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General Category => General Talk => Topic started by: Bisse on December 17, 2007, 01:54:15 am

Title: Riddle thread
Post by: Bisse on December 17, 2007, 01:54:15 am

Seen a lot of riddle threads (people post riddles, other people try to figure them out) here and there, they're great. Was thinking about it and as a coincidence, I just ran into the hardest riddle on the face of the earth, (courtesy of [ur=http://xkcd.com/blue_eyes.htmll]xkcd[/url]) so let's kick it off, see if you guys can do it. Also, feel free to post your own, have at it!

Blue Eyes:
The Hardest Logic Puzzle in the World[/center][/b]

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. If anyone has figured out the color of their own eyes, they [must] leave the island that midnight. 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."


don't post the answer if you already know it ok :)​))

Title: Riddle thread
Post by: AdderallApocalypse on December 17, 2007, 02:25:48 am

I actually know the answer to this already, but I won't spoil it. Good luck everybody!

Title: Riddle thread
Post by: Casey and His Brother on December 17, 2007, 03:53:52 am

Wouldn't any/all of the blue-eyed people leave after counting 200 people on the island without the guru, counting 100 brown-eyed people and 99 blue-eyed people, and assuming that there is an equal amount blue-eyed and brown-eyed people then assuming that they are the missing blue-eyed person? Maybe they all get to leave since they are all perfect logicians.

Title: Riddle thread
Post by: Standard Toaster on December 17, 2007, 04:06:12 am

Quote from: El Nerdo on December 17, 2007, 03:53:52 am

Wouldn't any/all of the blue-eyed people leave after counting 200 people on the island without the guru, counting 100 brown-eyed people and 99 blue-eyed people, and assuming that there is an equal amount blue-eyed and brown-eyed people then assuming that they are the missing blue-eyed person? Maybe they all get to leave since they are all perfect logicians.

they don't know how many of each person are on the island.

also i have a theory for this one.. not sure about it yet though.

Title: Riddle thread
Post by: lampshade on December 17, 2007, 04:13:53 am

Quote from: NinjaPirate on December 17, 2007, 04:06:12 am

they don't know how many of each person are on the island.

also i have a theory for this one.. not sure about it yet though.

Quote from: Bisse on December 17, 2007, 01:54:15 am

\ 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.
"I can see someone who has blue eyes."

Hmmm....

I'm trying to figure out the importance of the guru. She is the only one with green eyes, and the only one allowed to talk. The one time she does talk, she confirms she sees someone with blue eyes.

So, before she says anything, the people on the island, segregated by their eye color, see/know the following:

Blue-99 blue, 100 brown, 1 green

Brown- 100 blue, 99 brown, 1 green

Green- 100 blue, 100 brown, 0 green

My head hurts......

I still can't figure out what would change after the Guru speaks. Statistically, nothing. I just don't understand how it can change anything because she is merely confirming someone has blue eyes, a fact which everyone on the island already knows.

Title: Riddle thread
Post by: Beasley on December 17, 2007, 04:26:49 am

Quote from: Kaptainkranium on December 17, 2007, 04:13:53 am

I still can't figure out what would change after the Guru speaks. Statistically, nothing. I just don't understand how it can change anything because she is merely confirming someone has blue eyes, a fact which everyone on the island already knows.

This. She's just confirming what everyone knows, I don't know how she's changing anything.

Title: Riddle thread
Post by: Ayolark on December 17, 2007, 04:38:48 am

Couldn't stand it...looked up the answer.  I would not have expected that...but it makes perfect sense.

Title: Riddle thread
Post by: AdderallApocalypse on December 17, 2007, 04:40:38 am

Ayolark, since you looked it up then PM me how the latter logic would work. I understand how it works given certain premises but in THIS situation, I just don't see how it could be.

Title: Riddle thread
Post by: xanque on December 17, 2007, 04:41:15 am

http://xkcd.com/solution.html

I read the solution, and it doesn't make a whole lot of sense to me.  I can kind of see where it's going, but it's not one of those "aha!" kind of riddles.  It's more like an "Oh... whatever."

