cRPG

Off Topic => General Off Topic => Topic started by: Vibe on March 28, 2012, 12:46:26 pm

Title: A logic puzzle
Post by: Vibe on March 28, 2012, 12:46:26 pm
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."


(Those who know the answer shut yo trap)
Title: Re: A logic puzzle
Post by: Mr. Hannibal on March 28, 2012, 12:56:51 pm
Who put so many poor,helpless scientists on a Island?

Oh,and can they poke 1 eye out and then see what's the color?
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 12:57:44 pm
Who put so many poor,helpless scientists on a Island?

Oh,and can they poke 1 eye out and then see what's the color?

No poking allowed.
Title: Re: A logic puzzle
Post by: Mr. Hannibal on March 28, 2012, 12:58:28 pm
No poking allowed.

Ok,i will shut mah trap :/
Title: Re: A logic puzzle
Post by: Stabby_Dave on March 28, 2012, 01:17:48 pm
The Guru leaves?
Title: Re: A logic puzzle
Post by: Bazinga on March 28, 2012, 02:32:03 pm
The Guru leaves?

Don't think so, he don't know his own eye colour, does he?

I guess no brown coloured people will ever leave this island, because they don't have any clue what eye colour they might have.
Title: Re: A logic puzzle
Post by: Stabby_Dave on March 28, 2012, 02:33:43 pm
Well that certainly is a pickle vibe.
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 02:41:44 pm
Guru does not leave. And yes, it's a huge pickle  :idea:
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 02:50:47 pm
how is it possible to figure out on which night?

It is possible, but far from easy. :mrgreen:

Clue in "Every night at midnight, a ferry stops at the island."
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 02:57:32 pm
Yeah, I know that this sentence is important, but I´m to stupid for it anyway  :mrgreen:

Well if it comforts you I didn't solve the puzzle either. Neither did any of my friends or anyone I know. We weren't even close :D
Title: Re: A logic puzzle
Post by: Stabby_Dave on March 28, 2012, 03:00:04 pm
Well really, what the guru says isnt important at all because it doesnt add any information all the islanders dont already know since they can all see that there is at least 1 blue eyed person.

Can the islanders just wait until all the blue eyed people except 1 die from old age then

Wait until all but 2 of the blue eyed people die from old age. When blue eyed person 1 (BE1) sees that BE2 hasnt decided to leave, BE1 must conclude that he also has blue eyes and so he leaves.  :P

Not the right answer and I dont have a clue what night its on but I like it.
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 03:03:27 pm
Well really, what the guru says isnt important at all because it doesnt add any information all the islanders dont already know since they can all see that there is at least 1 blue eyed person.

What kind of information the guru adds by saying "I see one with blue eyes" is as mind-boggling as the puzzle itself.
Title: Re: A logic puzzle
Post by: Tomas_of_Miles on March 28, 2012, 03:17:24 pm
100 nights and then they all get on the boat?
Title: Re: A logic puzzle
Post by: Christo on March 28, 2012, 03:18:10 pm
Well, if they are on an island.. why don't they go and check it in the water for crying out loud.

I know you said no reflective surfaces but it's common sense. o.O
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 03:19:41 pm
100 nights and then they all get on the boat?

Close, but not it. Was it a wild guess?
Title: Re: A logic puzzle
Post by: [ptx] on March 28, 2012, 03:21:22 pm
Alright, how about this - everyone leaves on the first night.

(click to show/hide)
Title: Re: A logic puzzle
Post by: Tomas_of_Miles on March 28, 2012, 03:22:56 pm
I am tired but still intrigued by this puzzle. I tried to follow up logic and then I gave up. I think I missed it by one night.
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 03:25:21 pm
I am tired but still intrigued by this puzzle. I tried to follow up logic and then I gave up. I think I missed it by one night.

You also missed who leaves, so I think you might be going in the wrong direction anyway :)
Title: Re: A logic puzzle
Post by: ThePoopy on March 28, 2012, 03:26:18 pm
the ferry leaves every night
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 03:27:33 pm
the ferry leaves every night

Yes it does. But that's obvious from the instructions :)
Title: Re: A logic puzzle
Post by: Stabby_Dave on March 28, 2012, 03:34:49 pm
100 nights and then they all get on the boat?

Why 100 nights?
Title: Re: A logic puzzle
Post by: ThePoopy on March 28, 2012, 03:40:38 pm
http://translationparty.com/#10135265
"Trick question is the logical answer"
Title: Re: A logic puzzle
Post by: Meow on March 28, 2012, 04:19:46 pm
Alright, how about this - everyone leaves on the first night.

Midnight = no...colours?

... 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) ...

So your solution only works if you ignore that they actually have to figure out their own eye color to leave and that everyone can see everyone else's eye color at all times.


