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Author Topic:   Puzzle
Primordial Egg
Inactive Member


Message 1 of 14 (90204)
03-04-2004 6:03 AM


Tricky one this. I received this on email yesterday:
You're on an island with natives from three different tribes. One tribe always tells the truth, one always lies, and one always gives random answers. You get to ask three yes-or-no questions, each one directed to the native of your choice. Then you have to identify which native is which. How do you do it?
I've got an answer to this, but I've had to make certain assumptions which I'm not altogether comfortable with. Unfortunately, the question above didn't come with any further elucidation, so I'm posting it here to see if anyone can do it without having to resort to the same assumptions I did.
Oh, and obviously I'm not going to say what those assumptions were, -it might taint the solutions you guys come up with.
PE
added by edit: sorry wrong forum - can this be moved to "Coffee House" please?
[This message has been edited by Primordial Egg, 03-04-2004]

Mrs Hardy: "And how is Mrs Laurel?"
Stanley: "Oh, fine thank you."
Mrs Hardy: "I'd love to meet her some time."
Stanley: "Neither do I, too."

Replies to this message:
 Message 2 by PaulK, posted 03-04-2004 7:01 AM Primordial Egg has replied

  
PaulK
Member
Posts: 17825
Joined: 01-10-2003
Member Rating: 2.2


Message 2 of 14 (90205)
03-04-2004 7:01 AM
Reply to: Message 1 by Primordial Egg
03-04-2004 6:03 AM


I think I see how to do it - the only assumption I use is that you have exactly one native from each tribe. That's pretty common to this sort of puzzle.

This message is a reply to:
 Message 1 by Primordial Egg, posted 03-04-2004 6:03 AM Primordial Egg has replied

Replies to this message:
 Message 3 by Primordial Egg, posted 03-04-2004 7:13 AM PaulK has replied

  
Primordial Egg
Inactive Member


Message 3 of 14 (90210)
03-04-2004 7:13 AM
Reply to: Message 2 by PaulK
03-04-2004 7:01 AM


So common, in fact, that I didn't even realise I was making that assumption!
Qu for PaulK only (and no peeking, anyone else):
Did you have to make any assumptions about the random answers you would get? e.g Could the random person have answered "yes" to the question "are you lying?"

PE

This message is a reply to:
 Message 2 by PaulK, posted 03-04-2004 7:01 AM PaulK has replied

Replies to this message:
 Message 4 by PaulK, posted 03-04-2004 7:30 AM Primordial Egg has replied

  
PaulK
Member
Posts: 17825
Joined: 01-10-2003
Member Rating: 2.2


Message 4 of 14 (90211)
03-04-2004 7:30 AM
Reply to: Message 3 by Primordial Egg
03-04-2004 7:13 AM


I make no other assumptions, so the answer to your e.g. is "yes".
On the other hand I've just discovered a problem so I have to think some more.
The random answers can be "yes" or "no" whatever the question. There are no questions for which the random tribe must answer "yes" and none for which they must answer "no"
[This message has been edited by PaulK, 03-04-2004]

This message is a reply to:
 Message 3 by Primordial Egg, posted 03-04-2004 7:13 AM Primordial Egg has replied

Replies to this message:
 Message 5 by Primordial Egg, posted 03-04-2004 7:38 AM PaulK has replied

  
Primordial Egg
Inactive Member


Message 5 of 14 (90214)
03-04-2004 7:38 AM
Reply to: Message 4 by PaulK
03-04-2004 7:30 AM


I'm impressed!
Back to the drawing board for me then....
PE
PaulK:
what, not even the assumption that each native knows the designation of the other two?

This message is a reply to:
 Message 4 by PaulK, posted 03-04-2004 7:30 AM PaulK has replied

Replies to this message:
 Message 6 by PaulK, posted 03-04-2004 7:52 AM Primordial Egg has replied

  
PaulK
Member
Posts: 17825
Joined: 01-10-2003
Member Rating: 2.2


Message 6 of 14 (90216)
03-04-2004 7:52 AM
Reply to: Message 5 by Primordial Egg
03-04-2004 7:38 AM


Oh yes, I assume that the natives know who is who.
Oh and read the edit.

