Choose a door
You are trapped in a room with two doors. You know there is a pack of hungry lions, certain death, past one door, and freedom behind the other. There are also two people, one guarding each door. They both know which door has freedom. One always tells the truth, the other always lies. You don't know who is who. You ask the person guarding door 1 one question. Then you need to choose a door. What question do you ask to give you a 100% chance of survival?
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1 solution
You should ask, "What would the person in front of the other door say if I asked them what is behind their door?" This will always work. There are 4 scenarios.
You ask the liar, and freedom is behind their door. Answer: freedom If you ask the liar and freedom is behind their door, then the truth teller is guarding the other door, which has lions. If I had asked what was behind that door, the truth teller guarding it would have said lions. The liar knows this, and lies about it, saying freedom.
You ask the liar, and freedom is behind the other door. Answer: lions If you ask the liar and freedom is behind the other door, then the truth teller is guarding the other door, which has freedom. If I had asked what was behind that door, the truth teller guarding it would have said freedom. The liar knows this, and lies about it, saying lions.
You ask the truth teller, and freedom is behind their door. Answer: freedom If you ask the truth teller and freedom is behind their door, then the liar is guarding the other door, which has lions. If I had asked what was behind that door, the liar guarding it would have lied and said freedom. The truth teller knows this, and tells the truth about it, saying freedom.
You ask the truth teller, and freedom is behind the other door. Answer: lions If you ask the truth teller and freedom is behind the other door, then the liar is guarding the other door, which has freedom. If I had asked what was behind that door, the liar guarding it would have lied and said lions. The truth teller knows this, and tells the truth about it, saying lions.
So for both of the ones where freedom is behind the other door, you get the answer lions, and for both of the ones where freedom was behind the person you asked door, you get the answer freedom. You know this, so you use it to inform your decision. The other answers are all vulnerable to whether or not you asked the liar or truth teller.