That day, the professor had dinner with his family. During the dinner, the smug professor asked the child prodigy sitting next to him: "Take any natural number from 1 to 100, and at least two of them are qualitatively different from each other. Is this conclusion correct? How should I prove it? " Ai Duoshi suddenly stopped eating. He was lost in thought and said nothing.

2. Group the hundreds of natural numbers from 1 to 100 in pairs (two adjacent ones are a group): (1, 2), (3,4), (5,6), (7,8) ... until (99,/kloc. If you choose any number of 5 1 from these 50 groups, you can certainly get at least two numbers from one of them.

3. Ai Duoshi solved the professor's problem satisfactorily. However, the proof method he used is just the "pigeon hole principle" that everyone knows. It is generally called "pigeon nest" abroad (pigeon hole principle).

4. Paul Ai Duoshi worked tirelessly in the field of mathematics until 1996, when he attended a mathematics conference in Warsaw, the Polish capital, and died of a heart attack at the age of 83.

Ai Duoshi is one of the eccentric and original mathematicians throughout the ages. He is competitive and likes to ask questions and solve difficult problems in number theory (the study of integer properties) and other fields, such as discrete mathematics (the basis of computer science). He is also one of the most prolific mathematicians in history, and has published more than 500 papers/kloc-0.