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Topic: BROWN EYES AND RED EYES (Read 80038 times) |
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StallionMang
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Re: BROWN EYES AND RED EYES
« Reply #175 on: Jan 2nd, 2008, 4:09pm » |
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Here's a little twist on the original that I thought up:
Immediately after making his statement, the tourist murders one of the monks in front of all the others.
How does this affect the result? Does the eye color of the murdered monk matter?
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StallionMang
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Re: BROWN EYES AND RED EYES
« Reply #176 on: Jan 2nd, 2008, 4:34pm » |
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Oh, and one other thing, I don't know if anyone posted this yet because I haven't read through all 8 pages of this thread, but here are my answers to the follow-up quesitons asked in the original riddle, as posted on this site.
What happens if we change the tourist's statement to each of the following?
"There are 10 Brown Eyed Monks" This will result in all of the REMs killing themselves on the first night, as they will all count 10 brown eyes and know that they must not have brown eyes.
"There are at lesat two Red Eyed Monks" All REMs will kill themselves on the N-1 night. The reason why it is no longer the N night is because 2 REMs now becomes the base case, rather than 1 REM.
"There is an odd number of Red Eyed Monks" All REMs will kill themselves on the first night, because each of them will count an even number of red eyes, and will therefore know that they must be the additional one that makes the number odd.
"There is an even number of Red Eyed Monks" Assuming the number of REMs is greater than 0, the result is the same as for odd.
"There is more than one Red Eyed Monk" This is the same as him telling them that there are "at least two", which is addressed above.
Now keep in mind, I am assuming in my responses that the explorer is always telling the truth when he makes these statements.
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towr
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Re: BROWN EYES AND RED EYES
« Reply #177 on: Jan 3rd, 2008, 1:35am » |
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on Jan 2nd, 2008, 4:09pm, StallionMang wrote:Here's a little twist on the original that I thought up:
Immediately after making his statement, the tourist murders one of the monks in front of all the others.
How does this affect the result? Does the eye color of the murdered monk matter? |
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I think that if he's a REM, none of the other REMs will kill themselves; but if he isn't, they will, and in the same time-frame.
What if the tourist says "the number of REMs is a a multiple of 3 or a multiple of 4"?
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StallionMang
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Re: BROWN EYES AND RED EYES
« Reply #178 on: Jan 3rd, 2008, 6:52am » |
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towr, you got it!
In response to your question, hmmmm.
3 REMs : All 3 die on first night
4 REMs : All 4 die on second night
6 REMs : All 6 die on first night
8 REMs : All 8 die on first night
9 REMs : All 9 die on second night
Okay, I think I have got it. Where N is a number of REM's that is a multiple of 3 or 4, then:
If N-1 is a multiple of 3 or 4, then all N monks will die on second night.
If N-1 is not a multiple of 3 or 4, then all N monks will die on first night.
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| « Last Edit: Jan 3rd, 2008, 6:52am by StallionMang » |
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StallionMang
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Re: BROWN EYES AND RED EYES
« Reply #179 on: Jan 3rd, 2008, 6:57am » |
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One other thing I forgot to mention. The only thing that could cause a different result than the ones I mentioned above would be if N, N-1, and N-2 were all multiples of 3 or 4. But I don't think there exist 3 consecutive numbers that fit that bill.
But I am not a big math guy, so I could be wrong.
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Grimbal
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Re: BROWN EYES AND RED EYES
« Reply #180 on: Jan 3rd, 2008, 7:25am » |
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No, you are right.
Along the same line, what now if the visitor just says: "The number of REMs is not a prime number".
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towr
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Re: BROWN EYES AND RED EYES
« Reply #181 on: Jan 3rd, 2008, 7:35am » |
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on Jan 3rd, 2008, 7:25am, Grimbal wrote:| Along the same line, what now if the visitor just says: "The number of REMs is not a prime number". |
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I was just going to suggest that as well.. 
I think the number of nights till the suicides will be N minus the largest prime number smaller than N. If they see a prime number of REMS, they must be one themselves. If they see one more than a prime number, then they consider that if they aren't a REM, the other REMs see a prime number and would kill themselves on day one, and if they don't he must thus be one; etc.
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| « Last Edit: Jan 3rd, 2008, 7:36am by towr » |
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towr
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Re: BROWN EYES AND RED EYES
« Reply #182 on: Jan 3rd, 2008, 7:48am » |
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We can say a similar thing in general.
If a set S of numbers is excluded (in the original case {0}), then the REMs kill themselves in night N - max{x  S | x < N}
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| « Last Edit: Jan 3rd, 2008, 7:49am by towr » |
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StallionMang
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Re: BROWN EYES AND RED EYES
« Reply #183 on: Jan 3rd, 2008, 8:20am » |
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Cool.
Okay, how about this?
The visitor gets greedy and decides that he would prefer to have the entire island to himself as quickly as possible.
Think of a statement he can make to get all of the monks on the island to kill themselves as expeditiously as possible.
Note: One assumption to be made is that monks kill themselves in the privacy of their own rooms. Either that, or they form a big gathering but in a dark enough environment that they can't see each other's eyes at the time of the suicide... 
