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   Author  Topic: BROWN EYES AND RED EYES  (Read 64737 times)
Axela
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BROWN EYES AND RED EYES  
« on: Jul 24th, 2002, 2:09am »
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I can think of only 3 cases:
1) All the monks have brown eyes: mass suicide
2) Only 1 monk has red eyes: he kills himself
3) There at least 2 monks with red eyes: nothing happen.
 
I'm missing something?
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SFoster
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Re: BROWN EYES AND RED EYES  
« Reply #1 on: Jul 24th, 2002, 3:22am »
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If 1 person has red eyes they commit suicide on the first night, if 2 people they both do the deed on the second night, in general if n people have red eyes all n commit suicide on the nth night.
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David Elstob
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Re: BROWN EYES AND RED EYES  
« Reply #2 on: Jul 25th, 2002, 1:51am »
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Yeh but whyHuh That explantion might be a reason but I can't see how you followed it through to get that answer.
 
Please explain this one hurts my head.
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David Elstob
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Re: BROWN EYES AND RED EYES  
« Reply #3 on: Jul 25th, 2002, 2:06am »
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Oh I get it now. Cool.  Cool
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Re: BROWN EYES AND RED EYES  
« Reply #4 on: Jul 25th, 2002, 3:34am »
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I thought they'd just use the reflection of the water surrounding the 'island monastary'.  Wink
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Eli
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Re: BROWN EYES AND RED EYES  
« Reply #5 on: Jul 25th, 2002, 5:23am »
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Ok, explain it to me then, because I am still not getting it.
 
As long as two monks have red eyes, noone should kill themselves.  As any 'red-eyed monk', can always see another red-eyed monk, and then not be sure that it is themself that is red-eyed, and therefore, noone kills themself.
 
So explain to me this 'n days' theory.
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SFoster
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Re: BROWN EYES AND RED EYES  
« Reply #6 on: Jul 25th, 2002, 7:48am »
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Say there's two monks with red eyes. They each look about on the first day and see one other guy, so they expect him to commit suicide that night. When that doesn't happen he figures out he must have red eyes too, so both guys commit suicide on the second night.
When there's 3 monks with red eyes they commit suidice on the third night, and so on.
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blahedo
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Re: BROWN EYES AND RED EYES  
« Reply #7 on: Jul 25th, 2002, 8:04am »
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That's what I thought at first too, until I read that solution.  Here's the reasoning.
 
Say I'm the only red-eyed monk.  When the tourist says that, knowing that everyone else has brown eyes, I commit suicide.
 
Now say that I'm one of two red-eyed monks.  When the tourist says that, I think, "I might be ok, that other guy has red eyes."  But when he *doesn't* commit suicide, I know that he must be seeing at least one *other* red-eyed monk, since otherwise he would have committed suicide the night the tourist said that (due to the reasoning in the previous paragraph).  Now I know that there are at least two red-eyed monks, and I can only see one, so I'm the other one, so I commit suicide---on the second night.
 
If I'm one of three red-eyed monks, when the first night goes by with no suicide I realise that the two red-eyed monks I can see are going through the reasoning in the previous paragraph, and will commit suicide that night (the second night).  But when they don't, I know that they must each see at least two others, and thus I know that one of them must be me.  So I commit suicide, on the third night.
 
The number of brown-eyed monks is actually totally irrelevant.
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ThatTallGuy
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Re: BROWN EYES AND RED EYES (solution)  
« Reply #8 on: Jul 25th, 2002, 8:32am »
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I think I got it...  you have to assume that every monk knows every other monk and knows how many _other_ monks on the island have red eyes.
 
Under those assumptions, look at the case where one monk has red eyes.  He knows, immediately after the visitor arrives, that _he_ is the one because he can see that everybody else has brown eyes.  Honorable hara-kiri follows that night.
 
If two monks on the island have red eyes, nothing happens the first night because each of the red-eyes sees that somebody _else_ has red eyes and the visitor might only have been referring to them.  But each of the red-eyes wakes up the next morning and realizes that there is _more_than_one_ set of red eyes on the island, because the one he can see didn't kill himself.  Since red-eyed monk A knows that there is only one _other_ red-eyed monk (B), since he can eliminate all the rest of the inhabitants (he knows their eyes are all brown), then _he_ (A) must be the one who has kept the other cursed fellow (B) alive -- the existence of A let B believe that the visitor might have only been talking about A.  So A and B now know they both have red eyes.  Everybody else knows that there were two red-eyed monks and so does nothing.
 
