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A truth teller's Love Triangle


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7 replies to this topic

#1 BMAD

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Posted 16 October 2013 - 05:50 PM

Here is the story of three unhappy people: Angelica, Bernardo, and Cameron. Angelica and Cameron have been friends since childhood. Cameron is hopelessly in love with Angelica, but Angelica has always thought of Cameron as "just a friend".

During high school, a new boy, Bernardo, moves into the area. Bernardo immediately catches the attention of Angelica, who falls head-over-heels for him. However, Bernardo is not interested in women--he is strongly attracted to Cameron. Cameron, of course, is jealous of Bernardo, because he has stolen Angelica's love away. Angelica is angry at Cameron, because she feels that Bernardo's lack of attention to her is Cameron's fault. Bernardo is jealous of Angelica, who recieves all of Cameron's attention. What are these three to do?

 

(this is a rhetorical question--there is no need to answer it)

 

One day, you meet them, all together in a chat room. They are all using nicknames: Uberkewl, Vaxxipaxx, and Willywutang (in no particular order). Because they are so jealous and screwed-up, each of them will only answer a question truthfully only if:

  1. one of your last two questions was to their sweetheart, and
  2. your last question wasn't to the person with whom they are upset.

Otherwise, they will answer spitefully--giving you the answer that will confuse you the most.

Your task is to figure out who is who. Is it possible? If so, how many questions might you have to ask?

 

And of course you cannot ask them for their name, gender, or where they are from.


Edited by BMAD, 16 October 2013 - 05:52 PM.

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#2 bonanova

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Posted 16 October 2013 - 08:11 PM

Can you ask about the other people?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 BMAD

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Posted 16 October 2013 - 09:15 PM

yes. you can ask any question about another person.


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#4 Kalamadorel

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Posted 17 October 2013 - 07:48 PM

Assuming they won't lie and give correct answers even if they're not compelled to tell the truth.

 

Spoiler for Solution


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#5 plasmid

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Posted 24 October 2013 - 05:52 AM

I believe that a spiteful answer could be truthful if the person you're asking thinks that telling the truth will screw up your strategy. (Otherwise the problem would be rather trivial.) I'll also assume that you can't pull shenanigans like "Ask both V and W such-and-such a question simultaneously, and then ask U whether the sky is blue, and then you can be assured that U must answer the next question truthfully." But correct me if I'm wrong about that.

The best I can do is determine one person's identity. And not the person of my choosing, just some person out of the three.
Spoiler for

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#6 ThunderCloud

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Posted 28 October 2013 - 04:15 AM

Spoiler for If spiteful answers are not truthful...


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#7 Prime

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Posted 28 October 2013 - 06:06 AM

Maybe I am misinterpreting the OP, but...

Spoiler for too simple?


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Past prime, actually.


#8 plasmid

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Posted 29 October 2013 - 06:40 AM

If a spiteful answer cannot be factually correct, then the problem is easy.

If a spiteful answer can be correct as long as the person thinks they can confuse you by giving a correct answer, AND if you're not allowed to do stuff like address a question to multiple people simultaneously, or ask a question using a real name instead of a username (for example, ask "O Angelica, where art thou?" and then ask Uberkewl "Who is Cameron?" knowing that the previous question went to Angelica), then I suspect that it's not possible to determine everyone's identity.

My suspicion of impossibility is based on what looks like an unbeatable strategy to conceal the truth. Suppose (without loss of generality) that Angelica is Uberkewl, Bernardo is Vaxxipaxx, and Cameron is Willywutang. If you ask a question and they are forced to tell the truth, then they will of course tell the truth. However, if they are not forced to tell the truth, then they will instead consider the alternate scenario where Angelica is still Uberkewl, but Bernardo is Willywutang and Cameron is Vaxxipaxx. If they would be forced to tell the truth if this alternate scenario were true, then they will tell what would be a truthful answer under that alternate scenario. If they would not be forced to tell the truth under either scenario, then they will just answer with "lol".
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