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SMQ
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Re: BROWN EYES AND RED EYES
« Reply #184 on: Jan 3rd, 2008, 8:36am » |
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on Jan 3rd, 2008, 8:20am, StallionMang wrote:| Think of a statement he can make to get all of the monks on the island to kill themselves as expeditiously as possible. |
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If the population consists entriely of REMs he can simply state the true number of REMs. Each will see one fewer REM than stated and immediately conclude he is a REM himself.
If the population consists of both REMs and BEMs he can state that there is one more REMs than there truly is. Each BEM will see one fewer REM than stated and immediately conclude (erroniously) he is a REM himself. Each REM will initially know the statement was a lie, but after seeing the BEMs' actions will deduce the true number of REMs.
--SMQ
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| « Last Edit: Jan 3rd, 2008, 8:38am by SMQ » |
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--SMQ
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Grimbal
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Re: BROWN EYES AND RED EYES
« Reply #185 on: Jan 3rd, 2008, 8:45am » |
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That was exactly what I was after. I thought it is an enlightening way to look at the problem.
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StallionMang
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Re: BROWN EYES AND RED EYES
« Reply #186 on: Jan 3rd, 2008, 8:56am » |
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OK. Cool.
Now....if the visitor lies, and any of the monks are able to immediately detect that he is lying, they will kill him before he can get off the island.
Think of a statement he can make that will allow him the opportunity to get off the island alive before the suicides commence.
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Icarus
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Re: BROWN EYES AND RED EYES
« Reply #187 on: Jan 3rd, 2008, 8:11pm » |
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He can state that there are an even number of REMs, if the actual number is odd, or an odd number of REMs, if the actual number is even.
No one will be able to tell that the statement is false until they see who didn't make it through the night.
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And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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ima1trkpny
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Re: BROWN EYES AND RED EYES
« Reply #188 on: Jan 3rd, 2008, 8:23pm » |
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on Jan 3rd, 2008, 8:11pm, Icarus wrote:
Icarus is back!  (You had us all worried!) 
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"The pessimist sees difficulty in every opportunity. The optimist sees the opportunity in every difficulty." -Churchill
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Aryabhatta
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Re: BROWN EYES AND RED EYES
« Reply #189 on: Jan 3rd, 2008, 9:40pm » |
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on Jan 3rd, 2008, 8:23pm, ima1trkpny wrote:
Icarus is back! (You had us all worried!) |
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Welcome back Icky! You did have us worried there...
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JiNbOtAk
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Re: BROWN EYES AND RED EYES
« Reply #190 on: Jan 4th, 2008, 2:20am » |
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on Jan 3rd, 2008, 9:40pm, Aryabhatta wrote:
And guess what ? Your nick name stuck !! 
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Icarus
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Re: BROWN EYES AND RED EYES
« Reply #191 on: Jan 4th, 2008, 5:34pm » |
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 Maybe I should go away again...
I've been under a considerable amount of stress at work this last year, and the time I was spending here wasn't helping, so I decided to stay away for awhile.
But things have loosened up a bit, so here I am.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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towr
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Re: BROWN EYES AND RED EYES
« Reply #192 on: Jan 5th, 2008, 11:12am » |
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Good to see you back, now we can get all those answers that eluded us the last year
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Ghost Sniper
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Re: BROWN EYES AND RED EYES
« Reply #193 on: Jan 5th, 2008, 1:09pm » |
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Icarus is back, but what about everyone else that went AWOL, such as Raven, BNC, etc.?
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*sob* I miss my mommy... *blows nose* huh, I'm on? oh right.
(thinks to self) Time for my speech to these college kids.
"Reason is more important than all emotions..."
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towr
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Re: BROWN EYES AND RED EYES
« Reply #194 on: Jan 5th, 2008, 2:00pm » |
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on Jan 5th, 2008, 1:09pm, Ghost Sniper wrote:| Icarus is back, but what about everyone else that went AWOL, such as Raven, BNC, etc.? |
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BNC posted in the last week, so he's not exactly awol*, although granted, not very active currently.
(* not that people need to get leave to be away from here in the first place  )
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Shadow
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Re: BROWN EYES AND RED EYES
« Reply #195 on: Oct 24th, 2008, 1:50pm » |
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I have just read this entire thread and I think a flawed mental model occurs for several posters in the middle of this thread.
I agree that the N REM will commit suicide on the Nth night if a change in the knowledge of all monks occur.
I do not agree that a tourist saying "at least one monk has red eyes" is the catalyst that sets this in motion for a monastery that has 3 or more REMs.
The premise is that these are logical monks, therefore all monks will realize this statement has added nothing new to their knowledge of how many monks have red eyes.
Take monks A,B, and C.
A hopes he has brown eyes
He knows B and C have red eyes
He knows both B and C know at least one monk has red eyes.
The same argument holds for B.
B hopes he has brown eyes
He knows A and C have red eyes
He knows both A and C know at least one monk has red eyes.
The same argument holds for C.
C hopes he has brown eyes
He knows A and B have red eyes
He knows both A and B know at least one monk has red eyes.
ALL BEM know their are at least three REM.
