I Just Want to Be a Quiet Top Student

"The difficulty of Shen Qi's question is not the answer, but the process of proving the answer." Vice President Tan said.

Director Liu continued: "That's right, the two-dimensional situation of this problem is very simple, we can consider the 4n-1 points in the outermost circle, if there is no straight line x=n or y=n, then each straight line is at most Two of these 4n-1 points, so at least 2n straight lines are needed. If there is a straight line x=n or y=n, it is not difficult to get the answer, it is still 2n. So the final result of two dimensions is 2n. "

"But when this method is pushed to three dimensions, troubles arise. In three dimensions, what is used to cover is not a straight line but a plane. The plane has three free variables, and it is not easy to select landmarks for inspection. But we can still easily Quickly judged that the final result of 3D must be 3n. Any high school student who has experience in competitions can infer the answer of 3n by intuition, but it is very difficult to rigorously prove 3n planes.” Director Liu looked To the blackboard, talked about his views.

"The conclusion is obvious, and it is difficult to prove this conclusion." Director Kong went to the blackboard, took off his reading glasses and looked at the question again: "Everyone, how do you say that at least 3n planes are required?"

"Logic game." Shen Qi smiled, and he picked up the chalk again, ready to give a proof.

Officer Liu rolled up his sleeves and seemed to have an idea: "As for this question, the most important point is to transform this seemingly combinatorial calculation setting into a pure algebraic problem. As long as you jump out of this limitation of thinking, you will immediately have a bright future."

"Officer Liu is indeed an expert, it seems that I have nothing to do." Shen Qi will never forget that Officer Liu was his algebra coach when he was in the Mathematical Olympiad training team.

"Shen Qi, we accept this question, thank you, this is a very good Mathematical Olympiad question." Vice President Tan said.

"That's okay, I'll take my leave first, there's an exchange meeting upstairs that I need to attend." Shen Qi left the conference room and went upstairs to the academic report hall.

Several young mathematicians reported their latest research results, and Shen Qi commented as one of the guests.

After the academic report was over, Shen Qi wandered downstairs and found Vice President Tan, Officer Liu, and Officer Kong staying in the meeting room.

The blackboard is full of mathematical symbols, and Shen Qi glanced through it quickly, and found that the Olympiad problem he posed was perfectly proved.

Shen Qi was full of praise: "It's a very beautiful proof. Express each plane in the form of a ternary polynomial, and then multiply these polynomials. Then there is only one thing that needs to be proved, that is, the multiplied polynomial has at least 3n degree. It's beautiful, Officer Liu."

However, Director Liu knocked on his watch with a sad face: "Lao Tan, Lao Kong and I spent two hours to complete the proof. We don't think any high school student can prove 3n within the prescribed answering time."

"If you don't do it, you don't know. If you do it, you will be shocked. This question is at the IMO finale level, and it is not suitable for the CMO competition." Vice President Tan concluded.

"If there is no Chinese Olympiad athlete who can prove this question in the national finals, it will also discourage the enthusiasm of young mathematics enthusiasts." Director Kong thinks this question is too difficult, and suggests that the difficulty should be reduced appropriately.

"You just said that this question is accepted." Shen Qi was speechless, you must have underestimated the contemporary high school students in China, you can't even imagine the terrifying strength of post-00s.

"Shen Qi, the question you asked, after in-depth proof, I found out that there are traps everywhere!" Officer Liu fumbled for something in his pocket in a hurry.

Shen Qi was shocked: "Officer Liu, are you having a heart attack again? Okay, okay, let's change the course to solve the problem, and reduce the difficulty appropriately!"

As a result, Director Liu took out an electronic cigarette, took two puffs, and felt relieved: "I haven't had a heart attack since you went abroad, and the control is quite stable."

"That's what you said, Old Liu, the image of me in your mind is probably a serious illness?" Shen Qi couldn't help but laugh.

Vice President Tan thought for a while and proposed a compromise plan: "The level of the question Shen Qi asked is indeed quite high. Only when high school students use their mathematical skills to the limit and break the conventional thinking mode can they give a better answer. Prove the correctness. How about this, in line with the principle of selecting super-high-level Mathematical Olympians, we will list this Mathematical Olympiad question as a question for the CMO national final election, no points will be deducted for mistakes, and points will be added for correct ones.”

"feasible."

"safe."

Shen Qi, Director Liu, and Director Kong all agreed with Vice President Tan's proposal, so this seemingly simple but extremely difficult question was listed as an optional question for this year's CMO National Finals.

Shen Qi made a bet with Lao Tan, Lao Liu, and Lao Kong. If there are less than 5 high school students in China who can complete this optional question, then I, Shen Qi, will lose.

"You are very likely to lose, let's bet with you!" Lao Tan, Lao Liu, and Lao Kong accepted the move, and the bet was a meal.

Things in the capital were basically settled. Shen Qi left the capital and flew to Nangang City. His other identity as a busy man is a Distinguished Professor of Physics at Nangang University of Technology.

Putting up a name, I have to stay in Nangang University of Technology for some time in a year. Shen Qi came to Nangang University of Technology and found Academician Shi: "Academician Shi, I can stay for more than ten days when I return to China this time. What does our institute need me to do?" ?"

Academician Shi is also the dean of the Academy of Sciences, and he said: "You can't do any big projects in more than ten days. Our school does not have rigid assessment indicators for you. Find faults with other colleges? Insufficient research, teaching, logistics, and other aspects, please give us some suggestions for improvement."

"It's okay to give suggestions for improvement, Academician Shi, can you lend me the equipment of our astronomical observatory?"

"Of course." Academician Shi immediately agreed, and then said: "But recently, the main equipment of the Astronomical Observatory of the Chinese Academy of Sciences is undergoing maintenance. If you can stay for a few more months, then it's OK."

"It's such a pity, it seems that it will be the next time." Shen Qi originally wanted to play with the radio telescope of Nangang University of Technology, but this time he didn't get to play.

Then help Nangang University of Technology School of Physics to give some suggestions for improvement. We have to make some contributions to the physics field of this school, otherwise what if the system does not recognize the completion of the task?

Shen Qi came to the University City, wearing a mask. The flu has been raging recently, and many people wear masks.

Most colleges and universities in Nangang City have campuses in the university town. Shen Qi came to the campus of Nangang University of Technology in the university town, entered the teaching building, sat in the last row, and listened to a section of "Quantum Mechanics" for physics majors.

After only listening to half a class, Shen Qi discovered many problems. He recorded them one by one and thought about the countermeasures.