Zhao Dongming's scalp will be tingled when he thinks that there may be CMO-level problems in the finals. If the final question of the college entrance examination is a small fight between small gangs, then CMO is a contest of strength at the level of Dongxie and Xidu, and the peak showdown of Huashan, the top master.

"If it is a CMO-level problem, it will be troublesome. Ouyang Zhe won the gold medal in CMO last time. Many CMO-level questions cannot be difficult for him, but they can stump the huge number competition students participating in the competition."

Zhao Dongming sighed lightly. He knew that there was a CMO-level problem in the final, and Ouyang Zhe was completely the first place to be reserved.

He didn't know how strong Ou Shen had reached, but to be honest, he felt that he was beyond his reach as a competition teacher. Competing with a competition student like Ou Shen was to make the top students in various schools suspect that he was a fool and make all students who thought they were awesome in mathematics feel frustrated.

But once Li Xuan has the hope of winning first, Zhao Dongming's idea of ​​Li Xuan winning will become stronger.

The first place has too many benefits. In addition to the extra bonus, there are other rewards. In the past, the top ten in the Chaoyang Cup country were qualified to participate in the Chaoyang Cup Mathematics Winter Camp, or even the Peking University Winter Camp, or go to famous foreign universities for a short period of study. I don’t know what will happen this year. If you want to enter Tsinghua University, you only have a few opportunities a year. The Peking University Winter Camp is one of the ways to obtain the Peking University qualification for admission. The fact is that as long as you study well enough, it is still easy to go to Tsinghua University. There are several opportunities to enter Tsinghua University every year, and you don’t have to take the college entrance examination.

The opportunity is right in front of you, it depends on whether you have the strength to seize it.

If Li Xuan can be ranked first in the finals, even as long as he tied for the first place with Ou Shen and won the first place in the province in the competition, he would be completely booked in the top ten in the country.

But no one knows what the final test questions are. In addition to math skills, the ability to adapt to the test is also very important. It is still useless to think too much.

Zhao Dongming patted Li Xuan on the shoulder and said to Li Xuan: "Ouyang Zhe this year's senior year, Li Xuan, you are only in the first year of high school. You still have one year to fully prepare for the National High School Mathematics League. It doesn't matter if you lose this time. It is not impossible to join the provincial team in the future and go to the national training team."

Chen Guang smiled and encouraged, "Don't think too much, go back tonight and have a good rest, and use your strength without leaving any regrets."

Li Xuan nodded, but he was afraid he couldn't sleep well at night.

It is impossible to say that there is no pressure. After all, the other party is half a member of the national team. For Li Xuan, it can be said that it is an insurmountable mountain. It is definitely without flaws in all aspects to represent the country in competition in the international arena. In addition to his terrifying mathematical talent, his psychological quality must be very strong, and his comprehensive abilities are among the top ten high school students in the country.

Don’t be impatient, Li Xuan told himself that even if he is stuck in a difficult problem tomorrow, you should not panic.

...

...

Ouyang Zhe participated in the Chaoyang Cup. Everyone who knew Ouyang Zhe’s famous thought that the first one was Ouyang Zhe’s possession. Who would have thought that an accident would happen? The first one was suspenseful at the beginning. Now Li Xuan and Ou Shen tied for the first place, and no one can guarantee that no accident would happen in the finals.

The final first place is still unknown.

Li Xuan is unknown and comes from No. 2 Middle School, which is not strong in mathematics competitions. For example, a meteor emerged from nowhere, even posed a threat to Ou Shen, which attracted many people's attention. Among all the participating students, only Li Xuan and Ou Shen got full marks. No one doubted Li Xuan's strength. In the mathematics competition, full marks have never been scored by luck alone.

In recent years, in terms of competition, Hualien High School and Pengzhong have always been competing for the Double Star Competition. At most, it is a strong school such as Experimental Middle School and Mingya Middle School. However, this time, there seems to be nothing wrong with Hualien High School. The competition students at Hualien High School are very embarrassed, but the competition students at Hualien High School are ranked third, so there is a possibility of competing for the first place.

In this competition, the students of Pengcheng Middle School did not go back and stayed in a hotel near Huajiao Middle School to prepare for the final of the next day.

