There are three elves, A, B and C. One of them only tells the truth, and the other only tells lies. The other randomly decides when to tell the truth and when to lie. You can ask these three elves three true and false questions (note: each question can only be asked by one elf, and all three questions can be asked by the same elf). Your task is to find out who is telling the truth, who is lying and who is answering randomly from their answers. The difficulty of this puzzle is that these elves will answer with "Da" or "Ja", but you don't know their meaning, only know that one word stands for "right" and the other word stands for "wrong". What three questions should you ask?

This logic problem was put forward by Raymond Smullyan, an expert. He claimed to be "the most difficult logic problem in the world" and said that no one could solve it except him.

The most difficult thing about this problem is that we don't know the language of elves. I don't even know whether the answer is right or wrong except true or false. We can all simplify the question first: we can assume that the three elves answer (yes or no) in human language without losing generality. Why can you assume this? The reasons are as follows.

When I want to ask an elf whether proposition P is correct, I won't ask directly. Let me first convert the proposition p into the following proposition Q.

Q = (P and (Da stands for yes)) or (not p and (Ja stands for yes))

If the person in front of him is elf C, what his answer is has no influence on reasoning at all. If there is a truth elf or a lie elf in front of him, his answer to proposition P in human language is affirmative if and only if his answer to proposition Q is Da. List all the situations and consider them one by one, and you will know. Through this proposition transformation, we can assume that Da stands for Yes from the beginning, or directly assume that they will answer in human language.

Now suppose they can answer in human language.

Because they answer in human language, the question is relatively simple. For the convenience of discussion, suppose three elves are arranged in a row on the left, middle and right.

First of all, I want to introduce a method to force a lying elf to tell the truth. If I really ask the elf in front of me if the proposition P is correct, I may lie, because that elf may be a lying elf or a C elf. What I want to do is to first convert proposition P into the following proposition Q:

Q = (P and you are the truth elf) or (not p and you are the lie elf)

If it's elf C in front of you, it doesn't matter what he answers. If he is a truth elf or a lie elf, if and only if the original proposition P is true, his answer to proposition Q is. That is to say, through this proposition transformation, I can force the lying elves to tell the truth (of course, the truth elves continue to tell the truth). After understanding the law of forcing out the truth, the problem is actually easy to solve. First, ask the elf on the left by forcing the truth, and ask him if the elf in the middle is a C elf. Because of the mandatory truth law, I know that either he is an elf or the answer must be the truth. If the answer is yes, I'm sure it's not elf C on the right. In other words, as long as I force him to ask a question, I will definitely get the truth answer. You can know that he is an elf by asking the truth once, and then ask him a question to know that he is a C elf. If the answer to the first question is no, the practice is basically the same, the only difference is that this time we know that the middle elf is not a C elf. (Then ask him questions by forcing the truth. )