Author Topic: Common knowledge (logic) - The blue-eyed islanders puzzle  (Read 4124 times)

paultyndale

  • Party - TUP
  • Posts: 192
Common knowledge (logic) - The blue-eyed islanders puzzle
« on: September 18, 2014, 01:48:40 pm »
There is an island upon which a tribe resides. The tribe consists of 1000 people, with various eye colours. Yet, their religion forbids them to know their own eye color, or even to discuss the topic; thus, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces). If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and devout, and they all know that each other is also highly logical and devout (and they all know that they all know that each other is highly logical and devout, and so forth).

Of the 1000 islanders, it turns out that 100 of them have blue eyes and 900 of them have brown eyes, although the islanders are not initially aware of these statistics (each of them can of course only see 999 of the 1000 tribespeople).

One day, a blue-eyed foreigner visits to the island and wins the complete trust of the tribe.

One evening, he addresses the entire tribe to thank them for their hospitality.

However, not knowing the customs, the foreigner makes the mistake of mentioning eye color in his address, remarking “how unusual it is to see another blue-eyed person like myself in this region of the world”.

What effect, if anything, does this faux pas have on the tribe?




Diakun

  • Hikikomori
  • Global Moderator
  • Posts: 13871
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #1 on: September 18, 2014, 01:53:58 pm »
how could they be highly logical if they follow an irrational and ridiculous religion
Nymeus - 5:56 PM
I've got a picture of diakun and his dick
he can easily make people ashamed of how small they are, cause his is big
need to know anything else?

paultyndale

  • Party - TUP
  • Posts: 192
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #2 on: September 18, 2014, 01:55:27 pm »
Note 1:  For the purposes of this logic puzzle, “highly logical” means that any conclusion that can logically deduced from the information and observations available to an islander, will automatically be known to that islander.

Note 2: Bear in mind that this is a logic puzzle, rather than a description of a real-world scenario.  The puzzle is not to determine whether the scenario is plausible (indeed, it is extremely implausible) or whether one can find a legalistic loophole in the wording of the scenario that allows for some sort of degenerate solution.





RodneyMcKay

  • Global Moderator
  • Posts: 2906
  • The Legion Commander
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #3 on: September 18, 2014, 03:07:10 pm »
Everyone would be required to kill themselves.


The person he addressed now knows their eye color, and all the other villagers could assume they now have Brown eyes (due to not being addressed), so in turn must kill themselves. 


Admiral Rodney McKay DSO
Commander of The Legion
ex-ESO Party President
Admiral of the fleet (Ret.

dougal4chaos

  • Political - Member of Parliament
  • Posts: 124
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #4 on: September 18, 2014, 04:35:43 pm »
nothing changes, he addressed them all and they learnt nothing new,
they already know brown is majority and that the foreigner has blue
they wasnt discussing the topic so no fault on their part
I pledge allegiance to the flag of the UK BUT not the flag of the EU to which it belongs.
"We find out who did it and we kill them, we kill their supporters and we kill their friends, and then we kill any one that liked what they did"

RodneyMcKay

  • Global Moderator
  • Posts: 2906
  • The Legion Commander
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #5 on: September 18, 2014, 04:40:47 pm »
How do they know he wasn't addressing them?



Admiral Rodney McKay DSO
Commander of The Legion
ex-ESO Party President
Admiral of the fleet (Ret.

Talon Karrde

  • Party - TUP
  • Posts: 3989
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #6 on: September 18, 2014, 04:58:35 pm »
He didn't address his comment to anyone in particular, and so none of them knew their own eye colour and none of them discussed eye colour. Therefore no ritual suicide. One of them may ask him to do the suicide though, since he did talk about eye colour.

Tuus in terra servus, nuntius fui; officium perfeci



dougal4chaos

  • Political - Member of Parliament
  • Posts: 124
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #7 on: September 18, 2014, 07:00:46 pm »
He didn't address his comment to anyone in particular, and so none of them knew their own eye colour and none of them discussed eye colour. Therefore no ritual suicide. One of them may ask him to do the suicide though, since he did talk about eye colour.

correct but suicide is only for knowing your eye colour, not for discussing it
I pledge allegiance to the flag of the UK BUT not the flag of the EU to which it belongs.
"We find out who did it and we kill them, we kill their supporters and we kill their friends, and then we kill any one that liked what they did"

Sir Digby Chicken-Caesar

  • Global Moderator
  • Posts: 13996
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #8 on: September 18, 2014, 07:23:43 pm »
Yeah, surely not much would happen since he wasn't speaking about anyone inparticular. They already know others have blue eyes so nobody would assume that they were talking directly about them (the individual). There is the fact he only potentially referred to one of them as having blue eyes rather than several, but I don't think that would mean anything.