Title: Riddle thread
Post by: Standard Toaster on December 17, 2007, 04:53:47 am

Well, I guessed which people would be leaving, and the amount of them. I just got the day wrong.

my theory (Click to reveal)

All of the blue eyed people would leave on the first day. Since its a no-lose situation for anyone to ask to leave, everyone would do so. However, only the blue-eyed people would answer the question correctly and thus would be the only ones able to leave.

Title: Riddle thread
Post by: Medieve on December 17, 2007, 05:26:30 am

Quote from: NinjaPirate on December 17, 2007, 04:53:47 am

Well, I guessed which people would be leaving, and the amount of them. I just got the day wrong.

my theory (Click to reveal)

All of the blue eyed people would leave on the first day. Since its a no-lose situation for anyone to ask to leave, everyone would do so. However, only the blue-eyed people would answer the question correctly and thus would be the only ones able to leave.

counter spoil (Click to reveal)

Theres no guessing allowed and they have to logically confirm it

Title: Riddle thread
Post by: Summoner on December 17, 2007, 07:49:19 am

Took me awhile to wrap my head around this one, but I think I got it.

Hidden content (Click to reveal)

  I figured that all the blue eyes would have to leave by the 100th night.  I put it into perspective from where the Guru is.  Say it is the blue eyed people who could speak, then one of them (or all of them) said they saw a  green eyed person (this is assuming that there is only one green eyed person still), so when the Guru sees that everyone else didn't have green eyes, they could only logically conclude that they themselves had green eyes, and then must leave.  Then say there were two green eyed people, then they would see the other green eyed person and wait for them to leave, if the other green eyed person did not leave on the the first night then they must conclude they themselves also have green eyes and must leave, and it goes the same for the other green eyed person, and this would take place on the second night, and it would keep going up with every extra green eyed person.  Apply this logic to the blue eyed people, it would take 100 nights, but in the end every single blue eyed person would logically conclude they themselves have blue eyes.

So am I right?  I'm not going to check the solution just in case I am not in fact correct.

Title: Riddle thread
Post by: Bobberticus on December 17, 2007, 08:08:11 am

Summoner, yes that's the one!

Title: Riddle thread
Post by: Summoner on December 17, 2007, 08:10:12 am

awesome.  I feel smart now.

Title: Riddle thread
Post by: Frankie on December 17, 2007, 12:21:55 pm

Its odd. The guru to me seems like a red herring, but if he indeed was one, the problem would no longer make sense: If they are all perfect logicians, you must logically conclude that the guru will use his only communication to the others in a meaningful and important way, and bend your mind all around his revelation. You must also conclude that the other island dwellers will also take into account the fact the guru SHOULD be saying something meaningful. I CALL BULLSHIT MUHUHU.

(in my opinion, if its the case, which sounds very likely, the guru was added by someone else who thought the problem could use some complication, not realizing that he is in fact harming the riddle and not making it better.)

Ill try like, making some hypothetical situations and ill prolly end up getting the solution, you just wait! :fogetscience:

Title: Riddle thread
Post by: Kalar on December 17, 2007, 01:21:13 pm

I almost fell in the same pit-trap as NinjaPirate at first, but I drew some nice pictures, talked to myself for fifteen minutes, re-read the question and the rules (this is where I got out of the loop) and after that I got it right. Great rush!

Anyone got some more nasty ones on top of their heads?

Title: Riddle thread
Post by: LORd on December 17, 2007, 02:19:36 pm

rant (Click to reveal)

Man, I hate it when the challenge of the riddle comes from finding out the restriction they didn't specify. After voiding our islanders of such human properties as creativity, vocal discourse, mundane vision and civilized tools, we're supposed to consider they also have the patience and memory to pull off a hundred-day trial-and-error process?