This message is a reply to:
 Message 5 by Primordial Egg, posted 03-04-2004 7:38 AM Primordial Egg has replied

Replies to this message:
 Message 7 by Primordial Egg, posted 03-04-2004 8:06 AM PaulK has replied

  
Primordial Egg
Inactive Member


Message 7 of 14 (90221)
03-04-2004 8:06 AM
Reply to: Message 6 by PaulK
03-04-2004 7:52 AM


Does this mean you're still working on it?
Your confidence has given me renewed vigour - there is a fiendish solution I can think of, but it involves bending the rules a little.
i.e using the fact that you can ask a yes-no question that the natives might not be able to answer, and then asking them a different question instead. Not really in the spirit of the question though.
PE

This message is a reply to:
 Message 6 by PaulK, posted 03-04-2004 7:52 AM PaulK has replied

Replies to this message:
 Message 9 by PaulK, posted 03-04-2004 10:23 AM Primordial Egg has replied

  
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Message 8 of 14 (90231)
03-04-2004 8:33 AM


Thread moved here from the Welcome, Visitors! forum.

  
PaulK
Member
Posts: 17825
Joined: 01-10-2003
Member Rating: 2.2


Message 9 of 14 (90255)
03-04-2004 10:23 AM
Reply to: Message 7 by Primordial Egg
03-04-2004 8:06 AM


I now have a solution I am more confident of. It took a rather disciplined analysis to work out what was needed but I am confident that it can be done with only 3 questions. And the real key is the first question - get that right and the rest is easy.

This message is a reply to:
 Message 7 by Primordial Egg, posted 03-04-2004 8:06 AM Primordial Egg has replied

Replies to this message:
 Message 10 by Primordial Egg, posted 03-04-2004 10:57 AM PaulK has replied

  
Primordial Egg
Inactive Member


Message 10 of 14 (90262)
03-04-2004 10:57 AM
Reply to: Message 9 by PaulK
03-04-2004 10:23 AM


...and all the natives answer their questions with either a 'yes' or a no' (and not a look of bemusement)?
I had to stop thinking about this for a few hours because it was hurting my brain. I'm ripped and ready for the next round now tho'
If I don't get this in the next few days, would you be so kind as to post your answer (to stop me from doing myself an injury)?
Cheers
PE

This message is a reply to:
 Message 9 by PaulK, posted 03-04-2004 10:23 AM PaulK has replied

Replies to this message:
 Message 11 by PaulK, posted 03-04-2004 11:05 AM Primordial Egg has replied

  
PaulK
Member
Posts: 17825
Joined: 01-10-2003
Member Rating: 2.2


Message 11 of 14 (90263)
03-04-2004 11:05 AM
Reply to: Message 10 by Primordial Egg
03-04-2004 10:57 AM


Assuming that the natives understand the questions :-) they give "yes" or "no" answers. Allowing anything more makes it too easy.
I'll make a note of my answer and post it when you feel the need.

This message is a reply to:
 Message 10 by Primordial Egg, posted 03-04-2004 10:57 AM Primordial Egg has replied

Replies to this message:
 Message 12 by Primordial Egg, posted 03-04-2004 2:36 PM PaulK has not replied

  
Primordial Egg
Inactive Member


Message 12 of 14 (90299)
03-04-2004 2:36 PM
Reply to: Message 11 by PaulK
03-04-2004 11:05 AM


I've worked it out now. See what you mean about the first question being the killer one.
Don't think I'd have been able to do it unless I knew there was a solution for sure - big up yourself.
PE

This message is a reply to:
 Message 11 by PaulK, posted 03-04-2004 11:05 AM PaulK has not replied

  
TechnoCore
Inactive Member


Message 13 of 14 (90332)
03-04-2004 4:10 PM


I get 3 yes/no questions to a native of my choice.
Does this mean that i know from what tribe the native i ask come from?
Or cant i tell any of the three from each other from the beginning ?
So I dont know which one im asking...
What does "native of my choice" else mean ? (little choice it seems

Replies to this message:
 Message 14 by PaulK, posted 03-04-2004 4:19 PM TechnoCore has not replied

  
PaulK
Member
Posts: 17825
Joined: 01-10-2003
Member Rating: 2.2


Message 14 of 14 (90333)
03-04-2004 4:19 PM
Reply to: Message 13 by TechnoCore
03-04-2004 4:10 PM


All it means is that you can decide to ask three different natives, one native two questions and one only one or even ask all three questions of the same native. (In this case the last is not a good idea for reasons that should be fairly obvious).

This message is a reply to:
 Message 13 by TechnoCore, posted 03-04-2004 4:10 PM TechnoCore has not replied

  
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