someone else with blue eyes. That person must be me since I see nobody else with blue eyes. Therefore all four of us leave on the fourth night knowing that we all have blue eyes, and necessarily using the guru's words.

The solution for 100 people is the same logic. Just more of the same. In conclusion, the guru's words are absolutely necessary for them to figure it out, even though what she said is something they all already knew.

_________________
No matter how long I've been into this stuff, I always learn new things. That's why it's impossible to get tired of it.


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 1:26 pm 
Offline
User avatar

Joined: Thu Dec 21, 2006 5:32 pm
Location: Bay Area, CA
Interesting, but what I don't like about the riddle is that it only works in the incredibly contrived example (no speaking,, perfect logician etc.). It assumes that means they will all arrive magically at exactly the same conclusions. If any one of them came to any other conclusion it all falls apart. Certainly this is a solution, but has anyone done the work to prove it is the only solution? This makes it seem reverse constructed, i.e. someone starts with a solution and works backwards to try to create a complex situation that falls into it, kind of like card tricks or number games that seem on the surface amazing but are grounded in inevitable mathematics.

Dave :)

_________________
Image
LitwinPuzzles.com has info on my puzzles.


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 1:29 pm 
Offline
User avatar

Joined: Thu May 20, 2010 1:22 am
Location: Sweden
Katten wrote:
dannyb21892: I believe your answer is correct. A few weeks ago one of my math classes discussed this, but with hats, not eye colors. And the solution my professor gave us at the end of the lecture is identical to yours. It's quite tricky, but once you first get it, it all makes perfect sense.

Also, my professor also specified that everybody in the room (his version of the riddle) were perfect logicians.


I've heard that riddle! I came up with the answer myself! here it is for anyone who haven't heard it:

~~~~~~
Rules:
~~~~
There is three professors sitting behind each other everyone looking at the same direction.
A man has a bag with hats in it. there is two black and three white hats, and he gives the professors a random hat each.
The professor furthest back can see the color of the two professors hats in front of him. The professor in the middle can only see the color of the hat of the professor in the front, who can't see any hats at all. They can't see their own hats, and they aren't allowed to cheat and look back.
when a professor knows what color his hat has he got to say the color out loud.
~~~~
you are the professor in the front, and no professor (who are perfect logicians) say a color. Which color has your hat?
~~~~~~

I solved this riddle, but I can't solve the 'blue eyes' riddle, should I be able to solve it, or is it way much harder?

_________________
If you have fun wasting time is it not wasted time


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 1:35 pm 
Offline
User avatar

Joined: Mon Mar 03, 2008 5:30 pm
Location: NYC
DLitwin wrote:
Interesting, but what I don't like about the riddle is that it only works in the incredibly contrived example (no speaking,, perfect logician etc.). It assumes that means they will all arrive magically at exactly the same conclusions. If any one of them came to any other conclusion it all falls apart.


Any other conclusions they arrive at would be incorrect conclusions so it would fall apart for sure. It seems to me that this requires a very methodical step by step approach of makign assumptions and proving them false due to lack of action each night. (no crude jokes please :roll: ) The conclusions drawn by each of them can only be correct one way, and must coincide if they are all smart enough, hence specifying that they are all perfect logicians.

_________________
No matter how long I've been into this stuff, I always learn new things. That's why it's impossible to get tired of it.


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 1:41 pm 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
dannyb21892 wrote:
In conclusion, the guru's words are absolutely necessary for them to figure it out, even though what she said is something they all already knew.
This is clearly a paradox, which tells us that something *must* be wrong with our logic, somewhere along the lines...

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 1:55 pm 
Offline
User avatar

Joined: Thu May 20, 2010 1:22 am
Location: Sweden
how many here have figured it out yourselves? and plz answer my question up there ↑

_________________
If you have fun wasting time is it not wasted time


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 2:06 pm 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
blueShinyApple wrote:
I've heard that riddle! I came up with the answer myself! here it is for anyone who haven't heard it: There is three professors sitting behind each other everyone looking at the same direction...

This riddle has already been discussed here and a similar one here.