But I'm probably just making excuses because I failed to lend enough credence to the element of time in the riddle :(
(though still I'd bet I'd have gotten it correct were it worded just "consider a set of 200 elements, 100 of which possess the property A and the rest property B yadda yadda yadda.)

Title: Riddle thread
Post by: xanque on December 17, 2007, 04:36:26 pm

Hidden content (Click to reveal)

The solution makes less and less sense the more I think about it.  If there were ten people, five with brown eyes, five with blue, and someone said "I see someone with blue eyes," it doesn't help them at all.  Five of the green eyed people would know that already, and so would four of the blue eyed people. 

But if the people don't know what color eyes they have, the blue eyed people can't all of the sudden just realize after five days "Hey, the other four blue eyed people haven't left, so I must be one of them!"  None of the others know their own eye color, because they haven't had any means of figuring it out.  So why would they assume that they themselves had blue eyes?

And what about the brown eyed people?  Why wouldn't they assume that they had blue eyes if they saw that all these blue eyed people weren't leaving?  Where do they come into play here?

Title: Riddle thread
Post by: Lifexplosion on December 17, 2007, 04:56:42 pm

The batman movie had fantastic riddles!! here is my favourite

Commissioner Gordon: What weighs six ounces, sits in a tree and is very dangerous?
Robin: A sparrow with a machine gun!
Commissioner Gordon: Yes, of course

 :incred:

Title: Riddle thread
Post by: kentona on December 17, 2007, 05:04:42 pm

spoilerz (Click to reveal)

Consider the situation if there were only 2 people with blue eyes. Everybody can see everybody else, and everybody already knew that the Guru could see someone with blue eyes. However, Blue-1 didn*t know that Blue-2 could see someone with blue eyes. After the Guru has spoken, Blue-1 still doesn*t know whether Blue-2 can see someone with blue eyes, so it might appear that no new information has been imparted. However, when midnight comes round, the fact that Blue-2 is still on the island imparts new information to Blue-1 - it tells him that Blue-2 must be able to see someone with blue eyes. This new information is enough to allow Blue-1 to work out that it must be his own eyes that are blue. Blue-2 reasons in a similar way. Therefore the two blue-eyed people leave on day 2.

Now consider the situation if there were 3 people with blue eyes. Blue-3 can work out the logic in the previous scenario, and expects Blue-1 and Blue-2 to depart on day 2. The fact that they don*t leave on day 2 imparts new information to Blue-3 - it tells her that Blue-1 and Blue-2 can each see more than one person with blue eyes. This new information is enough to allow Blue-3 to work out that it must be her own eyes that are blue. Therefore the three blue-eyed people leave on day 3.

The same reasoning can be extended to the situation where there are 3, 4, 5, 6,... 100 people with blue eyes. Since they all argue perfectly logically, they can work out that N blue-eyed people will leave on day N.

This is from Yahoo! Answers.

Best riddle:
"What have I got in my pocket?"

Title: Riddle thread
Post by: LORd on December 17, 2007, 05:35:23 pm

Quote from: Xanqui on December 17, 2007, 04:36:26 pm

Hidden content (Click to reveal)

The solution makes less and less sense the more I think about it.  If there were ten people, five with brown eyes, five with blue, and someone said "I see someone with blue eyes," it doesn't help them at all.  Five of the green eyed people would know that already, and so would four of the blue eyed people. 

But if the people don't know what color eyes they have, the blue eyed people can't all of the sudden just realize after five days "Hey, the other four blue eyed people haven't left, so I must be one of them!"  None of the others know their own eye color, because they haven't had any means of figuring it out.  So why would they assume that they themselves had blue eyes?

And what about the brown eyed people?  Why wouldn't they assume that they had blue eyes if they saw that all these blue eyed people weren't leaving?  Where do they come into play here?

Hidden content (Click to reveal)

I can't wrap my head around how the guru's statement suddenly spurs them into action either, but the reason the brown-eyed people don't play a part is because they always require one more iteration: if there are n blue-eyed people, brown-eyed people see them all, but the blue-eyed people can only see n-1 people with blue eyes, hence reducing the trial-and-error process by one day.

