Chapter 37 Critical Attack
After Teacher Zhang led Wu Tong into the school, he first took her to the place where they would rest for the night.
"This time we are going to Hainan to participate in the competition. The provincial team has a total of ten people participating, and they are also the top ten in the provincial competition. Two from No. 1 Middle School, three from Foreign Language School, plus you and two from other urban areas, are temporarily staying in the Young Teachers Apartment here, and the two from No. 7 Middle School are staying in their own dormitories!"
"Every apartment is for two people. Your roommate is Feng Yueyue, from Shangdu Foreign Languages College. She is also the second place winner of this league. She has already moved in. You and Feng Yueyue are the only girls selected for the provincial team this time!"
Teacher Zhang briefly introduced the basic situation of the provincial team to Wu Tong as they walked. Although the number of men in the provincial team this year is still more than women, with boys in the majority, the first and second places are occupied by two girls, so no one dares to underestimate them. Feng Yueyue performed well in the provincial team training a week in advance, and beat all the boys in the training class. She has a family background in science and has received training for the Olympic Games since she was a child. After the training of the provincial team, she has obviously made further progress compared to the time when she participated in the Mathematical Union. She is also one of the seeded players in the province to impact the national team this time. The teachers of the training camp, including the Provincial Mathematical Society, are optimistic about her. She is their direct descendant.
Wu Tong topped the list with full marks in the provincial competition, demonstrating her absolute excellence. However, she did not attend the training in advance, and some teachers and society members were somewhat dissatisfied, thinking that Wu Tong came from a small place and was proud and complacent just because she got good grades.
However, no matter the questions they faxed over for follow-up training, whether they were simulation questions from previous national CMO competitions or real questions from the International Mathematical Olympiad IMO, could stump this girl.
With such a high level, it doesn't matter whether they come for centralized training or not! A truly talented player cannot be created by cramming and indoctrination!
Deep down, he was more optimistic about Wu Tong! This year's Mathematical Union Competition, not everyone can get full marks, a full 40 points gap from the provincial second place!
Moreover, according to the records they retrieved afterwards, the supplementary test contained questions that were beyond the syllabus, but this girl was still able to hand in her paper two hours in advance, proving that this year's questions were difficult. However, compared with other candidates, this girl was not stumped. She may have already started to learn university textbooks in mathematics, and her high school foundation is very solid!
"I live here too, in Room 102. You can always come to me if you have any questions!" He is not one of the teachers, but a member of the Provincial Mathematical Society. He currently teaches in the Department of Mathematics at Zhongyuan University. He was specially seconded here to train the provincial team members.
As they were talking, Teacher Zhang took Wu Tong to Room 106 on the first floor of the Young Teachers' Apartment and swiped his card to open the door. The apartment was quite nice, with a separate bathroom at the entrance and two single beds inside, complete with bedding, a desk at the head of the bed, simple and bright colors, clean and tidy.
At this moment, my roommate Feng Yueyue should be in the classroom, and there was no one in the dormitory. However, it can be seen that Feng Yueyue has chosen the bed by the window, and Wu Tong directly put the suitcase near the door.
She didn't bring much with her this time, just some books and some clothes. Fearing that she would need money, Teacher Jin put 1,000 yuan in cash and a bank card in her wallet before she left, and told her many times to add money in time if she needed anything, and to ask the teacher to accompany her to the bank to withdraw money if she didn't have enough money.
"Student Wu, why don't you take a rest and walk around first, or go to the training classroom? We will gather together tonight to have a simple meal to celebrate the end of the training!"
"Teacher Zhang, please take me to the training classroom!" Without hesitation, Wu Tong picked up his backpack and prepared to go out with Teacher Zhang. There was no need to waste time in the dormitory.
The training classroom is in the first teaching building outside the dormitory area. It is not far from the residence and is very conveniently arranged. At this moment, the students participating in the training are all frowning and thinking about the questions given by the training teacher on the blackboard. Only a few of them are writing.
In addition to the provincial team members sitting in the front, there were some students at the back of the classroom who were obviously more confused when reading the questions. According to Teacher Zhang's introduction, Wu Tong knew that they had received sponsorship fees to participate in the training.
Some of them ranked high in this year's Mathematics League, while others are preparing for the next one. The quality of this training camp is superb, so naturally parents who want their children to be successful will spare no effort to send their children here.
When Teacher Zhang brought Wu Tong in, the atmosphere in the training class became tense.
Everyone is not stupid, on the contrary, those who are good at math have high IQ. At this time, there is only one student who can be brought in by the teacher, the one who got the first place in the province with full marks in this year's Mathematics Union. They knew about this on the first day of the training camp, and this person will come here today.
The one in charge of teaching in the class is another team leader, Zhang Ping, the recent head coach of the provincial team this year. He is tall and strong, with a fierce appearance like Zhang Fei. Together with the gentle and refined teacher Zhang, they form a black and white duo in the eyes of students. He has profound qualifications and is a provincial special teacher. He has trained many first prizes in national competitions, and even members of the national team.
Seeing Wu Tong, he raised his eyebrows. He had seen many provincial firsts, but perfect scores were rare. Since he had just arrived, he might as well show off his skills and abilities to see if he could control the situation!
"Wu Tong, right? Put your schoolbag somewhere and go to the stage to do this question on the blackboard!"
Today was the last day, and the question he had come up with was a difficult one. If Wu Tong could solve this question on the spot, he would have no problem with Wu Tong not attending the training these days.
The student is capable, it doesn't matter if you treat him like a nobody and let him go, Mr. Zhang is very tolerant.
There weren't many students attending the training, and apart from the fact that the provincial team and ordinary trainees were separated in front and back, everyone sat wherever they wanted. There was an empty seat at the edge of the first row.
There were not many words on the blackboard. Wu Tong put his schoolbag down casually and read the questions while walking up to the stage.
If n is a positive integer, S={x, y, z·····, try to find the minimum number of planes whose union contains S but does not include (0, 0, 0).
When Wu Tong read the question in the first year of junior high school, she clearly felt that the difficulty of this question was not low. It was comparable to the difficulty of the classic sixth question of IMO in 1988 that she had done before.
Instantly entering a deep learning state, Wu Tong quickly deduced and extracted the key points in her mind, and a storm of thoughts unfolded in the invisible depths of her mind. Instantly, inspiration lit up her train of thought, and she was able to introduce the Lagrange mean value theorem. She picked up the chalk and began to write on the blank space on the blackboard.
Solution: Let the degree of the polynomial p(x) be N, and define the difference operator △ to satisfy...
Let I be the constant operator. According to Lagrange's mean value theorem, we know that:
△p(x)=p(x+1)-p(x)···
·····
Take x=y=z=0, and we get f(0,0,0)=`····
This contradicts f(0, 0, 0) ≠ 0, so m ≥ 3n, and the equality holds as in the previous example...
After writing down the proof process that took up nearly an entire blackboard, Wu Tong softly explained, "This is a relatively simple and clear solution. There is a more complicated solution that cannot fit on the blackboard, so I will not go into details here!"
Hehehe···Hehe···
The other provincial team members in the audience felt like they were hit hard twice. "God" on the stage, please consider the heartbreak of the people in the audience. Is this the gap between them and the first place with full marks?
They have been thinking hard and still haven't found a way, while the person on the stage casually reads the question and writes down the proof on the blackboard. They seem to be struggling and haven't fully understood it yet, but she tells them that she has another solution, but she doesn't write it down because it doesn't fit on the blackboard?
How can we survive this?
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