From Martin Gardner’s book, Hexaflexagons and other mathematical diversions: (you can see why I was reading that!)
Here’s a recent twist on an old type of logic puzzle. A logician vacationing in the South Seas finds himself on an island inhabited by the two proverbial tribes of liars and truth-tellers. Members of one tribe always tell the truth, members of the other always lie. He comes to a fork in a road and has to ask a native bystander which branch he should take to reach a village. He has no way of telling whether the native is a truth-teller or a liar. The logician thinks a moment, then asks one question only. From the reply he knows which road to take. What question does he ask ?
Think about it carefully….
Read this when you figured it out.
If we require that the question be answerable by “yes” or “no,” there are several solutions, all exploiting the same basic gimmick. For example, the logician points to one of the roads and says to the native, “If I were to ask you if this road leads to the village, would you say ‘yes’?” The native is forced to give the right answer, even if he is a liar! If the road does lead to the village, the liar would say “no” to the direct question, but as the question is put, he lies and says he would respond “yes.” Thus the logician can be certain that the road does lead to the village, whether the respond- ent is a truth-teller or a liar. On the other hand, if the road actually does not go to the village, the liar is forced in the same way to reply “no” to the inquirer’s question.
There are plenty other answers too- as long as they work, then yay for you! 😀