Suppose that there was only one blue-eyed person. When the guru says that he sees at least one blue-eyed person, each of the brown-eyed people considers that he, too, has blue eyes, but since the blue-eyed man knows he's the only one he's gone the following day and the brown-eyed people give up. With two blue-eyed people, they both see that the other has waited a day, and since no other blue-eyed people are around they know they both have blue eyes. Brown-eyed people still need to know whether or not they happen to be the lucky third one, but alas, the two are gone the following morning.

Title: Riddle thread
Post by: xanque on December 17, 2007, 08:19:14 pm

Quote from: LORd on December 17, 2007, 05:35:23 pm

Hidden content (Click to reveal)

I can't wrap my head around how the guru's statement suddenly spurs them into action either, but the reason the brown-eyed people don't play a part is because they always require one more iteration: if there are n blue-eyed people, brown-eyed people see them all, but the blue-eyed people can only see n-1 people with blue eyes, hence reducing the trial-and-error process by one day.

Suppose that there was only one blue-eyed person. When the guru says that he sees at least one blue-eyed person, each of the brown-eyed people considers that he, too, has blue eyes, but since the blue-eyed man knows he's the only one he's gone the following day and the brown-eyed people give up. With two blue-eyed people, they both see that the other has waited a day, and since no other blue-eyed people are around they know they both have blue eyes. Brown-eyed people still need to know whether or not they happen to be the lucky third one, but alas, the two are gone the following morning.

Okay, most of that makes sense, but nobody knows how many blue eyed or brown eyed people there are.  Brown eyed people can only know that there is either 100 or 101 blue eyed people, but blue eyed people can only know there are 99 or 100 blue eyed people.  They can't know definitively without knowing their own eye color. 

Hidden content (Click to reveal)

And with each passing day, no one is learning their own eye color.  So why on the 100th day would anything change?  Let's look at the situation with five people; 2 blues, 2 browns, and the guru.  The guru says "I see someone with blue eyes."  One person with blue eyes will see that there are two people with brown eyes, and one person with blue eyes.  Here's what each person can deduce from that:

Brown eyed people:
There are:
2 blue eyed people
1 brown eyed person
1 unknown

Blue eyed people:
There are:
2 brown eyed people
1 blue eyed person
1 unknown

Why would anything change the following day?  There's a HUGE leap of logic to think that since the other person has blue eyes and hasn't left, that they can leave the next day.  The other blue eyed person doesn't know that he has blue eyes, which is why he didn't leave in the first place.

Title: Riddle thread
Post by: AdderallApocalypse on December 17, 2007, 08:38:11 pm

Quote from: Xanqui on December 17, 2007, 08:19:14 pm

Why would anything change the following day?  There's a HUGE leap of logic to think that since the other person has blue eyes and hasn't left, that they can leave the next day.  The other blue eyed person doesn't know that he has blue eyes, which is why he didn't leave in the first place.

Hidden content (Click to reveal)

Here is what I think (Click to reveal)

I can see how it works for TWO blue eyed people. The guru says that she sees someone with blue eyes. Let's look at this from the perspective of one of those blue eyed people. He sees the next day that the other blue eyed person is still around, so he infers that he must see someone with blue eyes. If he didn't, then he'd see all brown eyes and deduce from that, that he is the only blue eyed. He doesn't leave since like I said, as far as he knows the guru is speaking of the other blue eyed person. So, due to the fact the one blue eyed didn't leave, the other one does. The other knows to leave next because the other one had to wait past the first night to leave which meant that he himself has blue eyes. See, it seems to get flawed past two people. Say you had 5 blue eyed people, how would any of them know to leave. Sure the others are there but that doesn't say anything since they could of seen any given one of the other blue eyed which they already knew they were blue eyed anyhow just by looking at them. I am really lost.  :fogetgrr:​

