Monks. (2 Viewers)

[RealiseNothing]

Which would lead to all 100 killing themselves?

 

[barbernator]

one monk was colourblind so he got lucky.

 

[DAFUQ]

one monk was colourblind so he got lucky.

haha. nice one

 

[seanieg89]

Yep, happy with Realise's explanation.

It is essentially an inductive proof of the statement:

If there are n blue-eyed monks, they will chill until the n-th night, when they will all commit suicide. (0<n<101)


As the monks are all intelligent, they are aware of this fact, so if a bunch of monks commit suicide on the n-th night, the remaining monks will know they must have brown eyes, and commit suicide the following night.

So every monk will have committed suicide by the 102nd morning.



Now the real enigma: Why should the strangers words change anything? If there are roughly equal numbers of brown/blue eyed monks, then the stranger is telling them something they already KNEW!

 

[barbernator]

Now the real enigma: Why should the strangers words change anything? If there are roughly equal numbers of brown/blue eyed monks, then the stranger is telling them something they already KNEW!

absolutely brilliant question.

 

[lvella10]

Now the real enigma: Why should the strangers words change anything? If there are roughly equal numbers of brown/blue eyed monks, then the stranger is telling them something they already KNEW!

Now that is an awesome question

 

[seanieg89]

Bent my mind when I first heard a form of this problem.

 

[RealiseNothing]

Yep, happy with Realise's explanation.

It is essentially an inductive proof of the statement:

If there are n blue-eyed monks, they will chill until the n-th night, when they will all commit suicide. (0<n<101)


As the monks are all intelligent, they are aware of this fact, so if a bunch of monks commit suicide on the n-th night, the remaining monks will know they must have brown eyes, and commit suicide the following night.

So every monk will have committed suicide by the 102nd morning.



Now the real enigma: Why should the strangers words change anything? If there are roughly equal numbers of brown/blue eyed monks, then the stranger is telling them something they already KNEW!

There is the chance that there is only 1 blue eyed monk or even no blue eyed monks at all.

Therefore the very first step of the induction does not work (the step where there is only 1 blue eyed monk who sees 99 brown eyes and thus knows he must be the one with blue eyes since there is atleast 1 blue eyed monk).

 

[seanieg89]

There is the chance that there is only 1 blue eyed monk or even no blue eyed monks at all.

Therefore the very first step of the induction does not work (the step where there is only 1 blue eyed monk who sees 99 brown eyes and thus knows he must be the one with blue eyes since there is atleast 1 blue eyed monk).

So this explains why the inductive argument from before wouldn't work if the stranger was not there...but the 'paradox' is more on the logical side: what additional piece of information has the stranger provided to the monks if there were say 50 brown 50 blue?

 

[kaz1]

Now the real enigma: Why should the strangers words change anything? If there are roughly equal numbers of brown/blue eyed monks, then the stranger is telling them something they already KNEW!

This was what I was thinking when I read the question.

 

[gr_111]

Do the monks know that they are born with either blue or brown eyes?

How do they come to know this? Is it inherent in their genes, or whatever, that they just know, or do they learn by looking at the other monks?

edit: Either way, the guy doesn't tell them anything new and therefore they would have all killed themselves before he got there. The problem is with the question, in assuming that things only start to happen after the guy leaves. There is no reason for the chain of events to begin at this point.

Bearing in mind that the blues and browns are complementary:
1. -If there are 0 blues and 100 browns, then these intelligent monks would have realised that there is at least 1 brown eyed monk, and would all commit suicide on the 100th or 101st day, whatever it is.
2. -If there is 1 blue and 99 browns, again they will have worked out that there is at least 1 brown eyed monk and 99 would have died by the 100th day and then the blue one the next day.
3. -if there is >1 blue and <99 brown they will die as others have explained already.
4. -if there is 99 blue and 1 brown, then the process occurs as in point 2.
5. -if there is 100 blue and 0 brown the process occurs as in point 1.

I think my reasoning is correct...

 

[seanieg89]

How do they come to know this? Is it inherent in their genes, or whatever, that they just know, or do they learn by looking at the other monks?

edit: Either way, the guy doesn't tell them anything new and therefore they would have all killed themselves before he got there. The problem is with the question, in assuming that things only start to happen after the guy leaves. There is no reason for the chain of events to begin at this point.

Bearing in mind that the blues and browns are complementary:
1. -If there are 0 blues and 100 browns, then these intelligent monks would have realised that there is at least 1 brown eyed monk, and would all commit suicide on the 100th or 101st day, whatever it is.
2. -If there is 1 blue and 99 browns, again they will have worked out that there is at least 1 brown eyed monk and 99 would have died by the 100th day and then the blue one the next day.
3. -if there is >1 blue and <99 brown they will die as others have explained already.
4. -if there is 99 blue and 1 brown, then the process occurs as in point 2.
5. -if there is 100 blue and 0 brown the process occurs as in point 1.

I think my reasoning is correct...

Inherent in genes, carved on a stone tablet, whatever...it is not the issue of the question.

And the guy has given them an extra piece of information...the process would not occur without his words. By what means would any monk deduce the colour of his/her eyes otherwise?

 

[barbernator]

Inherent in genes, carved on a stone tablet, whatever...it is not the issue of the question.

And the guy has given them an extra piece of information...the process would not occur without his words. By what means would any monk deduce the colour of his/her eyes otherwise?

Is it a starting time to count days of suicide from? assuming that they all didn't get put on the island initially in a single day originally and are told to go nuts, because then they would not need the extra information.

 

[seanieg89]

Is it a starting time to count days of suicide from? assuming that they all didn't get put on the island initially in a single day originally and are told to go nuts, because then they would not need the extra information.

Nope, starting date is irrelevant. Even if they were all "put on the island initially in a single day", this chain reaction would not occur without the strangers words...

 

[SunnyScience]

Because curiosity killed the cat.

 

[RealiseNothing]

1. -If there are 0 blues and 100 browns, then these intelligent monks would have realised that there is at least 1 brown eyed monk, and would all commit suicide on the 100th or 101st day, whatever it is.

This doesn't work without being told that there is atleast 1 blue eyed monk, which can't be true since you stated there is none, so the case of having no blue eyed monks can't happen.

 

[barbernator]

but all the monks have at least 1 brown eye!

 

[deswa1]

Nope, starting date is irrelevant. Even if they were all "put on the island initially in a single day", this chain reaction would not occur without the strangers words...

Wait- so to clarify: Even if they were all placed there on the same day and everyone already knew that there was at least one monk with blue eyes, the process still wouldn't occur until the stranger's words?

 

[barbernator]

Wait- so to clarify: Even if they were all placed there on the same day and everyone already knew that there was at least one monk with blue eyes, the process still wouldn't occur until the stranger's words?

yes :/

 

[SunnyScience]

Why has everyone got CarrotSticks display picture - am i missing something?

I was always terrible at riddles :S