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 2:06 pm 
Offline
User avatar

Joined: Fri Feb 06, 2009 2:57 pm
Location: Pittsburgh
"What is the quantified piece of information that the Guru provides that each person did not already have?" is quite a question to ask yourself, and is on the page linked in my OP.

I pasted an answer to it above in SPOILER TEXT

_________________
3x3x3 PB: 00:48.10
"Study gravitation, it's a field with a lot of potential."
Image


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 2:17 pm 
Offline
User avatar

Joined: Mon Mar 03, 2008 5:30 pm
Location: NYC
This picture shows a progression of assumptions which leads to a solution for 4 people with blue eys. Expanded, it would be the same as the 100 person solution. There isn't a paradox; the guru's information is absolutely necessary even though it's something they all already know.
SPOILER ALERT: IF YOU DON'T WANT THE SOLUTION TO THE RIDDLE, DO NOT READ THE TEXT IN THIS PICTURE.


Attachment:
blue eyes.png
blue eyes.png [ 34.32 KiB | Viewed 5052 times ]

_________________
No matter how long I've been into this stuff, I always learn new things. That's why it's impossible to get tired of it.


Last edited by dannyb21892 on Fri Oct 22, 2010 3:11 pm, edited 1 time in total.

Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 2:53 pm 
Offline
User avatar

Joined: Thu May 20, 2010 1:22 am
Location: Sweden
dannyb21892 wrote:
This picture shows a progression of assumptions which leads to a solution for 4 people with blue eys. Expanded, it would be the same as the 100 person solution. There isn't a paradox; the guru's information is absolutely necessary even though it's something they all already know.





plz make a link to the pic instead! Some people actually wants to solve it themeselves! (like me)

_________________
If you have fun wasting time is it not wasted time


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Fri Oct 22, 2010 4:20 pm 
Offline
User avatar

Joined: Thu May 20, 2010 1:22 am
Location: Sweden
blueShinyApple wrote:
how many here have figured it out yourselves? and plz answer my question up there ↑


OMG,OMG,OMG!!!!

I DID IT!!!

without cheating or looking or anything! I told the riddle to my dad, but he couldn't solve it (but he didn't have that much time..), I tried to explain the solution, but he didn't understand (maby because of my low xplaining skills..).

the gurus information is pretty important, i think.., but btw what happens to all the brown eyed guys? they'll have to stay, huh?
I might make some neat chart for how the whole thing works, to clarify it for everybody who aren't as smart as us...(and to clarify it for me, lol)
I got it when I first tried with two blue-eyed, and then three, and so on...
:D :D :D
highlight^

_________________
If you have fun wasting time is it not wasted time


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 6:24 am 
Offline
User avatar

Joined: Fri Feb 06, 2009 2:57 pm
Location: Pittsburgh
You can work up that way, but the more confusing way (that feels more right) starts from the top down.

_________________
3x3x3 PB: 00:48.10
"Study gravitation, it's a field with a lot of potential."
Image


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 9:05 am 
Offline
User avatar

Joined: Sun Jun 13, 2010 1:00 am
Location: Colorado
For me I solved it while I was still reading the riddle! :lol:

I then spent half an hour thinking about other solutions because it felt way to easy. I guess my brain is just wired to think the correct way for this problem, I'm usually really bad at riddles :lol:

_________________
My Shapeways Shop
My YouTube Videos
My Museum Puzzles


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 11:28 am 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
PuzzleMaster6262 wrote:
For me I solved it while I was still reading the riddle! :lol:

I find that difficult to believe considering that the main question appears only at the end (not to mention the complexity).

Anyway, I've been thinking about some other interesting scenarios with alternative solutions:

What if the Guru says "I see at least one person with blue eyes and ..."

1. "...at least one has brown eyes" OR
2. "...everyone I see has blue or brown eyes" OR
3. "...at least one has neither blue nor brown eyes" (let's assume this is the case).

So who would leave when in these cases?

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 1:54 pm 
Offline
User avatar

Joined: Mon Mar 03, 2008 5:30 pm
Location: NYC
Out of kelvin's 3 situations:

1-the guru says she sees at least one with brown eyes. This is the same as the original riddle, except with brown instead of blue. Solution: the 100 brown eyed people would leave on the 100th night.

2-guru says everyone I see has either blue or brown eyes.solution: nobody will leave. Nobody can possibly deduce their own eye color.