Title: Riddle thread
Post by: kentona on December 17, 2007, 09:04:52 pm

Xanqui, did you read my post?  it explains that 100 people leave on the 100th day.  New information is imparted every time midnight rolls around and another blue eyed person doesn't leave.  Say I'm a blue eyed guy.  Once 99 nights pass and 99 blue eyed people that I see hasn't left, that means that those 99 other blue eyes see one more person with blue eyes!  Thus it must be me!  We all realize this at the same time thus we all leave the next night, on the 100th day

Title: Riddle thread
Post by: Frisky SKeleton on December 17, 2007, 09:42:03 pm

the guru leaves, she's not allowed to talk

Title: Riddle thread
Post by: AdderallApocalypse on December 17, 2007, 09:58:33 pm

I have a solution. At 11:55, everyone rips their eyeball out and looks at the color and leaves on the ferry at 12:00, and while on it they get help from doctors.

Title: Riddle thread
Post by: xanque on December 17, 2007, 10:22:38 pm

Oh!  I get it now!  Thanks Omcifer and Kentona. 

The reasoning behind everything is still a bit shaky, and I'm still not sure why what the guru says makes any difference.  There must be something in it that I'm just not getting. 

Title: Riddle thread
Post by: kentona on December 17, 2007, 10:32:10 pm

Quote from: Omcifer on December 17, 2007, 09:58:33 pm

I have a solution. At 11:55, everyone rips their eyeball out and looks at the color and leaves on the ferry at 12:00, and while on it they get help from doctors.

It appears that this version of the riddle is missing the "No Mutilation" requirement...

Quote from: Xanqui on December 17, 2007, 10:22:38 pm

Oh!  I get it now!  Thanks Omcifer and Kentona. 

The reasoning behind everything is still a bit shaky, and I'm still not sure why what the guru says makes any difference.  There must be something in it that I'm just not getting. 

It's a critical element because...after 99 days, 99 blue eyed people still havn't left, and the Guru said I see someone with blue eyes.  Those 99 other people are still unsure what their eye color is.  After the 99th midnight rolls around and still no one leaves, the people realise that there must be 100 blue eyed people (since there are only 200 people, and 100 are brown eyed, and there are 99 blue eyed, leaving just 1 person left, who now knows that they have blue eyes because after 99 nights none of the blue eyes left and the Guru said I see someone with blue eyes and the other 99 didn't leave and thay just leaves themselves having blue eyes!  All 100 blue eyes figure this out at once at the same time, because from their perspective they all see the other 99 blue eyes and they themselves are the ones that are unsure.

Holy crap I'm bad at explaining things...

Title: Riddle thread
Post by: AdderallApocalypse on December 17, 2007, 10:40:39 pm

Quote from: Xanqui on December 17, 2007, 10:22:38 pm

Oh!  I get it now!  Thanks Omcifer and Kentona. 

The reasoning behind everything is still a bit shaky, and I'm still not sure why what the guru says makes any difference.  There must be something in it that I'm just not getting. 

Hidden content (Click to reveal)

Well, let's look at it this way. Say she did not say the statement and the next day, would the one blue eyed guy deduce the same logic and think that there must be another blue eyed person? No, but why not? It lies in the head of one or each of the blue eyed people. Here is what they are thinking after her statement.

Blue eyed person: "Hmmm since the other person has not left, then that must mean someone else with blue eyes is on the island, it must be me since I don't see anyone else!"

Now suppose she didn't say anything: "I see a blue eyed person here"

Now since he is still here then her statement now gives some valuable insight into the mind of one of the blue eyes and into the other's.
He knows that the other one knows there is more than one blue eyed because he knows he that the other knows that there aren't 101 brown eyed, one of the people in his observation field HAS blue eyes which must be him.

I know it sounds confusing, but hopefully you will get it soon.

EDIT: You know, maybe the guru DIDN'T have to say that after all. Either way hopefully you get the basic gist of it all
EDIT2: Well, maybe it does. However I think it only matters after that first midnight.

