Chapter 293

In the National High School Mathematics League, the content of the test questions mainly covers four branches of mathematics: plane geometry, algebra, elementary number theory, and combinatorics.

Of course, not only the mathematics competition, but also in the IMO arena, it is also the main test of these four aspects. However, this does not mean that a certain type of problem must be solved with a certain level of knowledge. Mathematics is an intrinsically interrelated discipline, and a problem can be solved by algebraic methods, and perhaps by number theory. Mathematics is always full of infinite possibilities and endless fun.

For ordinary people, the formula that feels big at a glance may have a different aesthetic sense for this group of students participating in competition training.

............

On the podium, Lao Tang held the tutorial book and wrote the topic on the blackboard first.

[Given a positive integer n, each of the six vertices of a positive hexagon has a non-negative integer, and its sum is n, now do the following: erase the number on one vertex, and then write the absolute value of the difference between the numbers on the two adjacent vertices, and find all n, so that no matter what integers there are at the beginning, you can perform a series of operations so that the number on each vertex is zero. 】

From the point of view of the question, this question is not simple, and it is quite different from the various types of questions encountered in high school. It is no wonder that only one of the more than 30 people who participated in the training was solved.

Comrade Lao Tang wrote the steps on the blackboard while explaining to everyone in the audience.

He first drew a regular hexagon.

"First of all, according to the title, we assume that the parity of the six points of the hexagon is even, odd, odd, even, odd, odd, odd, odd, odd In this case, no matter how you do it, the parity of these six numbers will not change, so ............"

“...... According to the above process, we can temporarily come up with a proposition: as long as the initial six numbers are not even, odd, odd, even, odd, odd, and not all even, then all numbers must be equal to zero through a finite number of operations. ”

"This proposition is just written by ourselves, and we don't know whether it is true or false, below, we need to prove that this proposition is a true proposition by way of classification and discussion, look at my discussion steps, let's start with ......"

“...... Do you understand the process on this blackboard, and I will wipe it if I understand it...... Next, let's talk about the case of |a2-a6|=k, since 0≤a2,a6≦k, then we might as well set ......"

Click, click!

The two blackboards were wiped back and forth twice by Lao Tang, and dozens of lines of dense formulas were written, and it took almost half an hour for Lao Tang to prove that this problem, which was extremely complicated in terms of both ideas and processes.

As for the students who participated in the training, as long as two-thirds of the students were still in a state of confusion.

Who am I, where am I, and why should I come to this training?

After being stunned for three times, they all set their eyes on the tall boy in the front row. His name is Chen Gong, and he has always been stable in the first place in terms of age, and he is a proper scholar. He was also the only student among the more than 30 people to solve this extremely complicated problem.

Some people say that perhaps Chen Gong will be the second student to become the top student in the college entrance examination after Cheng Nuo of Qingcheng No. 2 Middle School.

A great god is a great god, and it really can't be compared to our group of mortals!

In the admiring gaze of everyone, Chen Gong's expression remained unchanged, and his face did not show any pride.

To be honest, he just thinks it's just a very basic operation. Winning the first prize of the Digital Federation, entering the national team, and winning the IMO gold medal are his goals in the future stage.

After talking for such a long time, Comrade Tang also had a dry mouth. He unscrewed the cap of the thermos cup on the lectern, took a sip, propped up the lectern with both hands, and habitually asked, "Do you have any questions about this question? If not, then we ......."

Before Old Tang finished speaking, he saw a hand in the back row of the classroom slowly raised, and a slightly lazy voice echoed in the classroom, "Teacher, I have a question." ”

Whew!

looked at them in unison, and as a result, they were greeted by a handsome but unfamiliar face.

But Old Tang, who was standing on the podium, trembled when he saw the figure with his hand raised in the back row of the classroom, and then couldn't help shaking his head and scolding, "Cheng Nuo, it turned out to be you kid." ”

Cheng Nuo?

The class was stunned for a few seconds, and then it was completely boiling.

Senior Cheng Nuo is a legendary existence in their Qingcheng No. 2 Middle School, and he is the goal pursued by countless students. However, due to the fact that Cheng Nuo's counterattack road was too short, the school really saw it

"Senior Cheng Nuo, it's Senior Cheng Nuo. I'm finally alive!"

"It turns out that the senior is not the legendary dick silk scholar.,I thought the senior had always been a dead fat house.。 ”

The two girls chatted together, and their eyes still glanced at Cheng Nuo from time to time, but the content of the conversation made Cheng Nuo have a black line.

The shadow of the name tree of man. I have to say that Cheng Nuo's fame is indeed big enough in Qingcheng No. 2 Middle School. Some students may not know what the principal's name is, but for Cheng Nuo, a legendary senior, everyone knows and knows it. Therefore, part of the reason why the 18-class classroom has become a place for competition training is to get rid of Cheng Nuo's fairy spirit of Cheng Nuo, who has a perfect score in mathematics in the college entrance examination.

The moment Old Tang said Cheng Nuo's name, even Chen Gong Xueba, who had been sitting in the first row, turned his head sharply and fell his eyes tightly on the boy who was not a few years older than himself.

He...... Is it Senior Cheng Nuo?

"Okay, everyone, be quiet, be quiet. Comrade Lao Tang motioned for everyone to be quiet, "Your senior Cheng Nuo will hold a lecture in the auditorium of our school in two days, and if you have anything to ask at that time, you can stay until that time." ”

Then, he said to Cheng Nuo, "You sit here for a while, and then I will talk to you about the past after I finish telling them the last few questions." ”

Cheng Nuo smiled and nodded.

The classroom became quiet.

Comrade Lao Tang continued the previous question, he pointed to the blackboard and repeated what he had just said, "Do you have any questions about this question......?

In the back row, Cheng Nuo raised his hand again.

Old Tang was a little confused, "Cheng Nuo, I didn't mean ......"

Cheng Nuo smiled bitterly, "Teacher, I don't mean anything else." It's just that I have my own opinion on the topic you just talked about. ”

Cheng Nuo's flat voice slowly echoed in the classroom.

Old Tang looked stunned. The familiar feeling in my memory resurfaced.

Sure enough, Cheng Nuo is still the same Cheng Nuo, and he hasn't changed at all.

He motioned for Cheng Nuo to come up, and scolded with a smile, "You will tear down the teacher's platform as soon as you come over!"