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Myth: A New Age CYOA

Discussion in 'Choose Your Own Adventure Land' started by Fangshi, Jan 15, 2014.

  1. Smashing Axe Arcane Patron

    Smashing Axe
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    I've gone over this before as part of a logic course. So I should probably stay out.

    I will say though that the first thing you want to do is to eliminate one of the three as not being random.
     
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  2. Nevill Arcane

    Nevill
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    Ok, so doing it in 4 turns is easy. The question that needs to be asked to each golem is this:

    - If I asked the other golems if you speak the truth, would they always reply in high tone no matter how many times I ask (e.g. if and only if they aren't speaking randomly)?

    A liar would answer this in high tone - if it means 'yes', then 'would always reply yes' part would be wrong, so the liar would answer that it is correct; and if it means 'no', then he would protest. Either way, the tone stays the same.

    Similarly, a truth-teller would always answer in low tone. The random golem would answer at random.

    Now, we would have either this 1) A: high tone; B: high tone; C: low tone, or this 2) A: high tone; B: low tone; C: low tone. If 1, then C is the one telling the truth. If 2, then A is a guaranteed liar, and we can ask him a simple question about, say, C - "Is C always telling the truth?". If he says no, then C is our guy, if he says yes, then it's B.

    There must be a way to unite some of these questions in a single construct.

    Sure. How do you do it in 1 question, though?

    Do you know the solution?

    Edit: and I missed the fact that we still don't know the meaning of high and low tones. So my solution is actually 5 turns long. Ideas how to optimize it would be welcome.
     
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  3. Smashing Axe Arcane Patron

    Smashing Axe
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    Just ask a question that true and false cannot answer but random can.
     
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  4. Kz3r0 Arcane

    Kz3r0
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    Just for curiosity' sake:
    1-A Bronze Golem
    2-B Silver Golem
    3-C Golen Golem
     
    Kz3r0 rolled 3-sided di(c)e: Which one always says the trut Total: 2
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  5. Nevill Arcane

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    Smashing Axe, are you sure your solution works?

    I am trying to come up with one that utilises something akin to the liar paradox, but the problem with questions that are neither true nor false is that the random golem can't answer them, too. It may lie or tell the truth, but it still operates under the same rules.

    And we need to address it to the right creature, too. What if you address it to the one that is not random? You'll learn that it isn't... and that would be it.
     
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  6. Zero Credibility Arcane

    Zero Credibility
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    Ok, maybe it's just my lack of sleep, but I admit I don't see this. How can you eliminate any of them if they both say no? Maybe A is always telling the truth (and C is a lying bastard while B is random), maybe B is (and A is random), maybe C is (while B is random). Or am I misunderstanding the problem or what you are saying here?
     
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  7. treave Arcane Patron

    treave
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    It does. Without giving too much away, the hint lies in random being random, as stated in the update.
     
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  8. Kz3r0 Arcane

    Kz3r0
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    I am not very lucid too.
    In the case of two noes B can be the one that always says the truth too.
    So we are back to square one.
     
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  9. Azira Arcane Patron

    Azira
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    I've googled the riddle, so I probably should also keep my mouth shut. :roll:
     
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  10. Nevill Arcane

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    So basically, if we guess the magic question for the random golem, it is easy to do it in 3 turns.

    Solution 1:
    1. Ask golem A the magic question
    1a. If A is random, proceed with the trivial solution.
    2. If A is not random, ask golem B the same question. This invariably determines the random golem.
    3. Proceed as in 1a.

    Solution 2:
    1. Ask golem A the question as in the 5-turn solution.
    2. Ask golem B the same question.
    3a. If (A=lt, B=lt, C=?), ask B the magic question, pick the non-random golem.
    3b. If (A=ht, B=lt, C=?), ask C the magic question, pick the non-random lt-option.

    I am sorry, I am clueless as to how to determine the random guy in just 1 question. I haven't even got a clue to what the question is in the first place.

    Fangshi, how resistant are those golems to division by zero? :lol: ;) Because all I have is taking two sequences of 1 and -1 corresponding to yes or no answers, having two of the guys sum their results over an infinite amount of answers to the same hypothetical question and having the third guy divide by the limit of the resulting sum. And then comparing the result to zero to turn it into a simple yes or no question.

    Yes, I lack imagination that much. :(
     
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  11. Zero Credibility Arcane

    Zero Credibility
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    So, everyone that knows the answer here is keeping quiet. I hope you guys will at least say something if the rest of us get it wrong. You are participating and not just spectating here, right?

    Anyway, going on the hint that we need to find one that isn't random, how about this question:

    Golem X, if I asked the other two if you always tell the truth, would their answers be the same or not?

    If X is not the random golem, he can't answer that one because he doesn’t know the answer himself (because he doesn't know how the random golem will answer) and can't tell the truth or lie. If he is random he can because he would know the answer (and wouldn't care about it anyway).
     
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  12. Smashing Axe Arcane Patron

    Smashing Axe
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    Don't have "or not" with that first question, if you want to be really pedantic the correct answer will be yes regardless of what the other golems would answer. You also need to work out how to phrase the later question/s in a manner that incorporates our ignorance of what yes and no mean.
     