Therefore no new is information is given to any of the monks and life goes on as usual.
The backward argument is made that this statement will cause all monks to notice how many others have red eyes and commit suicide on the Nth night. However, no change is made in the what they knew. All monks already knew that at least one monk has red eyes AND they also knew that all monks already knew that at least one monk has red eyes.
A rewording that would cause all REM monks to commit suicide on the Nth day is for god to declare on day 0 that all REM must commit suicide at midnight. This would set into motion N REM commit suicide on the Nth day.
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towr
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Re: BROWN EYES AND RED EYES
« Reply #196 on: Oct 24th, 2008, 2:13pm » |
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on Oct 24th, 2008, 1:50pm, Shadow wrote:| I do not agree that a tourist saying "at least one monk has red eyes" is the catalyst that sets this in motion for a monastery that has 3 or more REMs. |
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Well, it's very unfortunate that you have both read the entire thread and still don't believe this. There's really not much more that can be done to readdress the misconception that hasn't been done.
Quote:| The premise is that these are logical monks, therefore all monks will realize this statement has added nothing new to their knowledge of how many monks have red eyes. |
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Yeah, but the point is that it adds to their knowledge about the knowledge^N of other monks. That's a point so often repeated in this thread it's hard to believe you missed it.
Even if you had only two REMs; obviously they both know there is at least one REM. But after the public announcement, they now know that the other one knows. It told them nothing about how many REMs there are, it told them something different.
Quote:| A rewording that would cause all REM monks to commit suicide on the Nth day is for god to declare on day 0 that all REM must commit suicide at midnight. This would set into motion N REM commit suicide on the Nth day. |
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Actually, it wouldn't. Not unless god also declared there was at least one REM.
Just take a course in multi-agent modal logic, if you haven't already, and then work it out. (I'd suggest using a model, rather than working it out syntactically, but both approaches are equivalent.)
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towr
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Re: BROWN EYES AND RED EYES
« Reply #197 on: Oct 24th, 2008, 2:21pm » |
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It seems some of the images I posted where unavailable (due to our faculty's sysadmin screwing around with the server over the past few years). I've modified the posts to make the available again.
On the off chance it brings the point across, they're here and here.
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| « Last Edit: Oct 24th, 2008, 2:22pm by towr » |
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rmsgrey
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Re: BROWN EYES AND RED EYES
« Reply #198 on: Oct 24th, 2008, 3:36pm » |
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on Oct 24th, 2008, 1:50pm, Shadow wrote:
Take monks A,B, and C.
A hopes he has brown eyes
He knows B and C have red eyes
He knows both B and C know at least one monk has red eyes. |
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A knows that B hopes he has brown eyes.
A knows that B knows that C has red eyes.
Before the announcement:
A knows that B knows that C knows that at least zero monks have red eyes.
After the announcement:
A knows that B knows that C knows that at least one monk has red eyes.
A knows that, if A has brown eyes, then B knows that, if B has brown eyes, then C knows that C has red eyes and will suicide overnight.
The next day:
A knows that, if A has brown eyes, then B knows that B doesn't have brown eyes, so must have red eyes, and will suicide overnight.
The next day:
A knows that A doesn't have brown eyes, so must have red eyes, and will suicide overnight.
The next day, A is dead.
Looking at it another way:
A knows he's living in one of two possible universes. In one, A, B and C are REMs; in the other, only B and C are. A, being good at logic, knows that, in the universe with only two REMs, they will both suicide on the second night. Why? Because in that universe, B would know that he were living in either a universe where C was the only REM, or one where both of them were, and, being good at logic, would know that, if C were the only REM, he would suicide on the first night. When C doesn't suicide, in this 2-REM universe, B knows that he's the second REM, so B (and C) would suicide on the second night if the three monks were in the universe where A was not an REM. When they don't, A knows that he's living in the universe where all three of them are REMs
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Shadow
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Re: BROWN EYES AND RED EYES
« Reply #199 on: Oct 24th, 2008, 9:21pm » |
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"Before the announcement:
A knows that B knows that C knows that at least zero monks have red eyes. "
This is one monastery. A knows that both B and C KNOW that at least one monk has red eyes.( these are not separate monasterys) Therefore the statement above makes no sense to the logical monk who KNOWS that it is not possible that "C knows that at least zero monks have red eyes".
Previous posts show that C already knows that at least one (not zero) monks have red eyes.
"After the announcement:
A knows that B knows that C knows that at least one monk has red eyes. "
This last quote is from your post, but this was known before the tourist arrived.
What caused anything to change?
Aside: TWOR - I agree that that I have ignored the all BEM / REMsituation.
Aside: TOWR is very upset that I have questioned his/her opinion. You have not addressed the opinions expressed by me, but have only attacked my right to express them. You are an Uberpuzzler and a moderator and I respect these credentials as a newbie. I contend that you have a mental model that prevents you from seeing any other option than the one your mental model agrees with. I respect your opinion, and would also appreciate if you would respect mine. Look at this from a new beginning and explain where my comments are in error. I am more than willing to admit I am missing something.
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| « Last Edit: Oct 24th, 2008, 11:09pm by Shadow » |
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