I would agree though that they will all leave during the first night since: "They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly."

Except if the solution needs some kind of system that takes multiple nights to complete :mrgreen:
Title: Re: A logic puzzle
Post by: Earthdforce on March 28, 2012, 04:26:14 pm
...wouldn't the ferries windows be reflective? If so, doesn't that mean anyone who walks up to it would see their own eye color? Seems too nitpicky to be the answer though.
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 04:55:08 pm
...wouldn't the ferries windows be reflective? If so, doesn't that mean anyone who walks up to it would see their own eye color? Seems too nitpicky to be the answer though.

There are no mirrors or reflecting surfaces
Title: Re: A logic puzzle
Post by: Tomas on March 28, 2012, 05:38:20 pm
All the people with Blue eyes leave on the 100th night?
Title: Re: A logic puzzle
Post by: ThePoopy on March 28, 2012, 05:41:04 pm
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:
Title: Re: A logic puzzle
Post by: Teeth on March 28, 2012, 05:43:06 pm
Ask the ferryman?

Can not get anything logic outta this. Not the night and not the people who leave. Maybe those blue eyes the Guru sees are something cosmic that is only visible on a certain night, but she said that during noon, and I doubt a puzzle would expect people to know something like that.

Are you sure the answer is something logically deductable?
Clue in "Every night at midnight, a ferry stops at the island."
This makes me fear its going to be something really stupid and then I'm going to be pissed.

No guessing own eye colours? If I could count 99 blue eyes and 100 brown eyes I would go for blue.
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 05:45:58 pm
Ask the ferryman?

Can not get anything logic outta this. Not the night and not the people who leave. Maybe those blue eyes the Guru sees are something cosmic that is only visible on a certain night, but she said that during noon, and I doubt a puzzle would expect people to know something like that.

Are you sure the answer is something logically deductable? This makes me fear its going to be something really stupid and then I'm going to be pissed.

No guessing own eye colours? If I could count 99 blue eyes and 100 brown eyes I would go for blue.

That's guessing.

That "clue" was just to show that that helps you solve how many days. It's not that helpful.


All the people with Blue eyes leave on the 100th night?

Bravo Tomas :)

Did you come by this yourself or did you have help? Or was it just a lucky guess?
 If you did this by yourself, please share how :)
Title: Re: A logic puzzle
Post by: Tomas on March 28, 2012, 05:59:33 pm
Err - this could get a little convoluted but i'll try and explian my logic - hopefully it is correct and i didn't just get lucky :D


- Imagine I am a blue eyed person on the Island
- I can see 99 people with blue eyes, 101 with brown eyes and 1 with green eyes
- There are therefore either 99 Blue eyed people or there are 100, depending on my own eye colour.
- Since the Blue eyed people didn't leave on the 99th night, then those 99 people must still not have been sure that they were blue eyed themselves which means I must have been confusuing them
- Therefore on the 100th night, I will know I have blue eyes for certain since there can't be 101 of us, so I will leave along with all the other blue eyed people who realise the same thing at the same time

Title: Re: A logic puzzle
Post by: [ptx] on March 28, 2012, 06:02:45 pm
So your solution only works if you ignore that they actually have to figure out their own eye color to leave and that everyone can see everyone else's eye color at all times.


I would agree though that they will all leave during the first night since: "They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly."

Except if the solution needs some kind of system that takes multiple nights to complete :mrgreen:
Let me help you to a bit of colour (http://en.wikipedia.org/wiki/Colour)

In any case, me and Vibe already agreed that i made a sort of a "trick answer", since it renders most of the given information as irrelevant and that it should be made clear that it is their eye colour during day time that they need to figure out or some such.
Title: Re: A logic puzzle
Post by: Overdriven on March 28, 2012, 06:02:59 pm
That makes no sense to me  :|
Title: Re: A logic puzzle
Post by: Tomas on March 28, 2012, 06:05:47 pm
That makes no sense to me  :|

I said it was convoluted :D
Title: Re: A logic puzzle
Post by: Meow on March 28, 2012, 06:09:34 pm
Let me help you to a bit of colour (http://en.wikipedia.org/wiki/Colour)

In any case, me and Vibe already agreed that i made a sort of a "trick answer", since it renders most of the given information as irrelevant and that it should be made clear that it is their eye colour during day time that they need to figure out or some such.

Sounds like you just keep refusing to accept that your answer is plain wrong according to the rules stated in the first paragraph but yeah, now I know a lot more about colors :mrgreen:
Title: Re: A logic puzzle
Post by: SixThumbs on March 28, 2012, 06:25:02 pm
Let's get to the real problem at hand and that's that after the 101st night the guru is going to be very lonely.
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 06:44:02 pm
Let's get to the real problem at hand and that's that after the 101st night the guru is going to be very lonely.