Better explanation (Click to reveal)

Ok I thought this out, I still don't know how it is possible with 3+ people, though. The second day when one blue eyed sees the other one there, this is what he is thinking.

"I see that blue eyed guy is still here. If he saw nothing but brown eyes, then he would of left last night because of the guru's statement. The statement would of told him that he was blue eyed if he saw no blue eyes. However he must see other blue eyes because he is still here, but I don't observe any blue eyes. Hmmm....well then it must be me!"

Now this logic and knowledge is mutual, thus they both leave on the second night.

Title: Riddle thread
Post by: Randy Moist on December 18, 2007, 10:08:56 am

The importance of the guru

Hidden content (Click to reveal)

The gurus words give insight into the other persons eye color. Pretend there is only 1 blue eyed person on the island. He is unaware he has blue eyes until the guru says "I see someone with blue eyes" and he realizes "Hey no one else has blue eyes." The same holds true then for 2 people. Person A and B have blue eyes. A and B know that there are 100 number of brown eyed people and at least 1 blue eyed person, the one opposite themselves. They can't use the logical solution of the riddle until the guru says "I see a person with blue eyes." Before this A may have counted 100 browns and 1 blue but he may have had red eyes. Person A knows that when the guru provides the statement, that if person B was the blue eyed person on the island, he would now be aware of it. Without the words, Person A could not be aware of what person B is aware of because he neither knows their own color.
This makes sense to me but I might be able to give a better explanation. The guru is necessary though.

Title: Riddle thread
Post by: Frankie on December 18, 2007, 01:45:58 pm

Quote from: bloodbath on December 18, 2007, 10:08:56 am

The importance of the guru

Hidden content (Click to reveal)

The gurus words give insight into the other persons eye color. Pretend there is only 1 blue eyed person on the island. He is unaware he has blue eyes until the guru says "I see someone with blue eyes" and he realizes "Hey no one else has blue eyes." The same holds true then for 2 people. Person A and B have blue eyes. A and B know that there are 100 number of brown eyed people and at least 1 blue eyed person, the one opposite themselves. They can't use the logical solution of the riddle until the guru says "I see a person with blue eyes." Before this A may have counted 100 browns and 1 blue but he may have had red eyes. Person A knows that when the guru provides the statement, that if person B was the blue eyed person on the island, he would now be aware of it. Without the words, Person A could not be aware of what person B is aware of because he neither knows their own color.[/spoiler]
This makes sense to me but I might be able to give a better explanation. The guru is necessary though.

Hidden content (Click to reveal)

My problem with this is that as soon as there is more than 2 people with blue eyes, this no longer holds up, because no matter whether you have blue eyes or not, you are sure that every other person with blue eyes can see one other blue-eyed person (since you yourself see at least two blue-eyed island dwellers, so no matter whether or not you yourself have blue eyes, you know that all other blue-eyeds see at least one other). I see the logic when there is one or two people with blue eyes, but it seems like it no longer works with three or more.

Title: Riddle thread
Post by: Bisse on December 18, 2007, 02:41:38 pm

Quote from: Psychoskull on December 18, 2007, 01:45:58 pm

Hidden content (Click to reveal)

My problem with this is that as soon as there is more than 2 people with blue eyes, this no longer holds up, because no matter whether you have blue eyes or not, you are sure that every other person with blue eyes can see one other blue-eyed person (since you yourself see at least two blue-eyed island dwellers, so no matter whether or not you yourself have blue eyes, you know that all other blue-eyeds see at least one other). I see the logic when there is one or two people with blue eyes, but it seems like it no longer works with three or more.

