Death By Irony
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Post by Death By Irony on Oct 14, 2007 21:48:21 GMT -5
- Flavor -
Nobody knows why, but the little Island of Liars has become quite the popular tourist spot lately, with everybody and their brother flocking to there to buy various overpriced souveniers like the "I went to the Island of Liars and all I got was this stupid T-shirt" t-shirt.
A sociologist who had been living among the natives for some time noticed that contrary to what's being advertised, not all of them are pathological liars.
He's published some of his case studies, but perhaps you can deduce his findings with a little logical reasoning, too.
- How to Play the Game -
I will post various logic puzzles in the thread, and anybody can participate by PMing me the answer. All correct answers received before deadline will get an Exalt from me, with bonus Exalt(s) for explaining how you got to the answer.
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Death By Irony
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Post by Death By Irony on Oct 15, 2007 6:55:22 GMT -5
Case Study #1
Tom, Dick, and Harry are three drinking buddies that the sociologist befriended and has since been stalking studying as part of his research. When asked about their respective truth values, they answered thus...
Tom: Harry is a liar. Dick: Either Tom or Harry speaks the trurth. Harry: Bah, we are all full of lies.
That seemed fairly straightforward, so the sociologist took his notes about them and moved on. Worth 1 exalt: What are Tom, Dick, and Harry's truth values?
Later, the sociologist discovered through independent means that all three men were married, so he wanted to ask about the truth values of their wives. He went to the bar and found one of the three friends there, but he couldn't remember this particular friend's name and he'd left his notebook at home. Worth 3 exalts: What's the fewest number of questions in which the sociologist could ask this friend to get his answer?
(Answers due via PM at midnight EST Monday, Oct 22.)
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Post by CatInASuit on Oct 15, 2007 7:19:40 GMT -5
Case Study #1 Tom: Harry is a liar. Dick: Either Tom or Harry speaks the trurth. Harry: Bah, we are all full of lies. Tom: Tells truth Dick: Tells Truth Harry: Lies
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Post by CatInASuit on Oct 15, 2007 7:20:53 GMT -5
Sorry dotchan, I missed the bit about the PM.
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Death By Irony
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Post by Death By Irony on Oct 15, 2007 7:25:51 GMT -5
Sorry dotchan, I missed the bit about the PM. You get an exalt anyway for being the first to answer. But since you did spoil the first question for everybody, do you mind sitting out for Part B?
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Post by CatInASuit on Oct 15, 2007 7:31:12 GMT -5
Sorry dotchan, I missed the bit about the PM. You get an exalt anyway for being the first to answer. But since you did spoil the first question for everybody, do you mind sitting out for Part B? I'll leave them alone. I love solving problems like this though. Good luck all.
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Blaster Master
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Post by Blaster Master on Oct 16, 2007 9:39:33 GMT -5
Well, since Cat already spoiled part A, I'll give the convoluted answer to it in First-Order Logic. We can rewrite the statements as the following, assuming that by "liars" you mean MUST be false, not potentially false. T <--> ~HD <--> T & ~H | ~T & HH <--> ~T & ~D & ~HThrough conjunction reduction, we can say that H <--> ~T & ~D & ~H can only be valid if H <--> ~H is as well. This is not a valid statement; therefore H must be false and at least one between T and D must be true to maintain the validity. Thus, knowing the truth valud of H, we can also determine that T is True by using reverse implication on T <--> ~H, because ~H must be true, therefore T must be true. Finally, D <--> T & ~H | ~T & H can be reduced to D <--> T & ~H through disjunction elimination. If we plug in the truth values for T and H, then the value of T & ~H is true, therefore D must also be true. Hence: T = TrueD = TrueH = FalseI'll work out the answer for part B in a PM for you.
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Death By Irony
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Post by Death By Irony on Oct 16, 2007 10:27:14 GMT -5
Clarification on Part B:
The sociologist wants to know whether Tom, Dick, and Harry's wives are truthtellers or liars, and he met one of them (without being sure which one he's talking to) at the bar.
Still, the correct answers on how to determine whether Tom, Dick, or Harry is speaking to him will also get exalted.
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Blaster Master
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Post by Blaster Master on Oct 16, 2007 10:35:52 GMT -5
Clarification on Part B: The sociologist wants to know whether Tom, Dick, and Harry's wives are truthtellers or liars, and he met one of them (without being sure which one he's talking to) at the bar. Still, the correct answers on how to determine whether Tom, Dick, or Harry is speaking to him will also get exalted. I'm still confused... so he ran into one of their wives, and he wants to know the truth values of each of the wives? If that's the case, are we trying to determine whose wife she is, or just the truth value of all of the wives? Or did we run into one of the guys and we want to know the truth value of the wives AND we don't knwo to whom we're speaking?
