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        riddles >> medium >> Brown eyes and Red eyes
        
(Message started by: adityamp10 on Oct 3^rd, 2007, 8:30pm)

Title: Brown eyes and Red eyes
Post by adityamp10 on Oct 3^rd, 2007, 8:30pm

I am confused about the solution of this puzzle. Could someone pls help?

As far as I understand, the tourist's statement "There is atleast one monk with red eyes" can only add information when there is only one monk with red eyes in the whole group.
Suppose there are 10 monks in the group and only one of them has red eyes. This fellow (with red eyes) sees that people all around him have brown eyes and he can't see the colour of his own eyes. When the tourist makes this statement, he will come to realize that he has red eyes (as every one else has brown eyes).

In a case where there are 10 monks (5 with red and 5 with brown eyes). Everyone knows the fact that "atleast one of them has red eyes". So how does the tourist's statement change anything?

Help!!

Title: Re: Brown eyes and Red eyes
Post by FiBsTeR on Oct 3^rd, 2007, 9:21pm

::) (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1027806383;start=0)

Title: Re: Brown eyes and Red eyes
Post by towr on Oct 4^th, 2007, 12:43am

on 10/03/07 at 20:30:16, adityamp10 wrote:

In a case where there are 10 monks (5 with red and 5 with brown eyes). Everyone knows the fact that "atleast one of them has red eyes". So how does the tourist's statement change anything?

firstly, there's already a thread about the subject, Fibster's smiley in the last post links to it

As for the information that is added; while every monk knows that at least one has red eyes, they don't know that everyone knows that everyone knows that everyone knows that everyone knows that at least one monk has red eyes. And that makes all the difference.
The tourist's statement increases [i]common knowledge[/b] (the information that people know everyone has.

Consider in the example one of the 5 red eyed monks (REMs), he only sees 4 REMs; if they're the only 4, he considers, then each of them only sees 3 REMs. So the 4 might consider that each of those 3 only see 2, and consider that the three may think these 2 only see 1, and that single one wouldn't see any REM, and thus might think there aren't any. So until someone comes along to inform that single (hypothetical) monk there's at least one REM, nothing will happen.
The tourist informs all monks, and so all hypothetical monks as well; and this gets a process started that leads all monks to deduce whether they're a REM or not

Title: Re: Brown eyes and Red eyes
Post by Grimbal on Oct 4^th, 2007, 1:09am

Take the simple case of 2 monks where both have read eyes.
Each knows that the other has read eyes and secretly thinks that if he knew he would kill himself. Each also ignores his own status. They don't know whether the other sees red eyes or brown eyes.

Let's call the monks A and B. A doesn't know whether he is red-eyed because he doesn't know whether B sees red eyes or not.

After the tourist told one of them has red eyes, the situation changes. If B saw brown eyes, he would know that he is the red-eyed one and would kill himself the next night. If B survives one night, that means he sees another red-eyed monk. So A can conclude he himself is also red-eyed. B can make the same conclusion because A didn't kill himself, so both will kill themselves on the second night.

So, even though both knew already that there is at least one red-eyed monk, the tourists statement adds some information. As towr said, they didn't know whether the other one knew.

Title: Re: Brown eyes and Red eyes
Post by RandomSam on Oct 4^th, 2007, 1:12pm

"There are at least two red eyeballs on this island."
Discuss. ;D
(I have solutions for 2, 3 and 4 eyeballs, but not for N yet. Monks can actually survive this time.)
(And I know there's another thread, but it seems to have degenerated into argument! Will repost there if someone says so.)

Title: Re: Brown eyes and Red eyes
Post by towr on Oct 4^th, 2007, 1:44pm

on 10/04/07 at 13:12:18, RandomSam wrote:

"There are at least two red eyeballs on this island."
Discuss. ;D

It could be a bit problematic, since a monk could have either one or two red eyes.
I would guess the monks would resolve the issue in [hide]#REB[/hide] days

Title: Re: Brown eyes and Red eyes
Post by RandomSam on Oct 4^th, 2007, 2:01pm

on 10/04/07 at 13:44:05, towr wrote:

It could be a bit problematic, since a monk could have either one or two red eyes.
I would guess the monks would resolve the issue in [hide]#REB[/hide] days

With n Odd Eyed Monks and m Red Eyed Monks, [hide]for n>1 they all seem to commit suicide on night m+n-1.[/hide] Not really sure how to prove that. Also, [hide]if there is one odd-eyed monk, he seems to survive. For n<2, the REMs die on night m.[/hide]