Hidden content (Click to reveal)

Think of the case with three people. Each one of the blue eyed's sees two other blue-eyed. As far as they know there are only two other blue-eyed people here, and as far as they know, each of these two blue-eyed people only sees one blue-eyed person. Since they're perfect logicians they know how the other ones would think, and when they don't leave on the second day, it can only be because there's a third blue-eyed person - me.
  To put it in mathematical style, each person in this case views a system of two blue-eyed persons. When the system doesn't work, it's must be because the other two blue-eyed ones are not seeing the system you are seeing - you're watching two of 'em, if there was only two, each of them would only see one. But they don't, so there must be more people. and there can only be one more, you.

Now think of the case with four people - the fourth person is viewing a system of three people. When they don't leave on the third they, it's because, in the same way, there must be more than three people. With five people, if the four other people don't leave on the fourth day, there must be five people. And so on - with N people, if the other N-1 people don't leave on the N-1'th day, there must be N people.

Title: Riddle thread
Post by: Frankie on December 18, 2007, 06:01:00 pm

Quote from: Bisse on December 18, 2007, 02:41:38 pm

Hidden content (Click to reveal)

Think of the case with three people. Each one of the blue eyed's sees two other blue-eyed. As far as they know there are only two other blue-eyed people here, and as far as they know, each of these two blue-eyed people only sees one blue-eyed person. Since they're perfect logicians they know how the other ones would think, and when they don't leave on the second day, it can only be because there's a third blue-eyed person - me.
  To put it in mathematical style, each person in this case views a system of two blue-eyed persons. When the system doesn't work, it's must be because the other two blue-eyed ones are not seeing the system you are seeing - you're watching two of 'em, if there was only two, each of them would only see one. But they don't, so there must be more people. and there can only be one more, you.

Now think of the case with four people - the fourth person is viewing a system of three people. When they don't leave on the third they, it's because, in the same way, there must be more than three people. With five people, if the four other people don't leave on the fourth day, there must be five people. And so on - with N people, if the other N-1 people don't leave on the N-1'th day, there must be N people.

Hidden content (Click to reveal)

We know that, we are not debating the solution, but rather the usefulness of the guru's revelation when there is at least three blue-eyed people. We know it still works with three or more people, but not if the gurus' revelation stays useful to the island dwellers.

Title: Riddle thread
Post by: Randy Moist on December 18, 2007, 08:24:15 pm

Hidden content (Click to reveal)

Yea I realize now that it doesn't make sense over 3 people. I had another question, are the brown eyed people even necessary?

Title: Riddle thread
Post by: Frisky SKeleton on December 18, 2007, 11:38:04 pm

Hidden content (Click to reveal)

No, they should go back to africa.
i still hold that the guru should get kicked off for talking and breaking the rules[/spoiler]

Title: Riddle thread
Post by: Bisse on December 19, 2007, 01:45:16 am

Quote from: Psychoskull on December 18, 2007, 06:01:00 pm

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We know that, we are not debating the solution, but rather the usefulness of the guru's revelation when there is at least three blue-eyed people. We know it still works with three or more people, but not if the gurus' revelation stays useful to the island dwellers.

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He gives them a piece of information they don't already know. I don't know what it is though. I'm thinking, if N is the number of blue-eyed people, then he's basically saying N >= 1.

Just now a few keypressed back though I realised he gives each person a chance to identify their own eye color. For every individual he is introducing a possibility that the individual can have blue eyes. If he said it to just one guy it would only help him, but when he says it to everyone [math time] he gives everyone a basis to evaluate a theorem about themselves on. So he gives everyone a specific bit of information. I'm thinking he's saying the possiblity for each individual being blue-eyed is 1/201.

I don't really have a goddamn clue exactly what he gives them though. But he gives them some piece of information they don't already know. Only things I can think of is N >= 1 and a possibility of 1/201 of being blue and the first one they already know (they can see 99 or 100 people which is > 1)  so i'm guessing it's the probability thing.