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Death By Irony
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Post by Death By Irony on Oct 16, 2007 10:38:03 GMT -5
I'm still confused... so he ran into one of their wives, and he wants to know the truth values of each of the wives? If that's the case, are we trying to determine whose wife she is, or just the truth value of all of the wives? Or did we run into one of the guys and we want to know the truth value of the wives AND we don't knwo to whom we're speaking? Option 3: We ran into one of the males (not knowing which), and we want to know the truth values of the wives.
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RoOsh
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Post by RoOsh on Oct 16, 2007 14:19:02 GMT -5
Jesus, we have a week of deadlines? that's too long! I was thinking it was like 48 hours max
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Post by RoOsh on Oct 16, 2007 14:19:21 GMT -5
Can you at least confirm the right answers as you get them?
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Merestil Haye
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Post by Merestil Haye on Oct 17, 2007 15:26:14 GMT -5
4 questions is easy. I'm trying to work out whether there is a way of doing it in 3 or not that gets the answer for all possible combos.
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Death By Irony
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Post by Death By Irony on Oct 23, 2007 6:52:10 GMT -5
Went to bed forgetting about this game.
I thought I had a possible answer, but I went over the logic in my head again this morning and I don't think it's the right answer.
(Yes, this wasn't a pre-constructed logic question, although maybe something similar does exist out there.)
Roosh and Blaster Master got exalts for answering how we figure out the truth value of the friend; after that, it'd be trivial to ask a second question determining whether the wives' are truthtellers.
But maybe there's one question you can where you'd be confident of the answer regardless of which friend you're asking.
Until this morning, I thought it might be: "If you were Harry, what would you say about the truthfulness of your wives?"
Now, Harry, if asked directly about the truth values, would of course lie. But since he's being asked about his potential answer, he would lie about THAT, and inadvertantly give the truth about the wives.
However, I'm no longer certain that Tom and Dick would give the same answer.
This question will remain as an open mental exercise.
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Post by RoOsh on Oct 23, 2007 11:40:23 GMT -5
Tom and Dick would truthfull respond how Harry would. Which is Harry would lie. Therefore The correct answer Harry would give would be a lie.
so if Tom and Dick were to truthfully respond as Harry would, they would have to state the lies as well.
Because they honestly know that Harry would lie. So if he's a liar, he gives false answers, therefore to give answers as a liar would, you would have to give false answers as well.
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Death By Irony
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Post by Death By Irony on Oct 23, 2007 12:12:54 GMT -5
Case Study #2 Bob, another frequent patron of the same bar where Tom, Dick, and Harry like to drink, changes truth values when intoxicated. (Sounds like some people we know in the real world. ) Anyway, for 1 exalt, what's a non-trivial way to determine Bob's current truth value? (i.e., a question like "What is 2 plus 2" would not qualify.) For an additional exalt, could you word this question to also determine whether he is drunk or sober? Answers due via PM 11:59 pm EST Friday October 26.
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Death By Irony
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Post by Death By Irony on Oct 23, 2007 12:20:24 GMT -5
Re: Case Study #1...
Let's say the wives' truth values are T, D, and H respectively.
If Harry were asked for the truth values directly, he would answer "Not(T), Not(D), and Not(H)".
So if Tom and Dick were asked for Harry's answer, they would answer (truthfully): "Not(T), Not(D), and Not(H)".
But if Harry were asked for his own answer, he would falsely answer "Not(Not(T), Not(D), and Not(H)"...that is, "T, D, and H".
Argh, where's that refresher on boolean logic when I need it?
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Post by RoOsh on Oct 23, 2007 12:23:23 GMT -5
What constitutes trivial?
Such as just asking him "Are you bob?"
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Merestil Haye
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Post by Merestil Haye on Oct 23, 2007 12:24:49 GMT -5
I think you have to ask one question per wife. You can't get it down to less than that. But I'm fairly sure that you can pose it to force the speaker to answer in the same way whether he is reliable or not.
(A reliable person will answer "yes" to the question "Does 2+2 equal 4?")
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Post by RoOsh on Oct 23, 2007 12:27:05 GMT -5
Re: Case Study #1... If Harry were asked for the truth values directly, he would answer "Not(T), Not(D), and Not(H)". So if Tom and Dick were asked for Harry's answer, they would answer (truthfully): "Not(T), Not(D), and Not(H)". But if Harry were asked for his own answer, he would falsely answer "Not(Not(T), Not(D), and Not(H)"...that is, "T, D, and H". I see what you're saying now. Gotcha. Why not just phrase the question then as such: "If you're Harry, tell me the truth value of the Wives, If you're tom or Dick, tell me the Truth Values that Harry would give?" Though at that point for Harry to lie, he would have to then answer the question as Tom/Dick would do it. And to do that, is to give thier answers.
