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Math Help - A Fun, Yet Tricky Problem

  1. #1
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    A Fun, Yet Tricky Problem

    "A hiker is lost in the mountains but stumbles into an area where it is known that all inhabitants are either True-tellers or Liars, meaning that an individual either always tells the truth or always lies. She meets a man at a fork in the road and wants to learn the way to the nearest village by asking only one question. Explain why she will not learn the way to the village by asking any of the following questions:

    a.) Are you a truth-teller AND does the left fork lead to the village?
    b.) Are you a truth-teller OR does the left fork lead to the village?
    c.) If you are a truth-teller, does the left fork lead to the village?
    Last edited by PhilipJ; May 9th 2006 at 09:40 PM.
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  2. #2
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    If you want to escape,
    "If I asked someone who was different in saying truths what would he say as the road that leads to the path?"

    If you want to tear a hole in the spacetime countinuum,
    tell him to say "I am a liar!"*


    *)Quoted in Greece by Euripedes.
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  3. #3
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    Thanks..though that was of no help! Anyone have a serious reply to this?
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  4. #4
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    Some more information that might help:

    "When considering how a Liar and Truth-teller will answer the question being asked, you need to figure out the truth or falsity of the whole question, not each piece of the question.

    That is, when the AND question is asked, you need to use the AND truth table to consider all the cases and then if the AND statement is True, the Liar will say No , the Truth-teller will say Yes. If the And statement is False, the Liar will say Yes, the Truth-teller will say No."
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  5. #5
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    So part a.):
    if they are a truth teller and it's the left, he will say yes.
    if truth teller and right, no.
    if liar and left, yes.
    if liar and right, yes.

    b.) if truth teller and left, yes.
    if truth teller and right, yes.
    if liar and left, no.
    if liar and right, yes.

    c.) how would that work??? they're not supposed to answer unless they're a truth-teller? So, what I'm asking, what is the person SUPPOSED to do if they're not a truth-teller? Are they meant to answer regardless? Help?

    I think I have a.) and b.) correct.
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  6. #6
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    Continuing

    C) This question does nothing because the liar would say he's a truth teller and answer the question anyway.
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  7. #7
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    i am pretty sure this has something to do with Boolean rules.

    ".....Explain why she will not learn the way to the village....."
    NOT = inverter "1=0 and 0=1"

    a.) Are you a truth-teller AND does the left fork lead to the village?
    liar : yes (1) yes(1) = 1>NOT> = 0 false reply
    truth: yes(1) no(0) = 0>NOT>= 1 true reply.
    b.) Are you a truth-teller OR does the left fork lead to the village?
    Only a liar will be able to reply you because "yes" which is a lie statement matches the question 1&1 = 1>NOT>0 negative reply
    and a truth-teller cant because its a "yes;no" answer.
    c.) If you are a truth-teller, does the left fork lead to the village?
    "NOT" reply
    liar say yes(1) >NOT>(0) = false
    true say no(0) >NOT>(1) = true....

    AND Truth table OR Truth table
    0&0 = 0 0&0 = 0
    0&1 = 0 0&1 = 1
    1&0 = 0 1&0 = 1
    1&1 = 1 1&1 = 1
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  8. #8
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    The way to the nearest village is not left or right but from where the hiker came.

    beens
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  9. #9
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    "If you weren't the kind of person you are, would you say the village is to the left?"

    LIAR (village to left): No.
    TRUTHTELLER (village to left): No.
    LIAR (village to right): Yes.
    TRUTHTELLER (village to right): Yes.

    Ask this, and no matter what kind of person the local is, No means the village is to the left, and Yes means it's to the right.
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  10. #10
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    We can come up with questions that would make him/her tell us the truth .....but.......answers should be based on the questions GIVEN....not so?

    beens
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  11. #11
    Super Member malaygoel's Avatar
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    Quote Originally Posted by PhilipJ
    "A hiker is lost in the mountains but stumbles into an area where it is known that all inhabitants are either True-tellers or Liars, meaning that an individual either always tells the truth or always lies. She meets a man at a fork in the road and wants to learn the way to the nearest village by asking only one question. Explain why she will not learn the way to the village by asking any of the following questions:

    a.) Are you a truth-teller AND does the left fork lead to the village?
    b.) Are you a truth-teller OR does the left fork lead to the village?
    c.) If you are a truth-teller, does the left fork lead to the village?
    She had no basis on which she could tell whether the man is a liar or a truth teller.She asked anyone of the questions to the the man, man either answered yes or no, but she could not deduce anything because in every question there are two statements and she is sure about none of them.
    If she had been sure about one of them, then she could deduce the validity of the other statement.
    For example, if she could have asked the following question
    Are you flying in a plane and does the left fork lead to the village?
    Here, she is certain about one question and she could find her way from the answer,whether the man is truth-teller or not.

    KeepSmiling
    Malay
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