But there's also brown eyed people on the island.
Title: Re: A logic puzzle
Post by: Kafein on March 28, 2012, 06:48:25 pm
This seems interesting to share :

Let's say N is the number of blue and brown eyed people (there are N blue, N brown and 1 guru).

Case N=1 is trivial. The blue leaves after the guru speech.

Case N=2 is simple. Let's say there's A blue and B blue. A knows that B knows A's color. Therefore if B does not leave the first day, that means that B could not conclude anything from what the guru said, which means A is blue. B does the same and both leave the 2nd day.

Case N=3 is equivalent to N=100, but easier to understand.

Let's say we have A,B and C blue. A knows that both B and C are blue, and that they know A's color and the other one's color, which is blue.

That means that A knows that from the point of view of B and C, there is always at least one other blue which is not A. In other words, B will see C is blue, and C will see B is blue. Everybody sees at least one blue, and that is for certain with only the information that one blue person has. It's the same from the perspective of a brown.

Therefore what the guru says will never have an impact on what they know, since it doesn't change their own direct knowledge, nor what they know of what the others see.
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 06:55:13 pm
Err - this could get a little convoluted but i'll try and explian my logic - hopefully it is correct and i didn't just get lucky :D


- Imagine I am a blue eyed person on the Island
- I can see 99 people with blue eyes, 101 with brown eyes and 1 with green eyes
- There are therefore either 99 Blue eyed people or there are 100, depending on my own eye colour.
- Since the Blue eyed people didn't leave on the 99th night, then those 99 people must still not have been sure that they were blue eyed themselves which means I must have been confusuing them
- Therefore on the 100th night, I will know I have blue eyes for certain since there can't be 101 of us, so I will leave along with all the other blue eyed people who realise the same thing at the same time

You're thinking in the right direction Tomas.

BUT there can be 101 blue eyes.

There can be 101 blue, 99 brown.
There can be 99 blue, 101 brown.
Or there can be 100 blue and 100 brown.

----------------

Kafein pretty much told you the solution. Did you come this by yourself Kafein?
Title: Re: A logic puzzle
Post by: Teeth on March 28, 2012, 06:57:11 pm
It makes so much sense for two people with blue eyes. Person 1 and person 2 know that there is 1 person with blue eyes. If after the first night 1 sees that 2 hasn't left, 1 knows that 2 wasn't sure because 1 himself must have blue eyes. Same thing the other way around.

I get how that works. But I don't understand how the 100 people find out their eye color after 100 days, when there is no new information at all since day 1.

Let's say there are 3 persons. You know the two others have blue eyes and you are unsure if you have blue eyes. Its the same for them. Then after one night, nobody will have left. That confirms that there are not one but two people with blue eyes. You already knew that.

So when comparing day 2 and day 3, there is no new information. Why do you know your eye color in night 3 and not at night 2, when nothing changed and there was no new information?

Oh yeah, and what Kafein said, the Guru seems quite the useless bitch. Kafein didnt tell the solution, he only described what every person in a 3 person situation sees. There is my problem, three people have the same thing where they are not sure about. Seems to be that from n > 2 there is no one leaving.
Title: Re: A logic puzzle
Post by: Vibe on March 28, 2012, 07:02:27 pm
Here's the full solution for better understanding:

The answer is that on the 100th day, all 100 blue-eyed people will leave.

If you consider the case of just one blue-eyed person on the island, you can show that he obviously leaves the first night, because he knows he's the only one the Guru could be talking about. He looks around and sees no one else, and knows he should leave. So: [THEOREM 1] If there is one blue-eyed person, he leaves the first night.

If there are two blue-eyed people, they will each look at the other. They will each realize that "if I don't have blue eyes [HYPOTHESIS 1], then that guy is the only blue-eyed person. And if he's the only person, by THEOREM 1 he will leave tonight." They each wait and see, and when neither of them leave the first night, each realizes "My HYPOTHESIS 1 was incorrect. I must have blue eyes." And each leaves the second night.

So: [THEOREM 2]: If there are two blue-eyed people on the island, they will each leave the 2nd night.

If there are three blue-eyed people, each one will look at the other two and go through a process similar to the one above. Each considers the two possibilities -- "I have blue eyes" or "I don't have blue eyes." He will know that if he doesn't have blue eyes, there are only two blue-eyed people on the island -- the two he sees. So he can wait two nights, and if no one leaves, he knows he must have blue eyes -- THEOREM 2 says that if he didn't, the other guys would have left. When he sees that they didn't, he knows his eyes are blue. All three of them are doing this same process, so they all figure it out on day 3 and leave.

