Omnipotent Data

Chapter 293

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, it's not just a math competition. In the arena of imo, these four aspects are also mainly tested. But this does not mean that a certain type of problem must be solved with a certain aspect of knowledge. Mathematics is an internally interrelated subject. A problem can be solved by algebraic methods, and perhaps also by number theory methods. Mathematics is always full of infinite possibilities and endless fun.

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

…………

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

[Given a positive integer n, each of the six vertices of a regular hexagon is written with a non-negative integer, and its sum is n. Now perform the following operation: erase the number on one vertex, and then write the number on two adjacent vertices. The absolute value of the difference, find all n, so that no matter what integers there are at the beginning, a series of operations can be performed so that the number on each vertex is zero. 】

From the point of view of the topic, this topic is not simple, and it is quite different from the various types of questions encountered in high school. No wonder, among the more than 30 people who participated in the training, only one person solved it.

Comrade Tang was writing the steps on the blackboard while explaining to everyone in the audience.

He first drew a regular hexagon.

"First, according to the meaning of the question, we assume that the parity of the six points of the hexagon is even, odd, odd, even, odd, and odd in counterclockwise order. In this case, no matter how you operate, the six numbers The parity will not change, then..."

"...According to the above process, we can temporarily draw a proposition: as long as the initial six numbers are not even, odd, odd, even, odd, odd, and not all even numbers, then it must be possible to make All numbers equal zero."

"This proposition is just written by ourselves, and we don't know whether it is true or not. Next, we need to prove that this proposition is a true proposition through classified discussions. See my discussion steps. Let's start with..."

"...Did you understand the process on this blackboard? I will erase it if I understand it!... Next, let's discuss the situation of |a2-a6|=k. Since o≤a2, a6≤k, Then we might as well set up…”

Ka Ka Ka Ka!

Old Tang wiped the two blackboards twice, and wrote dozens of lines of densely packed formulas. It took almost half an hour for Old Tang to prove this extremely complicated question, both in terms of thinking and process.

As for the students participating in the training in the audience, as long as two-thirds of the students are still in a dazed state.

who am I? where am I? Why should I come to this training?

After being confused for three consecutive times, they all turned their eyes to the short boy in the front row. His name is Chen Gong, and he has always been ranked first in terms of age, and he is a proper academic master. He was also the only student among the 30 or so who solved this extremely complicated problem.

Some people said that perhaps Chen Gong would be the second student from Qingcheng No. 2 Middle School to become the number one student in the college entrance examination after Cheng Nuo.

A great god is a great god, it really is not comparable to a group of mere mortals like us!

In the eyes of everyone admiring, Chen Gong's expression remained unchanged, and there was no expression of pride on his face.

To be honest, he only thought it was a very basic operation. Winning the first prize in the number federation, entering the national team, and winning the imo gold medal are his goals in the future.

After talking for such a long time, Comrade Tang is also a little dry. He unscrewed the bottle cap of the vacuum flask on the lecture table, took a small sip, propped the desk with both hands, and asked habitually, "About this question, do you have any questions? If not, then we..."

Before Old Tang finished speaking, he saw a hand slowly raised in the back row of the classroom,

A slightly lazy voice echoed in the classroom, "Teacher, I have a question."

Swish Swish Swish!

They looked at each other in unison, and in the end, what caught their faces was a handsome but unfamiliar face.

On the other hand, Old Tang, who was standing on the podium, trembled when he saw the figure raising his hands in the back row of the classroom, and then he couldn't help shaking his head and cursing with a smile, "Cheng Nuo, so it's you."

Cheng Nuo?

The whole class froze for a few seconds, and then completely boiled over.

Senior Cheng Nuo is a legendary existence in their Qingcheng No. 2 Middle School, and he is the goal pursued by countless students. But because Cheng Nuo's counterattack was too short, the school really saw

"Senior Cheng Nuo, it's Senior Cheng Nuo. I finally saw a living one!"

"It turns out that the senior is not the legendary scumbag. I thought the senior was always a fat nerd."

The two girls got together to chat and discuss, and they still glanced at Cheng Nuo from time to time, but the content of the conversation made Cheng Nuo's head black.

The shadow of a famous tree. It has to be said that Cheng Nuo's reputation in Qingcheng No. 2 Middle School is indeed big enough. Some students may not know what the principal's name is, but for Cheng Nuo, a legendary senior, everyone knows it, everyone knows it. Because of this, part of the reason why Class 18 classrooms became the place for competition training was to impress Cheng Nuo, who had a perfect score in mathematics for the college entrance examination.

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

Is he... the senior Cheng Nuo?

"Okay, everyone, be quiet, be quiet." Comrade Tang signaled everyone to be quiet, "Your senior Cheng Nuo will give a lecture in the auditorium of our school in two days. If you have any questions, you can leave it there. when."

Then, he said to Cheng Nuo, "Sit here for a while, and I'll catch up with you after I finish explaining the last few questions to them."

Cheng Nuo smiled and nodded.

The classroom became quiet.

Comrade Tang continued the previous question. He pointed to the blackboard and repeated what he had just said, "About this question, do you have any questions? If..."

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 wryly, "Teacher, I don't have any other intentions. It's just that I have my own opinion on the question you just mentioned."

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

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

Sure enough, Cheng Nuo was still the same Cheng Nuo, nothing changed.

He motioned for Cheng Nuo to come up, and scolded with a smile, "You're going to demolish Teacher and me as soon as you come here!"

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