If there are three monks on the island, same thing happens, except it takes three days for the realization to strike.  Etc., etc.
 
Cool.
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bl@ke
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Re: BROWN EYES AND RED EYES  
« Reply #9 on: Jul 25th, 2002, 7:01pm »
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Taking a different view - the tourist is color blind!
 
They all have brown eyes but the color blind tourist tells them that "at least one of them has red eyes". Every monk then looks to every other monk to see that they actually have brown eyes. By the process of elimiation every monk thinks that they are the one with red eyes and so every monk commits suicide.
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jkl
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Re: BROWN EYES AND RED EYES  
« Reply #10 on: Jul 25th, 2002, 10:12pm »
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what if there are 4 monks with red eyes?
then if i am one of them.. and i see the three other monks not killing themselves.. what am i supposed to think??
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Rhaokarr
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Re: BROWN EYES AND RED EYES  
« Reply #11 on: Jul 26th, 2002, 1:07am »
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And on the N+1 night, all the remaining monks breath easily...
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KNOWITALL
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Re: BROWN EYES AND RED EYES  
« Reply #12 on: Jul 26th, 2002, 10:14am »
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Answer to Red Eyes/Brown Eyes
 
We know the following:
 
1. No monk had killed themselves to date.
2. A tourist has introduces new information that causes a definitive action.
 
Hence the tourist's information must have been unknown to at least one monk. The tourist's information is that at least one monk has red eyes. Therefore, at least one monk must have been unaware that there were any monks with red eyes.
 
However, there could not have been more than one such monk, If there were two monks with red eyes, they would certainly have seen each other and already knew the tourist's information. If they both already knew the tourist's information, there would have been no 'definitive' action as a result. Likewise with three, etc.
 
Therefore, there was exactly one monk with red eyes. After the tourist revelation, he knew that he must be the monk with red eyes (he can see that one else has red eyes), and he properly kills himself at midnight.
 
Answer: Exactly one red-eyed monk kills himself at midnight, leaving no more red-eyed monks.
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Alex
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Re: BROWN EYES AND RED EYES  
« Reply #13 on: Jul 26th, 2002, 10:30am »
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Respectfully, taking your scenario where there are two monks with red eyes:
Until the tourist introduced the information, each monk would be uncertain whether he had red or brown eyes, and would be uncertain if the other monk was aware that he had red eyes. From each monk's point of view, the other monk may simply be "unaware of his eye color." When the tourist announced that there is at least one with red eyes, the resolution then becomes unavoidable, as both become aware that the other is aware that at least one monk has red eyes.
The same scenario being true as well with more than two. The information in these scenarios that changes is not what the monks know of themselves, but what they know of the knowledge of other monks.
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tot
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Re: BROWN EYES AND RED EYES  
« Reply #14 on: Jul 26th, 2002, 11:51am »
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on Jul 24th, 2002, 2:09am, Axela wrote:
I can think of only 3 cases:
1) All the monks have brown eyes: mass suicide
2) Only 1 monk has red eyes: he kills himself
3) There at least 2 monks with red eyes: nothing happen.
 
I'm missing something?

 
In the case 3, mass suicide on the second night?  After the first night, when nobody kills himself, everybody thinks that they must have red eyes too.
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tot
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Re: BROWN EYES AND RED EYES  
« Reply #15 on: Jul 26th, 2002, 11:52am »
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on Jul 24th, 2002, 2:09am, Axela wrote:
I can think of only 3 cases:
1) All the monks have brown eyes: mass suicide
2) Only 1 monk has red eyes: he kills himself
3) There at least 2 monks with red eyes: nothing happen.
 
I'm missing something?

 
In the case 3, mass suicide on the second night?  After the first night, when nobody kills himself, everybody thinks that they must have red eyes too.
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S. Owen
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Re: BROWN EYES AND RED EYES  
« Reply #16 on: Jul 26th, 2002, 12:25pm »
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The answer given by others above is correct: if there are N monks with red eyes, then they will all kill themselves on the Nth night.
 
They have been told that at least one person has red eyes.
 
If there is exactly one, the one will easily deduce his eye color and kill himself on the first night. If nobody kills themselves the first night, then all can deduce that there must be at least two red-eyed monks in total.
 
If there are exactly two, then each of the two will see only one other red-eyed monk and easily deduce that his own eyes must be red, and both will commit suicide on night 2.
 
