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Prisoner standing next to 2 doors and 2 guards

  1. Aug 21, 2009 #1
    This is really old but some of you might not know it, if you heard it before dont answer.

    Prisoner is put in a room with 2 doors. 1 door leads to freedom, the other to excecution.
    Next to the doors are 2 guards. One of the guards always lies, the other always tells the truth. The prisoner is allowed to ask one of the guards one question to figure out what door leads where. What does he ask?
     
  2. jcsd
  3. Aug 21, 2009 #2
    I've heard this before but I've never seen the solution or worked out the answer. At first glance, it seems to be unsolvable, as you need two pieces of information. You must determine which door is the one that leads to freedom and which guard is which, but either guard you ask has a 50% chance to be either:

    If you ask, "Are you the liar?" the liar would say no, truth teller would say no, and you've gotten nowhere.

    If you ask, "Which door leads to freedom?" the liar would point to execution, the truth-teller would point to freedom, and you've gotten nowhere.


    What's interesting is that nearly every question you ask to either guard about the doors will have opposite answers, but any question you ask about the truth-content of their answer will have an identical answer. So you must ask a question about the door that would make the liar lie about lying, and thus give an identical answer to that of the truth-teller who would tell the truth about telling the truth.


    So you ask, "If I asked you which door leads to freedom, what would your answer be?"

    The liar would lie about the lie he would have given (execution), and point to freedom.
    The truth teller would tell the truth about the answer he would have given (freedom), and point to freedom.
     
  4. Aug 22, 2009 #3
    I thought a little about this,and my best shot for now would be the question:

    "If you were the other guard, which door would you say leads to freedom?"

    They will both point towards the door that leads to an execution, so you pick the other one.

    How?
    The guard that always tells the truth, will be truthful/honest and say what the guard that always lies would have said, so he will point towards the execution door (that would be the answer of the "dishonest" guard).
    The guard that always lies, will lie this time as well, and won't answer what the other guard would answer, so he would also point towards the execution door (that wouldn't be the answer of the "honest" guard, and hence a lie).

    Is this reasoning correct? :)
     
    Last edited: Aug 22, 2009
  5. Aug 22, 2009 #4
    Yeah that's correct. It goes along the same lines as getting the liar to lie about lying.

    Although, it would potentially fail if the two guards didn't have knowledge of the other (the truth guard doesn't know the other always lies and the lie guard doesn't know the other always tells the truth).

    I'd venture that any hypothetical question that asks about a guard's answer in regards to which door is which would be a valid solution. The truth teller would always tell the truth, and the liar would always flip his response. No matter what their answer would be, you could infer which door was which by the answer given, as long as your question was meaningful with respect to the doors.
     
    Last edited: Aug 22, 2009
  6. Aug 22, 2009 #5
    well, these details are usually implied in any riddle.

    but if the 2 guards wouldn't have knowledge of the other, then I think the same type of question will work again, because the honest guard will say "I don't know what the other guard would answer" and the dishonest guard would point towards the wrong door...
     
  7. Aug 22, 2009 #6
    Call me stupid but why the question "If I asked you which door leads to freedom, what would your answer be?" from question "Which door leads to freedom". If he points the bad doors in first question doesnt he lie? Why must he lie about lie ? its not he's job.

    In the answer ''If you were the other guard, which door would you say leads to freedom'' i see also some paradox. ''The guard that always tells the truth, will be truthful/honest and say what the guard that always lies would have said'' So truth teller would give the same answer as liar? So if you give the same answer as a liar doednt it make you a liar too, both you say wrong fact? And if you are forced to quate other person and you quete him where did you lie? For me, the person says a lie and says the truth in the same time. What answer would you get if you asked truth teller ''lie to me''? Same thing.
     
  8. Aug 25, 2010 #7
    ''Prisoner is put in a room with 2 doors. 1 door leads to freedom, the other to excecution.
    Next to the doors are 2 guards. One of the guards always lies, the other always tells the truth. The prisoner is allowed to ask one of the guards one question to figure out what door leads where. What does he ask?'


    I think if you read the actual scenario carefully you'll see that the prisoner is only allowed to ask one of the guards one question. Not, both guards one question. Therefore, I must inform you, ladies and gentlemen, that all your solutions are incorrect, based as they are on a misreading of the above text.
    I will be most interested to see if anyone can come up with an answer to the teaser now!
     