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  13. Azira Arcane Patron

    Azira
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    I've googled the riddle, found a solution which will take me some time to understand.. Apparently, this is a riddle that's usually solved in three questions, if you get the sequence right? Haven't found a two-questions solution yet.

    Seems the trick lies in how you phrase the questions, and taking into account we do not know if high-pitch/low-pitch is yes or no, we need to ask about the pitch in the question itself.

    Nevill is on to something.
     
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  14. Smashing Axe Arcane Patron

    Smashing Axe
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    You can do it in two, either just from luck using the more standard method, or from two overly specific questions.
     
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  15. Jester Arbiter

    Jester
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    I assume Golems know each other.
    We Can ask 5 questions before telling one to give its gift?
    If so:

    If i ask question will golem C tell the truth? golem A,B.
    There are 3 answers Yes, No, Silence.

    If we ask this question we will get:
    There is no YY answer.

    SS - Answers given by Liar and True, because they do not know answer of random.
    Asking Random a question. He will answer Y. Ask either of L or T did Golem C answered my last question by Y? True will say Yes, Liar will say No.

    Yes/No, No - We got Random Here.
    Asking Golem C is it possible that Golems A and B give same answer? Liar will say No, True will say Yes.
    If C say Y he is our guy.
    If he say No ask him "Can golem A say lies?" if he will say No it mean its random, iif he will say Y he is True one.
     
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  16. asxetos Augur

    asxetos
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    1st: Golem X, if I asked the other two if you always tell the truth, would their answers always be the same?

    This should count as one question only, since the other 2 golems will not answer at all. X will be the random Golem.

    2nd: Ask one of the two remaining golems: Golem Y, if i ask Golem Z if Golem X is answering in random, what will it answer?
    3rd: Ask the last golem: Golem Z, is Golem X answering in random?
    If Y and Z make the same tone, Y is the truth Golem, else Z is the truth Golem.
     
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  17. Nevill Arcane

    Nevill
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    I don't think it works that way. A question is a question - whether you receive your answer or not, you have asked it.
     
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  18. asxetos Augur

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    Well, then it goes up to 5 questions wich is still valid but we dont roll for the extra reward.
    I guess we can keep it as a last resort until someone finds an optimal solution (i wont bother with google since i am at work).
    It is going to work though, or did i fail a logic check somewhere in there?
     
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  19. Nevill Arcane

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    As far as I see, yes. And in 4 turns, too. We can determine the random golem in 2 questions.

    Still, the 3-turn solution already exists. I wonder if we can upgrade that.
     
    • Brofist Brofist x 1
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  20. Zero Credibility Arcane

    Zero Credibility
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    I think I figured out the 3 step solution. I think. I'll try writing it down.

    1. step is finding one that is not random
    2. step is eliminating the random one and determining the signal that means no
    3. step is finding the correct one

    Here, maybe someone can spot an error if you can make sense of the mess I made (I just barely do):

    Show Spoiler
    Code:
    A: If we ask B will he tell us the truth                                           
                                               
    A    T        F        T    F    R    R                   
    B    F        T        R    R    T    F                   
        h (NO)    h (NO)    -    -    h/l    h/l                   
                                               
    If -: B random                                           
    If h or l: A or C random                                           
                                               
    Answer: -                                                        Answer: h or l                   
                                               
    A: If we ask C will he tell us the truth                        B: If we ask C will he tell us the truth                   
                                               
    A    T        F                                                        B    T        F        T    F   
    C    F        T                                                        C    F        T        R    R   
        h (NO)    h (NO)                                                        h (NO)    h (NO)    -    -   
                                               
    If h: h means NO                                                If h: A random; h means NO                   
                                                                    If -: C random; previous h means NO                   
                                               
    Answer: h                                                        Answer: h                                                        Answer: -
                                               
                                               
    A: What will C tell us if we ask him if he has the gift?        B: What will C tell us if we ask him if he has the gift?        A: What will B tell us if we ask him if he has the gift?
                                               
    A    T        F                                                    B    T        F                                                    A    T        F
    C    F        T                                                    C    F        T                                                    B    F        T
        l (YES)    h (NO)                                                    l (YES)    h (NO)                                                    l (YES)    h (NO)
                                               
    If l: A                                                            If l: B                                                            If l: A
    If h: C                                                            If h: C                                                            If h: B    

    edit: ok, to present this in a slightly more readable format:

    Show Spoiler
    1. Ask A: If we ask B will he tell us the truth?

    The answers can be low or high tone or silence. If it is silence we know that B is the random one (because A doesn’t know the answer). If it is tone, we know that either A or C are the random ones (if it is A, it can be either "no" tone or "yes" tone, if it is C, it will be "no" tone). There are two options now:


    If the answer to 1) was silence:

    2. a) Ask A: If we ask C will he tell us the truth?

    Since we know that B was the random one, this question serves to determine the "no" tone, because that is the only possible answer to that question.


    If the answer to 1) was a tone:

    2. b) Ask B: If we ask C will he tell us the truth?

