Chapter 80 IMO
In addition to the test paper translated into Chinese, the Chinese team also asked for an original English version.
The team members who can participate in IMO have strengthened their English translation skills. For example, Guo Jiachen and Chu Xiaosheng have learned English since elementary school, so they have no problem with translation papers.
This is also what the Chinese national team does to ensure rigor and accuracy and safeguard its practices.
After receiving the test paper, Wu Tong completely entered into his usual state of concentration. The first question was about functions in the field of numbers and algebra. The difficulty was not too difficult. After Wu Tong finished reviewing the question, ideas emerged. He started writing down the reasoning process on the draft paper.
Let Y = 0, we get f(0) = ···
Eliminate the negative conditions, substitute the necessary factors, and prove the interval values of all solutions. Finally, substitute again and you will get the desired satisfaction condition.
After completing the first question, Wu Tong copied it onto the test paper and moved on to the second question, geometric proof.
She raised her eyebrows slightly. The difficulty of this geometry problem seemed to be quite high. Among the IMO questions she had done, it was ranked in the middle. It seemed that the IMO question setter had really raised the difficulty this year.
Of course, this was still not a problem for Wu Tong. Twenty minutes later, Wu Tong solved the problem again.
The third question was also a function question. After reading it through, Wu Tong confirmed that this year's IMO was really full of traps. Today's sinkhole appeared. If you are not careful, you will probably be completely buried in the pit.
Wu Tong continued to write about the solution process fluently, starting with the proof of injection, obtaining the judgment basis she needed from the known conditions, using the method of proof by contradiction to compare the two formulas to deduce the contradiction, and then deducing from this to eventually determine the conditions that meet this requirement, and finally find all the solutions, where C is a non-negative integer.
After finishing the three questions, Wu Tong checked again and looked at the time. Well, it was still the usual speed, not exceeding an hour.
As usual, everyone raised their hands to hand in their papers in advance. In the entire competition, except for the Chinese team, who were used to it, everyone else was shocked. Many of them hadn't figured out the direction to solve the first question yet, and someone from the Chinese team had handed in their papers?
Hasn’t the game just begun?
Many contestants felt like their mentality was about to collapse! How could they compete with others who finished a problem in one hour that they might not be able to finish in four and a half hours?
What happened to friendship first and competition second?
The other five members of the Chinese team continued to write furiously, as expected. This was a common and basic operation for the academic genius. They had gone from being shocked to being numb; they were too used to it.
The invigilator who was collecting the papers from the organizing committee shrugged his shoulders not surprisingly. They had indeed selected the questions very carefully, but it was obvious that no matter how much they selected, there was still a limited range and it could not trap this talented young mathematician who had recently become famous.
Wu Tong secretly made a cheering gesture to the other members of the Chinese team, and then she left the examination room with the chocolates provided by the organizing committee on the table. Perhaps considering the long examination time, there were some chocolates and other small snacks on the table at each position to replenish energy.
Wu Tong simply took away everything that was not going to be wasted, and ate it while she was waiting outside.
"How was it? How difficult was the exam?" Seeing Wu Tong coming out of the examination room, the deputy leader of the Chinese team, Professor Cheng, asked with a smile, without any surprise. The difficulty he mentioned was naturally not for Wu Tong, but for other ordinary contestants.
"The organizing committee has put a lot of thought into this. It's not an easy task. The third question is quite interesting!" Wu Tong raised her eyebrows and handed two chocolates to Professor Cheng. Anyone who saw it could get one.
Wu Tong took the paper and pen from Professor Cheng and wrote out the three questions for today. The questions were not too long and would not take her much time.
Professor Cheng took a look at the third question that Wu Tong mentioned was very tricky. After reading the question and thinking about it carefully, he couldn't help but slap his forehead. It was really a trap. It was possible that one of the participating teams would fall into it and use the wrong theorem.
I hope that the kids on the national team won’t fall into traps. I don’t ask them to get full marks on this question, but just don’t make weird mistakes.
"Everyone has a good understanding of the common methods of using polynomial properties to consider functional equations!" Wu Tongdao was not too worried. This knowledge point was emphasized during the training camp, and she even gave a class on this subject.
"Pure Hanfang method and understanding, pure Hanfang beauty!" Professor Cheng discussed the problem-solving method with Wu Tong, and after listening to Wu Tong's problem-solving process, he couldn't help but applaud.
"If you use the right method, this question is not too difficult!" Wu Tong commented casually. The difficulty of this question is not as difficult as those in history. It just requires a precise thinking angle.
"Let's wait for them to come out!" Professor Cheng smiled and spread his hands. It was not too difficult, basically only relative to Wu Tong.
Sure enough, when the actual time to hand in the papers came, candidates came out of the examination room one after another. Candidates of different skin colors, using different languages, were all expressing the same question.
"What kind of a hell of a question is this?"
"This doesn't seem like a problem that a human can solve. Are they kidding us?"
"I think I might not get any points for the third question, or if I am more confident and remove the word 'maybe', I won't get any points!"
Of course, there are some who are full of confidence, such as the North Koreans, who seem to be doing quite well? They all look a bit arrogant!
The Chinese team didn't all have sad faces, but their expressions weren't very good either.
However, after a deeper understanding of the situation, Professor Cheng felt that it should not be so pessimistic, so he comforted and encouraged: "Okay, everyone, cheer up, put your mind at ease, don't think about anything tonight, have a good rest, and prepare for tomorrow with all your strength. Every question tomorrow is crucial, and you must go all out for the final sprint!"
Basically, this IMO is the last chance for these students to participate. After returning home, none of these national team members will go back to high school.
Based on the solid psychological foundation laid by the training camp in recent days, the Chinese team was in good shape. After a simple dinner, everyone went to rest early. The next day, they entered the examination room again with full energy to meet the challenges of the last day of the competition.
As long as they finish today's exams and wait until the IMO awards ceremony, they will have a nearly two-month vacation and can have fun until the start of school in September, when they will enter university and start their fresh university life.
"Come on, I'll be waiting for your triumphant return and will pick up your Professor Li in a while. Starting tomorrow we will have four days of free time to go around and have a look. It won't be a wasted trip to Nur-Sultan!" Before entering the examination room, Professor Cheng patted everyone on the shoulder to encourage and boost morale.
The exam started again. The fourth question was still from the geometry section. This year's simple number theory questions were a bit evasive. The regular geometry proof questions were considered easy points!
The atmosphere at the start of today should be okay.
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