  9. Aug 25, 2010 #8
    Ask:
    Did you know they're serving free beer at the bar for the next 10 minutes?
    Then follow the guard out the door.
     
  10. Aug 26, 2010 #9
    There are 2 guards. Presumably they both exit via the same door - but how do you know that the bar isn't situated near the execution lounge?
     
  11. Aug 30, 2010 #10
    Is not the answer "If I were to ask you which door lead to freedom, which door would you choose?" still a correct answer?

    E.g., You ask the guard who lies and he points to the door of freedom because he has to lie about the lie he would tell if the question wasn't hypothetical.

    Or you ask the truth teller and he honestly answers the question.
     
  12. Aug 30, 2010 #11

    Office_Shredder

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    I think the meta question is legitimate. The guard's job is to lie, he doesn't get to pick what he lies about. If you ask him how we would respond to a question, he should lie about what his response would be.


    There have been two answers given that don't rely on asking both guards so I'm not sure what you're referring to
     
  13. Sep 2, 2010 #12
    But these answers assume that the asker is aware of which guard lies and which one doesn't, but this is not stated in the scenario given. Only by asking both guards a question can this be found - but again, the original scenario does not allow this.
     
  14. Sep 2, 2010 #13
    Nope. Works for both:

    1) Assume we ask the truth teller: "If I were to ask you 'which door leads to freedom?', which door would you tell me?", then he'll point to the correct door. Everything's peachy.

    2) Assume we ask the liar: "If I were to ask you 'which door leads to freedom?', which door would you tell me?" Now, this is a little more complicated. If we had asked him "Which door leads to freedom?", then he would have lied, and pointed to the incorrect door. Therefore, he must lie about his lie. He WOULD have said the wrong door, so he has to LIE about it tell you that he WOULD have said the correct door. Hence, he too must respond with the correct door, and everything's cool.

    DaveE
     
  15. Sep 2, 2010 #14

    BobG

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    Worse yet, you'll be killed in a bar room brawl, making the whole issue moot.
     
  16. Sep 2, 2010 #15
    Well, in your first solution (1) this is only of practical use if you know he is the honest guard - which, according to the scenario, you do not. As for your second solution (2), you have simply strayed into the realms of sophistry by suggesting that the guard must double guess the prisoner because to merely lie would not be true to his given character and that, as you put it, 'he must lie about his lie' in order to be dishonest, an act which actually negates and cancels out his essential dishonesty by leading him to provide the correct answer. This aside, I'm afraid you are completely missing my original point which is actually that the original wording of the scenario that generated this discussion was actually incorrect to begin with. This age-old problem originally allows the prisoner to ask one question to each guard.
     
  17. Sep 3, 2010 #16
    What part of this bizarrely hypothetical situation do you regard as suddenly crossing into the realm of sophistry? The whole situation is ludicrous to start with!

    Those are the rules of the problem. I didn't make them. He MUST lie. It's not his job to mislead me, it's his job to provide me with incorrect information. If my use of his misinformation leads to a successful interpretation, that's not a failure on his part.

    I believe the age-old problem allows you to ask ONE question, not one to each guard. And the age-old solution is to ask: "If I asked the other guard which is the correct door, which would he tell me?" Then, pick the other door. The solution posited above works just as well.

    DaveE
     
  18. Sep 3, 2010 #17
    You're absolutely right - forgive my mischief! The solution is of course to choose the opposite door to whichever guard replies to the question "What would your colleague say if I asked which was the door to freedom?"
     
  19. Sep 6, 2010 #18
    I have the answer below.

    Ask either one of them the following question: Which door would the other guard tell me to go to if I asked him "which door is the good one?". The liar would tell you the truthful guard would say door #2 (we'll assume that's the bad door), because he is lying. The honest guard would say the liar would tell you to go to door #2 as well. So, you just choose the door opposite to the one either of the guards would say the other guard would say.
     
  20. Sep 6, 2010 #19
    This assumes that both of the guards know which door is which.
     
  21. Apr 17, 2012 #20
    You could simply ask 'what is my name?'. If the guard you asked gave you your true name then you go through their door, if the guard you asked gave you the wrong name you know to avoid his door.
     
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