Title: Riddle thread
Post by: EvilDemonCreature on December 19, 2007, 03:13:59 am

Guru's relevance(?):

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I think it's not what the guru says that gives the information, but the context in which it was said. That is, the guru gave everyone the "same" information, causing them to synchronize their own logical deductions. That is, the guru told each person something they already knew, but the guru inadvertently told them how every other person is going to behave. From the guru's cue, the person can now watch as the other people make their deductions. This would have to be under the assumption that the people already knew that every other person participating was a perfect logician aswell.

If it's kinda hard to wrap your head around, think about it from the point of view of one blue eyed person. Now, he sees 99 other blue eyed people, so he's got two options, there are either 99 blue eyed people, or there are 100 blue eyed people and he's one of them. If there are 99 blue eyed people, then he can watch one of them (in lieu of the fact they all behave the same, I'm singling one out to simplify the train of thought) and figure out if he realises there is 98 people or if there are 99 people and he's one of them. Now the 100th blue eyed person knows that 98 people being there is impossible, so if the person doesn't see from his perspective the answer by the 99th day, it can only be because there are 100 blue eyed people and he is one of them (and the person he was watching is really waiting 99 days to discover this himself). That is, the person has two possible answers for wether or not he has blue eyes, and the validity of either one is based on the total number of blue eyed people. The only one that can deduce that is another blue-eyed person, and can only communicate it by leaving on the logically correct day based on his own perspective, which is the only peice of information that the initial person has access to. This means the relevance of the guru must be he incites the behavior that gurantees the needed information is given at a certain day.

I don't know if that cleared anything up, but I tried.

Title: Riddle thread
Post by: Five Little Blah on December 19, 2007, 08:05:39 am

Correct answer:

They wouldn't leave...

Chuck Norris wouldn't let them.

Title: Riddle thread
Post by: Roman on December 19, 2007, 08:15:24 am

this was a stupid fucking riddle

Title: Riddle thread
Post by: Grin Tree on December 19, 2007, 12:08:12 pm

Quote from: Five Little Blah on December 19, 2007, 08:05:39 am

Correct answer:

They wouldn't leave...

Chuck Norris wouldn't let them.

We could do without that. 




Someone post up a new riddle, I didn't even want to bother with this one--the solution just seemed ridiculous to me.  As Xanqui said, it wasn't a riddle with a clever solution/answer, it was more like "I see...well then."

Title: Riddle thread
Post by: kentona on December 19, 2007, 03:37:33 pm

Quote from: Grin Tree on December 19, 2007, 12:08:12 pm

Someone post up a new riddle, I didn't even want to bother with this one--the solution just seemed ridiculous to me.  As Xanqui said, it wasn't a riddle with a clever solution/answer, it was more like "I see...well then."

What's green and fuzzy and if it fell out of a tree onto you it could kill you?

Title: Riddle thread
Post by: Cheshire Cat on December 19, 2007, 03:56:44 pm

When is a door not a door?

Kentona:
a snooker table

Title: Riddle thread
Post by: xanque on December 19, 2007, 06:06:54 pm

Quote from: Cheshire Cat on December 19, 2007, 03:56:44 pm

When is a door not a door?

When it's ajar

Title: Riddle thread
Post by: AdderallApocalypse on December 20, 2007, 12:02:36 am

Quote from: kentona on December 19, 2007, 03:37:33 pm

What's green and fuzzy and if it fell out of a tree onto you it could kill you?

A pool table.

Title: Riddle thread
Post by: alphasmart on December 21, 2007, 07:56:05 pm

hmm...how's about:

I like food but I don't like drinks
I like cheese but I don't like crackers
I like boobs but I don't like breasts
I like little things but I don't like big things

Assuming you're into the same kinds of things as me, what are your preferences?

Title: Riddle thread
Post by: AdderallApocalypse on December 21, 2007, 11:08:49 pm

Quote from: alphasmart on December 21, 2007, 07:56:05 pm

hmm...how's about:

I like food but I don't like drinks
I like cheese but I don't like crackers
I like boobs but I don't like breasts
I like little things but I don't like big things

Assuming you're into the same kinds of things as me, what are your preferences?

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Words with two of the same adjacent letters?