    We know that B isn't the random one. If the answer to this question is a tone, C isn't random either (again, because B knows it) and the random one must be A. And since the only possible answer to this question is no, we determined the "no" tone.

    If the answer to this question is silence, the random one must be C. But in that case the question 1) must have been answered with a "no" tone, so we have again determined it.


    And now that we have eliminated the random one and determined what the "no" note sounds like:

    3) Ask one of the remaining ones that aren't random: What will the other non-random golem say if we ask him if he has what we are looking for?

    If he answers yes to that, we have a winner. He will truthfully say that the other guy would lie to us. If he answers no, he is lying himself and the other guy is the one we are looking for.

    There, I hope that makes some kind of sense.
     
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  21. Nevill Arcane

    Nevill
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    Zero Credibility, the easiest 3-step solution would be asking A about B, B about C, and C about A this question:
    - If I asked the other golem if you speak the truth, would they reply in high tone?
    One of them will be silent. That determines the random golem, and the question can find out who is who in a non-random pair.

    I think I got it.

    Solution? (open)
    Let's ask A this, first:
    - Golem A, if I took you and golem B and asked it first if you speak the truth, and then you second if what he just spoke of was true, would you both reply in the same high pitched tone?

    Now, there are the following possibilities:

    1) If B is random, then A would be unable to answer, because he would have no way of knowing what would B answer.

    This deserves a better explanation, since this is where I was mistaken the first time.
    Suppose high tone means 'yes', A is a liar and B is random. Then the following is possible:
    These lead to different results, and A has no way of knowing which one would be correct.
    Similarly, suppose high tone means 'no', A is a liar and B is random:
    Suppose high tone means 'yes', A is a truth-sayer and B is random. Then the following is possible:
    Similarly, suppose high tone means 'no', A is a truth-sayer and B is random:
    This only works if A's answer depends on what B says.

    A's silence allows us to know the random golem in a single question, and therefore find the answer with the second one:
    - Golem A, if I asked golem C if you speak the truth, would it reply in a high pitched tone?
    If A replies in low tone, he speaks the truth, otherwise it's C.

    2) If A is random, then he would answer randomly, however, B would still not be random. This is important.

    3) If A is a liar, and B in not random, then B speaks the truth.

    Therefore, if high tone means 'yes':
    would both result in the same answer and in the same low tone. So, they would not both answer in the same high tone. Since A is a liar, he would then reply 'yes' to our question - that is, answer in high tone.

    If high tone means 'no':
    They would both answer in the same high tone. Since A is a liar, he would reply 'no' - again, in high tone.

    4) If A tells the truth, and B in not random, then B lies.

    Therefore, if high tone means 'yes':
    would both result in the same answer and in the same low tone. So, they would not both answer in the same high tone. Since A is a truth-teller, he would then reply 'no' to our question - that is, answer in low tone.

    If high tone means 'no':
    They would both answer in the same high tone. Since A is a truth-teller, he would reply 'yes' - in low tone.

    So if A answers in low tone, then he either speaks the truth, or is random. If A answers in high tone, then he either lies, or is random. In both of these cases B is not random.

    Thus we only need to ask B the same question about C.
    - Golem B, if I took you and golem C and asked it first if you speak the truth, and then you second if what he just spoke of was true, would you both reply in the same high pitched tone?

    If B is silent, then C is random, and A is not. Therefore if A is a liar, then B is the answer, if he is a truth-teller, then we have the answer already.

    If B answers in high tone, then B is a liar, and C is not random, and therefore is the truth-teller.
    If B answers in low tone, then B speaks the truth.

    When all is said and done, there are only 2 questions asked.

    Somebody please double-check this. :)

    Edit: aaand there is a mistake. Of course. If B is random, then to find out if they both reply in high tone we don't need to know what B would say. If A does not reply in high tone, the answer is automatically no. *sigh*.

    Edit2: Ooh! I think this might be circumvented if we make the second golem in the pair go first, and then have the first determine the truthfulness of his answer. If the second is random, the first one would not be able to predict what he would say.
     
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  22. asxetos Augur

    asxetos
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    For your 3-step solution, lets say:
    - A answers high
    - B is silent
    - C doesnt matter (because it is random)

    If A = liar and high = No Then A should say Yes (but yes = low, so this path cannot exist)
    If A = liar and high = Yes Then A should say Yes (valid path)
    If A = truth and high = No Then A should say Yes (but yes = low, so this path cannot exist)
    If A = truth and high = Yes Then A should say Yes (but yes = low, so this path cannot exist)

    It will work.
     
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  23. Nevill Arcane

    Nevill
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    Who are you replying to?

    The questions would be from A to B, from B to C, and from C to A.

    A answers high - he is either a liar or random. B is silent, so C is random. Therefore, A is a liar, and B is a truth-sayer.

    If A should say Yes, and high=No, then A can't answer high. So here is the contradiction.
     
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  24. asxetos Augur

    asxetos
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    But what i posted means that A can be either liar or truth.
    You sir are correct.
     
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  25. Nevill Arcane

    Nevill
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    This is not a valid path.
     
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