This induction can continue all the way up to THEOREM 99, which each person on the island in the problem will of course know immediately. Then they'll each wait 99 days, see that the rest of the group hasn't gone anywhere, and on the 100th night, they all leave.


Stolen from xkcd.
Title: Re: A logic puzzle
Post by: Kafein on March 28, 2012, 07:10:42 pm
(warning : solution)

(click to show/hide)

Title: Re: A logic puzzle
Post by: Kafein on March 28, 2012, 07:12:35 pm
Damn you vibe, I swear I got it from my own reasoning. Yet I think I wouldn't have found without teeth :

Then after one night, nobody will have left. That confirms that there are not one but two people with blue eyes.
Title: Re: A logic puzzle
Post by: Teeth on March 28, 2012, 07:15:37 pm
Okay I get it, fucking hurts my brain though.

Now I wonder, does the puzzle work without the Guru? If there is no one revealing that there is atleast 1 person with blue eyes, Theorem 1 is false. Theorem 2 is still correct though. Theorem 99 is still correct too. Do you need Theorem 1 to formulate Theorem 2 and up? I don't think you really do, please correct me if I'm wrong. Would make this puzzle even more puzzling.

Gash, its so fucking retarded, 100 blue eyed people need to wait 99 nights to get confirmed that there are not 99 people with blue eyes, but a 100. They all know no one is going to leave up until the 98th night, still they have to wait 98 nights to see what happens in the 99th night. It's really weird, but its still correct.

Damn you vibe, I swear I got it from my own reasoning. Yet I think I wouldn't have found without teeth :

Lol, I stated the obvious information that in the case of N amount of blue eyed people, every blue eyed person always knows for sure that there are N-1 amount of blue people on the island. Because everyone is only unsure about their own color. I'm sure you already thought of that without me as its kinda required to get anywhere.
Title: Re: A logic puzzle
Post by: Kafein on March 28, 2012, 07:29:45 pm
Okay I get it, fucking hurts my brain though.

Now I wonder, does the puzzle work without the Guru? If there is no one revealing that there is atleast 1 person with blue eyes, Theorem 1 is false. Theorem 2 is still correct though. Theorem 99 is still correct too. Do you need Theorem 1 to formulate Theorem 2 and up? I don't think you really do, please correct me if I'm wrong. Would make this puzzle even more puzzling.

Gash, its so fucking retarded, 100 blue eyed people need to wait 99 nights to get confirmed that there are not 99 people with blue eyes, but a 100. They all know no one is going to leave up until the 98th night, still they have to wait 98 nights to see what happens in the 99th night. It's really weird, but its still correct.
Lol, I stated the obvious information that in the case of N amount of blue eyed people, every blue eyed person always knows for sure that there are N-1 amount of blue people on the island. Because everyone is only unsure about their own color. I'm sure you already thought of that without me as its kinda required to get anywhere.

Well it sort of pointed out what I knew but what I was forgetting. Made me think that B and C in N=3 are exactly like A and B in N=2, if the A in N=3 is not blue.

And you definetly need the guru. Otherwise, in the N=1 and N=2 case, nobody would leave, because supposing A is not blue, from A's point of view, B has no reason to leave on the first day. B is in the N=1 case, which does not work without the guru.
Title: Re: A logic puzzle
Post by: Teeth on March 28, 2012, 07:31:12 pm
True, Theorem 2 isn't correct at all if the Guru is not there, cause Theorem 2 relies on Theorem 1 being correct. Silly me.
Title: Re: A logic puzzle
Post by: Wookimonsta on March 28, 2012, 07:48:48 pm
find a guy who has a blue eye fetish, everone he has sex with has blue eyes, fuggin problem solved.
Title: Re: A logic puzzle
Post by: Tomas on March 28, 2012, 10:15:37 pm
You're thinking in the right direction Tomas.

BUT there can be 101 blue eyes.

No - My logic started by me assuming the role of a blue eyed person and only seeing 99 blue eyed people in front of me.  Therefore the max blue eyed people from my perspective was 100.

You are right that had i assumed the role of a Brown eyed person, i would have seen 100 Blue eyed people and there could have been 101 in total with me, however this does not tell the point at which a blue eyed person realises that they are blue eyed.

Title: Re: A logic puzzle
Post by: Stabby_Dave on March 29, 2012, 12:14:47 am
I had figured tge theorems out up to 3 blue eyed people but until you explained it Vibe I couldnt figure how it worked higher than 3 but now all is clear :D

Im going to claim that I partially figured it out, I just didnt KNOW that I partially figured it out  :mrgreen:
Title: Re: A logic puzzle
Post by: Earthdforce on March 29, 2012, 04:45:09 am
Oh my gawd, my head hurts.