There is a small village where there are 50 families, each with a dog. Once upon a time, there was a mad dog in the village Let's discuss it together: we should go to every house every morning to check the dog's situation. Once you find that your dog is a mad dog, you must shoot it that night. People in this village have such a skill that they can tell whether other people's dogs are mad dogs, but they can't tell whether their own dogs are mad dogs. You can't tell each other the truth. The first day and the second day, there were no gunshots in the village. On the third night, gunshots rang out in the village and all the mad dogs in the village were killed. How many mad dogs are there in the village?

First of all: everyone knows that mad dogs must exist.

Suppose: a person finds that among the 49 homes he observes, except himself, 48 are good dogs, and 1 is mad dog.

Unable to judge his own dog, he came to the conclusion that there are at least 1 mad dogs and at most two (plus his own).

If it is 1, then there are 49 good dogs, belonging to the "49 good dog camp"; If it is 2, then there are 48 good dogs, which belong to the "2 mad dog camps"

Although he is not sure whether it is 1 or 2, he will reason:

If it is 1, it means that his dog is also a good dog. Only he can see that the dog is the only mad dog, so let its owner be A.

Then A will see that other people's dogs are all good dogs, and A knows that there must be mad dogs, only A's own dogs.

So A will pat the dog on the first day.

But on the first day, no one shot,

This shows that A didn't see that "other people's dogs are all good dogs",

So the number of mad dogs is not 1, but 2. "A man" belongs to "2 bad dog camps" instead of "49 good dog camps"-except himself and A, 48 are good dogs.

So he will shoot his dog the next day.

A is exactly the same as There's a Man. Based on the same reasoning, it will be filmed the next day.

Therefore, if someone shoots the next day, it means that the number of mad dogs is two.

But no one shot the next day,

Therefore, the hypothesis that "a person found that 48 of the 49 homes he observed were good dogs except himself, and 1 dog was sick" was not established.

The number of mad dogs is not 2, and certainly not 1.

Let's continue to suppose that a person finds that 47 of the 49 homes he observes are good dogs and 2 are mad dogs besides himself.

Because I can't judge my dog, I come to the conclusion that there are at least two mad dogs and at most three (plus my own).

If it is 2, then there are 48 good dogs, belonging to the "48 good dog camp"; If it is 3, then there are 47 good dogs, which belong to the "3 mad dog camps"

Although he is not sure whether it is 2 or 3, he will reason:

If it is 2, even his dog is a good dog. He sees that both dogs are mad dogs, and their owners are A and B.

A or b can also do reasoning. For example, A will infer that the number of sick dogs is 1 or 2, and the reasoning process has been mentioned before.

If it is 2, both A and B will make moves the next day, but no one will make moves the next day.

So it can only be 3, which means that "one person" does not belong to the "48 good dog camp" but belongs to the "3 sick dog camp"

So on the third day, someone shot, which means "there is a person". A and B realized that their dogs were sick and shot.

Conclusion: Reasoning can go on all the time. There were several mad dogs a few days before shooting.