3-guru says at least one person has neither blue nor brown eyes. Solution: nobody will leave. At best, some can determine if their eyes are neither blue nor brown, but not what precise color of course.

_________________
No matter how long I've been into this stuff, I always learn new things. That's why it's impossible to get tired of it.


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 2:01 pm 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
I actually meant that the Guru says one of these things *in addition* to the fact that at least one person has blue eyes...

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 2:13 pm 
Offline
User avatar

Joined: Thu May 20, 2010 1:22 am
Location: Sweden
What if the guru in addition said "..but nobody have [every color except for brown and blue]",
then all the brown eyed would leave on the 101st night
highlight^

_________________
If you have fun wasting time is it not wasted time


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 4:33 pm 
Offline
User avatar

Joined: Sun Jun 13, 2010 1:00 am
Location: Colorado
@kelvin
After the question it still explains that there are no mirrors and such. I understand it should be complex but it isn't to me. Usually I find riddles really hard but for some reason this one is an exception. In white I have my logic. I put myself on the island when I first started reading and gave myself blue eyes but assumed I had brown. I then assumed everyone else assumed this until only one person had blue eyes. When the question was asked who leaves and on what night, I figured out everyone would not leave until the 100th night when all 100 blue eyed people leave.

_________________
My Shapeways Shop
My YouTube Videos
My Museum Puzzles


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 8:01 pm 
Offline
User avatar

Joined: Tue Mar 10, 2009 7:06 pm
Location: Nowhere in particular.
I thought about this one all day, and eventually came to the conclusion most of you came to.

I assume that the brown-eyed people leave on day 101, and that the guru stays on the island forever? Or does he/she leave?

highlighted above

EDIT: Ah, forgot about that, Danny.

_________________
~Kapusta

PB: At home (In Competition)
2x2 1.xx (2.88)
3x3 11.xx (15.81)
4x4 1:18.26 (1:24.63)
5x5 (3:00.02)
6x6 4:26.05 (6:34.68)
7x7 6:38.74 (9:48.81)
OH (35.63)

Current Goals:
7x7 sub 6:30
4x4 sub 1:10


Last edited by Kapusta on Sat Oct 23, 2010 8:17 pm, edited 1 time in total.

Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 8:12 pm 
Offline
User avatar

Joined: Mon Mar 03, 2008 5:30 pm
Location: NYC
Kapusta, highlight:
the brown eyed people don't leave after the blue eyed people because they don't know that they have to be brown. For all they know they could be red or grey or something.

_________________
No matter how long I've been into this stuff, I always learn new things. That's why it's impossible to get tired of it.


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 9:02 pm 
Offline
User avatar

Joined: Sun Jun 13, 2010 1:00 am
Location: Colorado
The brown eyed people never leave. Only those that know they have blue eyes can leave.

_________________
My Shapeways Shop
My YouTube Videos
My Museum Puzzles


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 9:17 pm 
Offline
User avatar

Joined: Sun Apr 16, 2000 3:17 pm
Location: Hong Kong
PuzzleMaster6262 wrote:
The brown eyed people never leave. Only those that know they have blue eyes can leave.


in typical Rox fashion: How do they survive? I mean, is the island self sustaining, or do they have food and supplies shipped in, and if so, then how do they keep those peoples eye color separate? Or all those people blind?

And if the brown eyed people never leave, do they procreate? And if so, then are the colors of their children's eyes all brown? And if not, do those that have blue eyes have to leave as well?

_________________
Rox's Rambling Blog
Katsmom's Puzzling Videos


Top
 Profile  
 
 Post subject: Re: Blue Eyes
PostPosted: Sat Oct 23, 2010 9:23 pm 
Offline
User avatar

Joined: Fri Feb 20, 2009 6:38 pm
They are immortal because of the guru!! :lol:

_________________
Puzzle Photography Group
Facebook

doctor who wrote:
I don't think I can make her pose without heavy sedation. The rendering doesn't have to be perfect, it just can't look like Oskar in drag.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 52 posts ]  Go to page 1, 2  Next

All times are UTC - 5 hours


Who is online

Users browsing this forum: No registered users and 4 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  

Forum powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group