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Merestil Haye
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Post by Merestil Haye on Oct 23, 2007 12:28:29 GMT -5
What constitutes trivial? Such as just asking him "Are you bob?" If you ask that you get a "Yes" answer if you're speaking to Harry. If you're speaking to Tom or Dick, the answer is "No." Actually, you can ask that and then ask what the truth values of the womenfolk are. That's better than 3 questions.
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Death By Irony
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Post by Death By Irony on Oct 23, 2007 12:39:55 GMT -5
Re: Case 2 What constitutes trivial? Such as just asking him "Are you bob?" It counts as trivial if based in factual information. You know that Bob's name is such, so that's not an eligible question.
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Merestil Haye
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Post by Merestil Haye on Oct 23, 2007 12:43:35 GMT -5
*bh*
I have the question to ask.
The question to ask is is "If I were to ask you what the truth value of each of your wives was, what would you say?"
The actual answer to the question "What are the truth values of Tom Dick and Harry's wives?" are "T, D and H."
If you ask Tom what the truth values of the three men's wives are you get the answer "T, D and H." Therefore if you ask him "If I were to ask you what the truth value of each of your wives was, what would you say?" he would answer "T, D and H."
The same applies if you are asking Dick.
If you ask Harry what the truth values of the three men's wives are, the one answer he cannot give is "T, D and H." Therefore if you ask him "If I were to ask you what the truth value of each of your wives was, what would you say?" he would answer "T, D and H," because he has to lie about what he would say if you asked the question directly, and "T, D and H" is the only answer he cannot give when asked the question directly.
*Completes revision to the actual question.*
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Death By Irony
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Post by Death By Irony on Oct 23, 2007 13:03:58 GMT -5
*ponders* *ponders* *smoke starts emitting from ears* Huh, you're right. (And this is why nobody invites the sociologist to any parties. ) 2 exalts for mhaye!
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Post by RoOsh on Oct 23, 2007 13:10:30 GMT -5
Hey... Mhaye's was the same thing as my previous answer of " Why not just phrase the question then as such: "If you're Harry, tell me the truth value of the Wives, If you're tom or Dick, tell me the Truth Values that Harry would give?" Though at that point for Harry to lie, he would have to then answer the question as Tom/Dick would do it. And to do that, is to give thier answers."
Though his was stated more clearly.... But i swear... that's what I was going for.
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Death By Irony
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Post by Death By Irony on Oct 23, 2007 13:19:19 GMT -5
Hey... Mhaye's was the same thing as my previous answer of " Why not just phrase the question then as such: "If you're Harry, tell me the truth value of the Wives, If you're tom or Dick, tell me the Truth Values that Harry would give?" Though at that point for Harry to lie, he would have to then answer the question as Tom/Dick would do it. And to do that, is to give thier answers." Though his was stated more clearly.... But i swear... that's what I was going for. Fine, fine...one exalt for Roosh for being on the right track.
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RoOsh
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Post by RoOsh on Oct 23, 2007 13:39:26 GMT -5
I sent you my answer for Bob.
I couldn't do it in 1 question. But I did solve it. Ask me if you have any Qs, as its messy and complicated.
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Death By Irony
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Post by Death By Irony on Oct 27, 2007 10:02:11 GMT -5
Another partial solution for Bob...
Part 1 is similar to the issue of Tom, Dick, and Harry and their wives. All you'd need to do is ask him something to the effect of: "if I asked you whether you are telling the truth right now, would you answer yes"? You could be guarenteed an accurate result either way.
Part 2, I haven't quite figured out how to word a question to determine both truth value AND sobriety in a way that isn't clunky, but all you'd need to do to determine whether he's been hitting the rum would be to ask him: "Do you tell the truth when sober?" or "Do you lie when drunk?"
A sober Bob would answer "Yes" regardless of truth value and a drunk one would answer "No".
(Furthermore, if asked "Do you lie when sober?" or "Do you tell the truth when drunk?", Sober Bob would answer "No" and Drunk Bob would answer "Yes".)
Roosh gets one exalt for being on the right track.
...and btw, because it is getting busier IRL for me and I'm playing two Mafia games and modding the LOLCATS one, I'm going to hold off coming up with any more questions.
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Merestil Haye
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Post by Merestil Haye on Oct 30, 2007 19:03:38 GMT -5
Dotchan, do you mind if I post a few questions?
*starts thinking of new questions.*
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Death By Irony
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Post by Death By Irony on Oct 30, 2007 20:23:52 GMT -5
Dotchan, do you mind if I post a few questions? *starts thinking of new questions.* Knock yourself out.
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