Ouyang Zhe’s classmate Huang Songbai learned about the results of this rematch and chatted with Ouyang Zhe in the hotel room. “Haha, I feel much more interesting now. If Ou Shen has always won the first place without any suspense, it would be meaningless.”

When Ouyang Zhe heard this, he said funny: "What the hell, do you think I will lose? I don't get the first place in the province, right?"

When Huang saw Ouyang Zhe, he felt that he was not a human being and was very helpless: "Okay, the first place must be you, God is God, and we all can only look up to you."

Ouyang Zhe smiled.

How to say, starting from the third year of junior high school, the math scores were scored every time, and the general math competitions were always scored. Except for meeting a group of perverts gathered in other parts of the country at CMO, other competitions have never been under much pressure. In his opinion, the so-called Chaoyang Cup full score was not good.

...

...

The next day, the finals began.

Li Xuan slept for five hours last night and was not sleepy. When he came to the examination room, his eyes were filled with war.

Ouyang Zhe's appearance did put a lot of pressure on him, because he knew that the possibility of winning was very low, so he wanted to win like never before.

The time has come, and the test papers have been sent out on time.

Li Xuan held his breath and calmed down, took a deep breath, picked up the pen, put down all his unnecessary thoughts, and focused on answering the questions.

Outside the examination room, Zhao Dongming won the final paper. He looked at these five major questions. At first glance, he had no idea. The more he looked, the more he felt that the final questions were abnormal. Don’t talk about the students, if he did it, it would be hard to say whether he finished it or not.

"Teacher Chen, you guessed it right. The questions in this final are really CMO level!" Zhao Dongming sighed and found that the difficulty was one level higher than the finals in previous years. This test paper seemed to be for Ouyang Zhe. Now the examination room is Ou Shen's world.

Chen Guang looked at the test paper, and these five questions made him frown and cursed: "It's so crazy, I'm completely clueless. The last two big questions are definitely CMO-level."

Who did the appearance of the CMO level test questions? A contest of CMO level appeared in the cup competition.

Zhao Dongming looked at the first question: "It's a bit unscientific when you look at the first question. How come this is like the first question? In the past, I can count the last two questions."

In the exam room, Li Xuan looked at the first question:

abdefc is the six points on the circle in turn, satisfying ab=ac, the straight line ad and be intersect at point p, the straight line af and ce intersect at point r, the straight line bf and cd intersect at point q, the straight line ad and bf intersect at point s, the straight line af and cd intersect at point t, and the line k on the line segment st, so that ∠skq=∠ace, prove: sk/kt=pq/qr.

Li Xuan focused his mind and thought.

The geometry question is what Li Xuan is good at. After a while, Li Xuan thought of it and started to prove it. He drew auxiliary lines on the circle and connected ae, cf, ef, ed, df, and bd.

The three points of pqr are proved by the Circular Pascal's theorem.

ab=ac, get the four points of tfds to be circled together, and derivate the edges inside with the previous one. Finally, it can be proved by the sine theorem sk/kt=pq/qr.

After stopping, Li Xuan breathed a sigh of relief and continued to look at the second question.

The second question is very short: let x and y be a positive integer, and find the minimum value of the root number (512^x-7^(2y+1)).

Li Xuan frowned. The question was very short, but it was really difficult. It felt even more difficult than the rematch of the high school mathematics league.

On the other hand, Ouyang Zhe thought about the first question for a while. In the past, he participated in such cup competitions, so he didn't even think about the first question, and it would never be possible to get stuck like this.

"Interesting, quite interesting."

Ouyang Zhe licked his lips and became a little excited.

He found that the Chaoyang Cup final test questions were very good. I was afraid that there was a big guy behind the scenes. Each question had a distinction. The simplest first geometry question stuck him for a few minutes.

At first I just came to play, but I didn't take it seriously, but the difficulty of the question made him excited.

There are five major questions in the entire test paper, including two questions in geometry, one question each, algebra, number theory, and combination. There are two questions in geometry. The Chinese team has been in IMO in recent years, and their geometry scores have not been very good. It seems that considering this point, the proportion of the Chaoyang Cup geometry questions has increased.

In the exam room, Jin Letian took a look at it and was unable to answer any questions.