They might politely ask him to do the ritual, but then he's not of their religion so pfft.
HRH Pope Digby V, Prince of Hanover, KC, KG, KP, GBE, OGS, FRSL, BGD, PhD
Chancellor of BBH Open University


Iain Keers

  • Party - TUP
  • Posts: 12057
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #9 on: September 18, 2014, 11:10:45 pm »
Nothing happens because:

1. Nobody specific was addressed

2. You already stated that nobody knew the statistical number of people with certain eye colours
"Come to me, all who labour and are heavy laden, and I will give you rest." ~ Mt 11:28

mickcain

  • Guest
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #10 on: September 19, 2014, 02:30:51 am »
His comments about eye colour has no effect whatsoever as each tribe member  still does not knowhis or her eye colour

mickcain

  • Guest
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #11 on: September 19, 2014, 02:36:02 am »
Although he has declared his own eye colour so the tribe could insist on his own suicide

dougal4chaos

  • Political - Member of Parliament
  • Posts: 124
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #12 on: September 19, 2014, 08:56:27 am »
so did you mistype the question or is the answer nothing changes ?
I pledge allegiance to the flag of the UK BUT not the flag of the EU to which it belongs.
"We find out who did it and we kill them, we kill their supporters and we kill their friends, and then we kill any one that liked what they did"

Niemand

  • MU - The Legion
  • Posts: 849
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #13 on: September 19, 2014, 10:27:13 am »
All those tribesmen that would give the answer they think is true and do hear the answers given by others (and seeing what colors of eyes they have), those that have given answers would all kill themselves.

All the ones that do hear would live their lives like before.
Lady of the Lake

Iain Keers

  • Party - TUP
  • Posts: 12057
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #14 on: September 19, 2014, 10:31:53 am »
It wouldn't work. If they knew the number of people with blue eyes, they'd be able to deduce their own eye colour. You would know everyone who had blue eyes, so you'd just assume he was talking about them.
"Come to me, all who labour and are heavy laden, and I will give you rest." ~ Mt 11:28

Niemand

  • MU - The Legion
  • Posts: 849
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #15 on: September 19, 2014, 12:16:22 pm »
There would be a tiny difference in between the percentage in the answers the ones gives who have brown eyes themselves and the ones who have blue eyes themselves when they say what is the percentage blue eyes they see.
When a tribesmen has blue eyes he sees 99 out of 999 (circa 9.9 %), the ones with brown eyes sees 100 out of 999 (circa 10%).

However it could be questioned whether these tribesmen that are absolute logical would ask first what is the precise question (what is what I see or is it what is what a general persons sees).
Then it depends of the answer of the visitor whether there would be any effect.
Lady of the Lake

VoodooMike71

  • What's a custom title then?
  • MU - Royal Navy
  • Posts: 162
  • Think of something interesting, and pretend I'm it
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #16 on: September 19, 2014, 01:12:43 pm »
Nothing happens.

All tribesmen have always been able to see at least one brown-eyed lunatic and one blue-eyed freak.

Adding an extra person who comments that he too can see a blue-eyed freak adds nothing to the equation, apart from adding one to the total number of people.

He could have said that he can see 100 blue-eyed freaks and still nothing would change. All he is doing is repeating one of the existing conditions.
Woldy's Royal Wench

xoxox nihil declarandum xoxox


Carlini8

  • MU - Command - The Legion
  • Posts: 678
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #17 on: September 19, 2014, 05:39:04 pm »
All they found out was that the colour blue is called blue...

If they didn't already know that.

Iain Keers

  • Party - TUP
  • Posts: 12057
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #18 on: September 19, 2014, 08:01:16 pm »
If he said there were 100 blue eyed people, they could count and say that there was one too few blues and deduce it is them who is blue eyed and an hero.
"Come to me, all who labour and are heavy laden, and I will give you rest." ~ Mt 11:28

paultyndale

  • Party - TUP
  • Posts: 192
Re: Common knowledge (logic) - The blue-eyed islanders puzzle
« Reply #19 on: September 19, 2014, 10:32:59 pm »
I'm pretty sure I typed it correctly and I'm equally sure we've not got the answer I'm looking for as yet  :lol:




 

With Quick-Reply you can write a post when viewing a topic without loading a new page. You can still use bulletin board code and smileys as you would in a normal post.

Warning: this topic has not been posted in for at least 120 days.
Unless you're sure you want to reply, please consider starting a new topic.

Name: Email:
Verification:
Type the letters shown in the picture
Listen to the letters / Request another image
Type the letters shown in the picture:
What precious metal is a currency in erepublik?:
How do you spell 'Frerk'?:
What social MMO is this forum linked to?: