You are in a country surrounded by water and/or impenetrable walls. There are two types of people there, those who always tell the truth and those who always lie. You start walking to the next village when the road splits into two branches. There are two local people standing there. Can you ask a single yes-no question to find out which way to go?
Reveal the answer
Yes, you can. You can point to one of the branches and ask each person, “Would you say this was the right way?” The non-liar would tell you reliably. The consistent liar, meanwhile, would have to lie in their report about what they would say, so reversing the lie, so telling the truth.
My own solution was clumsier. I’d pointing to one of the branches and ask whether someone from the other group would say yes or no when asked if it was the right way? The liar would have to continue to give the wrong answers, while the truth teller would accurately mimic a liar and give the wrong answer too. So you then just have to do opposite of what they both say.
It is an extension of a similar puzzle with just one liar or non liar, where you can reverse a perpetual liar’s answer by asking, “What would you say if I asked you if you were a liar?” The honest person would say no. But the liar would have to say the opposite of what they would say if asked directly, so telling the truth.
The modelling of real-world liars is simplistic. Real liars are unlikely to feel the need to lie in reporting their own hyperthetical answers, instead they are more likely to lie just as if they had been asked the direct question. Real world liars also have the options of dodging clear questions, by not answering, by giving confusing answers or by giving a clear answer to a different question.
An enterprising liar might ask, “That is an interesting question, but it oversimplies the situation. You might also want to considered the possibility that it might be in the direction you just came from?” Liars don’t lie consistently. Anyone wishing to win people’s trust needs to do so by sticking to a broadly factual basis, expanding this trust on warping accounts in areas which specifically serve them.