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Fairly easy brain teaser

  1. Dec 7, 2004 #1
    A man wants to get through to the another room. There are two doors up for the option of entering into the room the man wants into. However, there is a guard in front of each door. One of the guards always tells the truth, and the other guard always lies. How can the man determine which door is the right one without being killed after his first incorrect guess?
  2. jcsd
  3. Dec 7, 2004 #2
    Can you ask more than one question? If so:

    Ask one 'Are you a liar?' They will both answer no. Then ask them something that's true like 'Is 5+5=10?' and the one who tells truth will say 'yes' and the one who always lies will say 'no'. So the one that says 'no' both times is the liar, and the one that says 'no', then 'yes' is the one who tells the truth.

    Or you could ask them 'will you answer this question?'
    Last edited: Dec 7, 2004
  4. Dec 7, 2004 #3
    You ask one of the guards,

    "if i were to ask the other guard which door is the right one, what would he say?"

    For example, the correct door is the door on the left, so if you asked the truth telling guard, he would say, "The other guard would say, the door on your right"

    If you asked the liar, he would say "The other guard will say, the door on your right" He says this, cause he always lies.

    Easy as pie.

    BTW i didn't put it in white, cause its like the 3rd response. If people didn't want the answer, they shouldn't've scrolled down.
  5. Dec 7, 2004 #4
    Okay that works as welll
  6. Dec 7, 2004 #5
    haha...well 'Noticeably F.A.T.' got the exact answer

    almost so exact it seems like he knew it

    but nevertheless, good job
  7. Dec 7, 2004 #6
    Couldn't the man just ask the guard what the door's color is?
  8. Dec 7, 2004 #7
    That depends on the colors of the doors though. eg. If one door is red and one is blue...
  9. Dec 7, 2004 #8
    But that lying guard will lie no matter what, right? So if you point at the blue door and ask the guard what color it is, the guard would either lie and say it's red, or tell you what it's true color is.
    Last edited by a moderator: Dec 7, 2004
  10. Dec 7, 2004 #9
    Yeah, but if you ask what color the correct door is... the lieing guard will say color a and the one who tells the truth will say color b.
  11. Dec 7, 2004 #10
    Okay, I think I misunderstood the question.

    There are two doors: one that leads to the right room and one that leads to the wrong room. Each door has a guard, and the guard either always lies or always tells the truth. Do you want to go into the door guarded by the guard who always tells the truth, or do you want to find out which door leads to the right room?
  12. Dec 7, 2004 #11
    'How can the man determine which door is the right one...' I interpret that as the man wanting to find out which door lead to the right room.
  13. Dec 7, 2004 #12
    Ah. I did misread it. :smile:
  14. Dec 8, 2004 #13
    anyone notice this is asked in the "Labyrinth" movie?
  15. Dec 8, 2004 #14
    Your right he did seem to know it rather than solve it,
    but the way you proposed the problem in post 1,
    askey has just as good a solution.

    The set up needed to include that you are allowed only one question of only one gaurd. They will kill you if you try ask another.

  16. Dec 8, 2004 #15
    ok sorry for the confusion

    there are two doors, both lead into different rooms

    your objective is to get into the right room through one of the doors

    however, u have dont know which door is the right one

    there are guards guarding both doors. One guard always tells the truth, one guard always lies.

    you have one question, a yes or no question, that u can ask the guards to figure out which door is the right one.

    You ask what would the other guard pick (for simplicity's sake, doors 1 and 2)
    the guard that always tells the truth would say door 2, the wrong door, because its the door that the lying guard would say
    the guard that always lies would tell the opposite of what the other guard would say, door 1, so he would say door 2.

    So at hearing them both say door 2, u pick door 1 and youre right.

    there may be different possible ways, but this is what i heard it as
  17. Dec 9, 2004 #16
    Yes, another solution is asking:
    "what would you answer if I asked you which is the right door?"

    If the right door is door 1:
    The liar (who would say door 2) will lie and say: "door 1"
    The truth-teller (who would say door 1) will speak the truth and say: "door 1"

    This would seem a more reasonable question because whoever you ask you always get the right answer.

    (This question has been asked here many many times, and is indeed also asked in the movie "Labyrinth")
  18. Dec 9, 2004 #17
    no that does not work
    the liar would answer door 2, because he's lying
  19. Dec 10, 2004 #18


    User Avatar
    Science Advisor
    Homework Helper

    Well then maybe he would give the wrong answer about asking the other person! The entire basis of these problems is that the guard HAS TO DO THE OPPOSITE OF THE TRUTH.

    He must do the opposite of himself, which would be the opposite.

    If his intention is to deceive, no question will work.
  20. Dec 10, 2004 #19

    I'd just put my hand on a door and ask the guard which door my hand is on. the liar will say the other door...
  21. Dec 10, 2004 #20
    Yes it does work.
    If the liar would say "door 2" he would not lie.
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