The difficulty of Shen Qi's question is not to give the answer, but to prove the answer. Vice President Tan said.

Secretary Liu continued: "That's right, the two-dimensional situation of this problem is very simple, we can consider the outermost circle of 4n-1 points, if there is no straight line x=n or y=n, then each straight line can exceed 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 come up with the answer, which is still 2n. So the end result of two dimensions is 2n. ”

"But when you push this approach to three-dimensionality, the trouble arises. In the three-dimensional case, it is not a straight line but a plane that has three free variables, and it is not easy to select a marker to investigate. However, we can still quickly determine that the final result of 3D must be 3n. Any high school student who has ever competed can intuitively deduce the answer to 3n, but it is very difficult to prove 3n planes rigorously. Mr. Liu looked at the blackboard and talked about his views.

"The conclusion is obvious, and it is difficult to prove it. Officer Kong walked to the blackboard, took off his reading glasses and examined the question again: "Everyone, how do you say that you need to prove that at least 3n planes are needed?"

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

Director Liu rolled up his sleeves and seemed to have an idea: "The most critical point of this problem is to transform this seemingly combinatorial calculation setting into a pure algebra problem. As long as you jump out of this thinking limitation, you will immediately open up the sea and the sky. ”

"Director Liu is really an expert, it seems that there is nothing wrong with me. Shen Qi will not forget that Officer Liu was the algebra coach of his Olympiad training team.

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

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

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

After the academic report meeting, Shen Qi slipped downstairs and found that Vice President Tan, Secretary Liu, and Secretary Kong had stayed in the conference room and had not left.

The blackboard was full of mathematical symbols, and Shen Qi quickly glanced through it and found that the Olympiad problem he came up with was perfectly proven.

Shen Qi was full of praise: "A very beautiful proof, representing each plane in the form of a ternary one-time polynomial, and then multiplying these polynomials, then there is only one point that needs to be proved, that is, the multiplied polynomial has at least 3n times." Well done, Director Liu. ”

However, Director Liu knocked on his watch with a sad face: "It took me two hours to complete the proof with Lao Tan and Lao Kong, and we don't think that any high school student can prove 3n within the specified answering time." ”

"I don't know if I don't do it, I'm shocked when I do it, this question is at the IMO finale level, and it is not suitable for the CMO arena. Vice President Tan concluded.

"If there is no Chinese Olympiad player who can prove this problem in the national finals, it will be too discouraged by young math enthusiasts. Officer Kong thinks that this question is too difficult, and suggests that the difficulty be reduced appropriately.

"You just said that this question has been accepted. "Shen Qi is speechless, you also underestimate the contemporary Chinese high school students, you can't imagine the terrifying strength of the post-00s.

"Shen Qi, this question you came up with, after in-depth proof, I found out that there are traps everywhere!" Director Liu hurriedly touched something in his pocket.

Shen Qi was shocked: "Director Liu, you have a heart attack again?" Okay, okay, let's change the question and reduce the difficulty appropriately!"

As a result, Director Liu took out an electronic cigarette, took two puffs, and felt comfortable: "Since you went abroad, my heart attack has never had again, and the control is quite stable." ”

"That's what I said, Lao Liu, my image in your mind is probably a disease, right?" Shen Qi laughed.

Vice President Tan thought about it and proposed a compromise plan: "Shen Qi's problem is indeed quite high, and high school students can only give correct proofs if they use their mathematical skills to the limit and break the conventional thinking mode." In this way, in line with the principle of selecting ultra-high-level Olympiad players, we will list this Olympiad question as a final selection question for CMO countries, and no points will be deducted if you make a mistake, and extra points will be added if you do it right. ”

"It works. ”

"Sure. ”

Shen Qi, Director Liu, and Secretary Kong all agreed with Vice President Tan's proposal, so this seemingly simple but actually super difficult topic was listed as an optional question for this year's CMO national decision.

Shen Qi made a bet with Lao Tan, Lao Liu, and Lao Kong that if there were less than 5 high school students in China who made this optional question, then I Shen Qi would lose.

"You have a great chance of losing, let's bet with you!" Lao Tan, Lao Liu, and Lao Kong took the move, and the bet was a meal.

Things are basically done here in the capital, 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.

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, do we need me to do anything?"

Academician Shi and the dean of the Institute of Physics, he said: "You can't do any big projects in more than ten days, and our school doesn't have a hard assessment index for you, or you can go around and find some faults in our Institute of Physics, Mathematics or other colleges? ”

"It's no problem to make suggestions for improvement, Academician Shi, can you lend me the equipment of the astronomical observatory of our Academy of Physics to open meat?"

"Absolutely. Academician Shi immediately agreed, and then said: "But recently, the main equipment of the astronomical observatory of the Academy of Physics is being maintained, if you can stay for a few more months, it will be OK." ”

"It's such a shame, it looks like we can only do it next time. Shen Qi originally wanted to play with the radio telescope of Nangang University of Technology, but he didn't have to play this time.

Then help us to improve the School of Physics of Nangang University of Technology, and make some contributions to the physics field of this school, otherwise the system will not recognize the completion of the task.

Shen Qi came to the university town, wearing a mask, the flu has been raging recently, and many people are wearing masks.

Most of the 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 the "Quantum Mechanics" of the physics major.

After only listening to half a class, Shen Qi found a lot of problems, and he recorded them one by one and thought about countermeasures.