Once, Alice found herself in one of two countries - A or Y. She knows that all residents of country A always tell the truth, while all residents of country Y always lie. Moreover, they often visit each other. Can Alice, by asking a single question to the first person she meets, find out which country she is in?
Try to find such questions that all people currently in country A would answer the same way, and then among these questions, choose those that people in country Y would also answer the same way, but differently.

## Solution

First, let's identify questions that all people currently in country $A$ would answer the same way, and then among these questions, select those that people in country Y would also answer the same way, but differently. In a country of honest people, Alice should ask a question to which both an honest local and a visiting liar would give the same answer, for example, "yes." The idea is that the answer "yes" to this question should be true for the local and a lie for the visiting liar. In other words, this question should pertain to circumstances of the person being questioned that are true only for the locals. There are two such circumstances: honesty and being a local. Therefore, there are two questions: either "Are you honest?" or "Are you a local?". On either of these questions, in country A, the answer will always be "yes." However, on the first question, "Are you honest?" in country Y, as anywhere in the world, anyone would also answer "yes." Therefore, the first question is not suitable for Alice, but the second one ("Are you a local?") is appropriate: in country $A$, the answer will always be "yes," and in country Y - "no."

## Answer

Yes. "Are you a resident of this country?"