## 36. A Minor Incident.

This puzzle is unusual. Moreover, it is based on a real incident. Once, when I was visiting the island of knights and liars, I met two locals. I asked one of them: "Is anyone of you a knight?" My question did not go unanswered, and I learned what I wanted to know.

Who was the islander I addressed: a knight or a liar? Who was the other islander? I dare assure you that I have provided you with sufficient information to solve the puzzle.
36. Solving this problem will be helped by the information provided in the conditions of the problem after the message that the islander gave an answer to my question: my remark that after his answer I learned the true answer to my question.

Suppose the islander I was talking to (let's call him A) answered my question "yes." Could I, after such an answer, know that at least one of the islanders I met was a knight? Of course not. Indeed, A could be a knight and truthfully answer "yes" to my question (his answer would correspond to the truth, since at least one islander, namely A, is a knight). Both islanders could have been liars. In this case, A, lying, would have answered "yes" to my question (which would have been a lie, since neither of the islanders was a knight). Thus, having received a "yes" answer from A, I would not have been able to know the true answer to my question. But, as stated in the conditions of the problem, after A's answer, I learned the correct answer to the question I asked. Therefore, A could only have answered "no."

Now let's figure out who the islander A and his friend, whom we will denote as B, are. If A were a knight, he could not have given a truthful "no" answer, so A is a liar. Since his negative answer is false, at least one of the two islanders must be a knight. Therefore, A is a liar, and B is a knight.