The Liar and Truth Teller At a fork in the road, there are two sisters. One always lies and one always tells the truth, but you don't know which is which. You can only ask one yes/no question to one of them. You must learn which direction to go. What do you ask? Suppose Hope (who goes by they) is holding a disk (Frisbee) under a cloth. The disk is either right-side-up or up-side-down but Hope cant see which. Hope can only learn this by handing it first to either Jeff or to Tarver. One of Jeff and Tarver is a flipper and the other is a non-flipper, but Hope does not know which. If a flipper is handed a disk, then he always flips it over and hands it back. If a non-flipper is handed a disk, then he always hands it back unchanged. If Hope hands the disk to one of them and gets it back, they can see the resulting orientation of the disk but does not know what the original orientation was. (because they don't know if had been handed it to the flipper or the non-flipper.) What can Hope do to learn the original orientation of the disk? How does this relate to getting out of prison? ================================================================= First Answer: Hand the disk to Jeff. Then hand it to Tarver. You know it gets flipped exactly once. So you know the original orientation is the flip of what you have now. This relates to asking one of the sisters to tell me what the other would say if I were to ask her which way to go. Then I know the opposite. Case 1: If I ask the lying sister which way to go, she tells me the wrong answer. If I ask the true-telling sister what the other sister would tell me, she tells the truth that the other sister would tell me the wrong answer. Hence, I learn the wrong answer. Case 2: If I ask the true-telling sister which way to go, she tells me the correct answer. If I ask the lying sister what the other sister would tell me, she lies and the flipped answer which is the wrong answer. Hence, I learn the wrong answer. First Answer: Hand the disk to Jeff and then hand it to Jeff a second time. You know it gets flipped zero or two times. So you know the original orientation is the same as what you have now. This relates to asking one of the sisters to tell me what she-herself would tell me if I asked her which way to go. Case 1: If I ask the lying sister which way to go, she tells me the wrong answer. If I ask the lying sister what she-herself would tell me if I were to ask her, then she must lie about lying. This flips the answer twice. Hence, I learn the correct answer. Case 2: If I ask the true-telling sister she just tells me the truth.