"I feel like I'm going to finish! I'll get zero points in the final."

Jin Letian was frowning and had an ominous premonition. Fortunately, the worst person to enter the final was the third prize, which is the only place worth comforting.

What can I do now? The first question looks the simplest. It seems that it is necessary to use the collinear and four-point cocircular theorem. There is no clue at all for other questions, and he even doesn't understand even if he suspects that he can't understand the answer.

I can only draw a few auxiliary lines to see if I can find out the solution to the first geometry problem. If my luck explodes and I draw that key auxiliary line, I might be able to answer it.

Liang Zhihui was also stuck in the first major question. Geometry questions were not his strengths, he was better at algebra.

Through the conclusion, he tried to reverse the conclusion and see if he could get a common circle.

...

...

Time passes, and the exam room is quiet.

When doing these five major questions, many candidates tend to collapse, and the difficulty is beyond everyone's expectations in advance. One question is more difficult than another. Most candidates can only do the first question, and the second question is just a little more meaningful.

Ouyang Zhe wrote it very easily before and quickly solved the first three major questions. The speed was probably the fastest among all the participants, but when he turned to the fourth major questions, he didn't know where to start.

After being blocked by the fourth geometry question for nearly half an hour, Ouyang Zhe was completely confused. In his opinion, this geometry question was even more difficult than the last big question. Only those abnormalities who participated in CMO who were good at plane geometry could be solved.

It directly proves that there is no idea, the relationship between the question is complicated, and the conditions for proof are cumbersome.

There is no way, Ouyang Zhe can only try it with the same method, but he is always one step away and proves that it is not symmetry.

The so-called same law refers to a method of proving the original proposition as a validity of its inverse proposition on the premise of conforming to the same law.

After working on the fourth question for more than an hour, I wasted my time and still didn’t get the final answer. Ouyang Zhe was a little annoyed. He was obviously here to abuse the vegetables, but how did he abuse the vegetables to the point of being a tough guy? It felt like he was participating in a CMO.

"Damn it, who has the question to ask about this!"

Ouyang Zhe frowned, and wanted to curse himself a little, and was still thinking about the fourth geometry question.

He has done three major questions now, and when he reaches the fourth major question, he has some quits. Of course, the last number theory is the part he is good at. However, in a small cup competition, he felt that he must be the first in his three major questions. He should be able to do the number theory in the end, and he doesn't want to read some.

How could it be abused by the Chaoyang Cup’s question? Is it because he is too good to have a geometry, or is the question really too difficult?

He doesn't believe it and can't think of the fourth question.

...

Li Xuan also wrote about the fourth question, and he got a headache when he saw the question.

Compared with the first geometry question, this geometry question needs to prove that the equilateral line is very difficult and extremely challenging. It cannot be like the first question, which theorem can be used immediately. The fourth question has no clue and the feeling of a standard CMO question. For questions of this level of difficulty, Li Xuan usually has to think about it for a long time before he can have some ideas.

Question 4 is so perverted, and the fifth question is hard to imagine.

I'm going to die.

Li Xuan frowned, and his best geometry problem was stuck. Li Xuan didn't even want to do the final question of the number theory in the following number theory, and even wanted to use analytical geometry to establish a coordinate system to get away with it.

However, I had done a geometry problem before, and the equiangular lines were transformed into tangents of the circumference. At this time, he suddenly remembered this conclusion. There are many points in this question that look like the center. In fact, if the graph has a good sense, it is easy to think of inversion.

Assume that point o and constant k are given in the plane (k is not equal to zero), for any point a in the plane, determine a′ so that a′ is a point on the straight line oa, and directed line segments oa and oa′ satisfy oaoa′=k.

This is the inversion transformation, characterized by the opposite of two images.

The circle of this question passes through the center of inversion, and its inversion graph is a straight line.

However, the inversion method is beyond the rules, and I don’t know if it can be used in Chaoyang Cup.

Li Xuan frowned and tried to do it in the same way, thinking about symmetry, but the process was so complicated that Li Xuan wanted to die, and he stopped halfway. No matter what, Li Xuan decided to use the inversion method, and the circle was inverted into a straight line to see if he could get the answer.
Chapter completed!