Same goes for 3, 4, ...
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I.M._Smarter_Enyu
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Re: BROWN EYES AND RED EYES  
« Reply #17 on: Jul 26th, 2002, 12:53pm »
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I think you've got the logical part down... but I don't think that's what really happens, though!  See the other post about the "Unexpected Quiz."
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S. Owen
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Re: BROWN EYES AND RED EYES  
« Reply #18 on: Jul 26th, 2002, 1:33pm »
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Really, then what do you think happens?
 
I don't think is the same sort of problem as the "unexpected quiz" puzzle you posted.
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Rhaokarr
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Re: BROWN EYES AND RED EYES  
« Reply #19 on: Jul 26th, 2002, 8:53pm »
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All that the tourists information does is set time to 'zero', acting as a marker point in time.  
 
There is also the assumption that every monk hears the tourist's statement, and also knows that every monk knows that the others heard as well.
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Frost
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Re: BROWN EYES AND RED EYES  
« Reply #20 on: Jul 28th, 2002, 4:52am »
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A long time ago, before the tourist visited, the first red-eyed monk came to live at an all-brown-eyed monestrary. Nothing happened. When a second red-eye arrived, all monks knew there was at least one red-eyed monk, but nothing happened yet. When a third red-eye came to live with the monks, all monks knew all others monks knew at least one of them had red eyes, and all red-eyes died three days later.  
 
Therefore, no more than two red-eyed monks can exists at the monestary.
 
 
 
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S. Owen
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Re: BROWN EYES AND RED EYES  
« Reply #21 on: Jul 28th, 2002, 8:04am »
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Interesting, but it's equally possible that all the red-eyed monks were there before any brown-eyed monks arrived. Surely this is not a material aspect of the problem though.
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Frost
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Re: BROWN EYES AND RED EYES  
« Reply #22 on: Jul 29th, 2002, 1:16am »
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If, at any time, the monestary has >2 red-eyed monks, each monk can see at least two red-eyed monks. From this information they know each other monk knows at least one of them has red eyes. This results a Nth-day suicide. There are only four stable situations in which this monestary can exists:
 
1) no red-eyed monks
2) one red-eyed monk
3) two red-eyed monks
4) a new red-eyed monk is added each day (hardly stable)
 
When the visitor reveals his additional information, this will happen in each of the above cases:
 
1) all monks kill themselves tonight
2) he kills himself tonight
3) they kill themselves tomorrownight
4) nothing happens
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Thott
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Re: BROWN EYES AND RED EYES  
« Reply #23 on: Jul 29th, 2002, 2:49am »
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I've done a similar riddle before, and I expect this one is intended to be a copy of it.  What is being assumed in previous posts, but is lacking in this riddle description, is the phrase 'every monk sees every other monk every day'.  Without that piece of information, it's impossible to solve.  One can't even assume that every monk has ever seen every other monk, much less it happening every day.
 
--Thott
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pa0pa0
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Re: BROWN EYES AND RED EYES  
« Reply #24 on: Jul 29th, 2002, 5:57am »
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There's lots of interesting stuff to discuss about this riddle.
 
For example, did you know that the tourist is actually giving out more information than he needs to? (Well, to be more precise, he's actually increasing the monks' knowledge more than he needs to.)
 
(Yes, and I'm aware that alot of people here think he isn't increasing the monks' knowledge at all.)
 
But before we get on to that, could we clear the ground by convincing Frost that his arguments don't hold water?  I'm not sure how to do that, but let's try this:
 
Frost, as soon as there are three red-eyed monks, BUT no tourist, it's true, as you say, that
 
 Everyone knows that everyone knows that there's
 at least one red-eyed monk.
 
It is also true that
 
  Everyone knows that there are at least two red-eyed  
  monks (BUT not everyone knows that everyone knows
  that there are at least two - in particular only the  
  brown-eyed monks know that everyone knows this)
 
It is also true that
 
   There are at least three red-eyed monks (BUT not  
   everyone knows this - in particular, only the
   brown-eyed monks know this.)
 
Can you see that without the tourist,  nothing will happen? In particular, nothing will change as a result of no one dying overnight on the first night.
 
However, IF it were ever true that
 
   Everyone knows that everyone knows that everyone  
   knows that there's at least one red-eyed monk
 
THEN on the second day it would become true (if no one died) that
 
   Everyone knows that everyone knows that there are
   at least two red-eyes
 
THEN on the third day it would become true (if no one died) that
 
   Everyone knows that there are at least three red-eyes
 
AS A COROLLARY OF WHICH the red-eyed monks would know their own eye colour.
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