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To Bloody Go...

 
 
Reply Sun 14 Mar, 2004 09:27 am
On a small planet not far away lived a strange race. A long time ago all the members of that species had one of three eye colors: blue, green or brown. In some point in history a famous war took place, initiated by the blue and brown eye faction. They genocided all green eyes, thus eliminating the green eye color from their race, and reducing the population of the planet to a few hundred. Soon after that war the factions were disbanded, and eye color was from that point on considered an inappropriate topic. Some rules were later established for the benefit of the whole society, so that something like this could never, ever happen again. The rules were as follows:

1. Nobody is allowed to talk about eyecolors.
2. If anyone gets to know his own eyecolor he must commit suicide at midnight in the town square.

Now I must explain the way this species was thinking, so you understand their reactions later on. You must understand that they all were really strict about those rules. In the beginning some people happened to accidently see their eyecolor in some reflective surface or puddle of water, and every last one of them faithfully comitted suicide the night after. After a few incidences all mirroring surfaces were removed from the cities, to minimize the risk. Also, this species was a very logical thinking. Although they still lacked knowledge in some areas, they thought clearly and logically, and trusted in the results they got, even if it led to their own death. Last, the way it worked after the rules were established was that everyone knew the eyecolor of everyone else on the planet, but not his own. Of course, on a small planet like this, they all saw everyone everyday, so a suicide was immediately noted.
Well, the people on this little planet were living for a few hundred years in peace and harmony, when something bad happened:

A little spacecraft crashed down in the desert near one of the large cities, leaving a big crater. Immediately the friendly people tried to rescue the astronauts, but it was too late. The only thing they recovered from the craft was a book about mathematics. In the same night a big meeting was called on, and everyone came together in a large hall. The book was read to the whole population, because it offered new concepts that were so impressive and striking that everyone had to know about them. But, knowledge isn't always a good thing. The knowledge in that book made the people aware of facts they didnt know about before, and made them realize a few things. In the following nights everyone was really nervous.

Then, in the 250th night after the dreaded meeting, all brown eyes committed suicide, thus eliminating the whole species, and leaving the planet an empty brick in the wide universe.

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Blue eyes present during the meeting:
Number of nights in which suicides happened:
Are there more blue or brown eyes in the meeting?
Which mathematical concept made them kill themselves?
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Iacomus
 
  1  
Reply Sun 14 Mar, 2004 08:27 pm
This question has been posted many times on A2K, most recently by 'Giggicat' on Feb 22, entitled 'Mythical village'
0 Replies
 
kev
 
  1  
Reply Mon 15 Mar, 2004 01:42 pm
Iacomus wrote:
This question has been posted many times on A2K, most recently by 'Giggicat' on Feb 22, entitled 'Mythical village'


Except Giggicats version is a lot simpler.
0 Replies
 
Iacomus
 
  1  
Reply Wed 17 Mar, 2004 07:53 pm
The question as posed seems slightly ambiguous. There could have been 249 blue eyes and a greater number of brown eyes, or there could have been 250 brown eyes and a greater number of blue eyes, surely? i.e. 250 brown eyes committed suicide the 250th night and the brown eyes committed suicide the following night or 249 blue eyes committed suicide on the 249th night and the brown eyes all committed suicide the following night.

Maybe not however; you did say 'thus eliminating the whole species', so it looks as though there were 249 blue eyes and a greater number of brown eyes, with the blue eyes committing suicide in the 249th night and the brown eyes on the 250th night.
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Halandriel
 
  1  
Reply Thu 18 Mar, 2004 02:54 am
But, what concept is this problem based on? Could you please explain a little bit more, please?

Greets

Halandriel
0 Replies
 
Iacomus
 
  1  
Reply Thu 18 Mar, 2004 05:12 am
Halandriel

Ah, now you are asking. The nearest I can come to answering your question is that the problem requires self-referent iteration and increments. I'm not so good at epistemiology.
0 Replies
 
GABOON
 
  1  
Reply Fri 2 Apr, 2004 02:40 am
The answers
The answers are as follows:

1. 249
2. brown
3. 2
4. induction

I know for a fact that they are correct.
ivancho
 
  1  
Reply Wed 19 May, 2004 07:21 pm
yes, that seems to be the answer that HackQuest wants... unfortunately, with all due respect, the problem is such an evil mess, it makes my dog cry.

First - all these problems - ie, Giggicat's, or if you prefer the version with the train passengers with dirty faces, have some sort of boundary condition - that is, we know what will happen in a situation with only one, say, blue-eyed, or red-spotted person, or only one dirty face. From there on, we can build by induction. In both cases, though, the boundary condition comes from the fact that everyone knows that the set of 'interesting' people - ie, blue-eyed, or dirty-faced etc. is non-empty - by having a stranger tell them, or when everyone who sees a dirty face laughs. Where is this feedback here? I mean, how do all those people know that there is at least one blue-eyed? If they don't, then no induction can start. Even if we know that 'a few hundred years ago' there were some blue eyes, how do we know that they all didn't perish in the puddle incidents? Better yet, how do those guys know it? I mean, if I was the only one blue eyed, someone else must tell me that there are some blue eyes for me to logically deduce I have them. That doesn't happen.

Second big assumption not mentioned anywhere is that they all know how quick everyone else is. That is, say there are 2 blue-eyed guys. Suppose someone told us there are some blue eyes. I am one of the 2. The second guy is not killing himself. How do I know logically that he is not killing himself, because he's seeing another blue-eyed person, rather than just him being quite slow in deduction? Or, even worse, suppose he killed himself. How do I know he killed himself because he made the 2 people deduction, rather than the one person deduction? In order to resolve that, either someone must tell us again there are still some blue-eyed people around, or we need everyone to make all logical steps within 1 day. Mind you, even if everyone does, we still need the initial step - information that both eye colors are present.

So, in conclusion, it is a nice problem, but it needs some more work on the setting.
0 Replies
 
SCoates
 
  1  
Reply Wed 19 May, 2004 07:31 pm
Anyone who has ever served as an advisor, couselor, or any other such position, (if they were any good at heir job) will tell you that no matter how good something looks on paper, or how perfecly logical it seems or sounds, some things simply will not work out that way in an actual situation. This reeks of that sort of event. It doesn't matter how well you define it, it simply would not work.
0 Replies
 
Morgaine
 
  1  
Reply Mon 13 Apr, 2009 01:00 pm
@GABOON,
But why are these the answers, I'm sorry but I just don't get it =(
Could you please help me?
0 Replies
 
 

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