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Mathematical reasoning in public examination
1.

A classic reasoning problem:

There are 50 people in a house, and everyone has a dog. Some of these dogs are sick, at least 1. Suppose.

(1) The dog's disease is not contagious, and it will not be cured without treatment, and the number of sick dogs will not change;

(2) The owner of a dog can't tell whether his dog is sick, so he can only judge whether his dog is sick by someone else's dog;

(3) Once the owner discovers that his dog is sick, he will kill the dog that day.

There were no gunshots on the first day, no gunshots on the second day, and gunshots on the third day. How many dogs were killed?

2.

Several families live in the apartment. Every family has a couple and their minor children. The number of children varies from family to family. In this apartment, there are more children than adults, more adults than boys, more boys than girls, and more girls than other families. Every girl has at least one brother but at most one sister. How many families are there in this apartment? How many boys and girls are there in each family?