Sunday, October 03, 2004
Door to Freedom
You have been knocked unconscious and kidnapped. You wake up in a bare and dungeon room that contains two identical doors, each guarded by a grim silent guard. A voice on a loudspeaker explains that one of these doors leads to freedom, the other to instant death. You are told that one of the guards will always tell the truth and the other will always lie, but you are not informed which guard is the liar. Nor you know which one speaks truth. You will be permitted to select a guard and ask him only one question that requires a yes or no answer. After receiving the answer to this one question, you must select a door and meet your fate. What question can you ask that will assure your freedom?
Answer:
Ask either guard, "If I asked the other guy if this door you are guarding is the door to freedom, would he say yes?" If you get a "no"answer, it is safe to use the door. Here's why: You might have talked to the LIAR guarding the door to FREEDOM. If so, you would get a "no" answer, since the other guard, the truth-teller, would say yes, so the liar you are talking to would say no. If you were talking to the TRUTH-TELLER guarding the door to FREEDOM, you would also get a "no" answer, since the other guard, the liar would say "no" and the guard you were talking to would truthfully report this to you. If you were talking to the LIAR guarding the door to DEATH, you would get a "yes" answer. If you were talking to the TRUTH-TELLER guarding the door to DEATH, you would also get a "yes" answer. There are no other possibilities.
Answer:
Ask either guard, "If I asked the other guy if this door you are guarding is the door to freedom, would he say yes?" If you get a "no"answer, it is safe to use the door. Here's why: You might have talked to the LIAR guarding the door to FREEDOM. If so, you would get a "no" answer, since the other guard, the truth-teller, would say yes, so the liar you are talking to would say no. If you were talking to the TRUTH-TELLER guarding the door to FREEDOM, you would also get a "no" answer, since the other guard, the liar would say "no" and the guard you were talking to would truthfully report this to you. If you were talking to the LIAR guarding the door to DEATH, you would get a "yes" answer. If you were talking to the TRUTH-TELLER guarding the door to DEATH, you would also get a "yes" answer. There are no other possibilities.
