In addition to the test paper translated into Chinese, the Chinese team also requested an original English version.
The team members who can participate in IMO have strengthened their English translation skills. People like Guo Jiachen and Chu Xiaosheng have learned English since elementary school and have no problem with translation papers.
This is also what the Chinese national team does to ensure rigor and accuracy.
As soon as he got the test paper, Wu Tong completely entered his usual state of concentration. The first question was about functions in the field of numbers and algebra. The difficulty was not too bad. After Wu Tong finished reviewing the question, ideas emerged. He started to write down the reasoning process on the draft paper.
Let Y = 0, we can 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 required satisfaction conditions.
After completing the first question, Wu Tong copied it onto the test paper and moved on to the second question, the geometric proof.
She raised an eyebrow slightly. This geometry problem seemed quite difficult. It ranked somewhere in the middle of the IMO exam questions she'd tackled. It seemed the IMO test setters had really cranked up 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 IMO was really full of pitfalls. Today's pitfall appeared. If you are not careful, you will probably be completely buried in the pit.
Wu Tong continued to write about the solution process in a smooth manner, 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, eventually determining the conditions that meet this requirement, and finally finding 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.
The usual practice was to raise hands and hand in their papers early. Aside from the Chinese team, who were quite accustomed to this, everyone else was in an uproar. Many of them hadn't even figured out how to tackle the first question yet, and yet someone from the Chinese team had already handed in their papers?
Hasn't the game just started?
Many contestants felt their minds were about to collapse! How could they compete when others finished in an hour what they might not have finished 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 practice for academic geniuses. 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 without surprise. They had indeed carefully selected the questions, 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 gave a cheering gesture to the other members of the Chinese team. 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 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?" Professor Cheng, the deputy leader of the Chinese team, asked with a smile, not surprisingly, when he saw Wu Tong coming out of the examination room. 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 Professor Cheng two chocolates, one for each person who saw 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, which Wu Tong said 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 their 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 taught a class on this topic.
"Pure Hankao techniques and understanding, pure Hankao 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 wasn't too difficult, basically only relative to Wu Tong.
As expected, when the time to hand in the papers actually 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 question is this?"
"This doesn't seem like a problem a human could solve. Are they kidding us?"
"I think I might not get any points for the third question, or if I'm more confident and remove the word 'maybe', I won't get any points!"
Of course, there are also some who are full of confidence, such as the North Korean group. It seems that they are performing well? They all have a bit of an arrogant attitude!
The Chinese team didn't all look miserable, but their expressions weren't particularly good either.
However, after taking a closer look at the situation, Professor Cheng felt that the situation wasn't so pessimistic, so he offered some comfort and encouragement: "Alright, everyone, cheer up, get your spirits up, don't think about anything tonight, get some rest, and focus on preparing for tomorrow. Your performance on every question tomorrow is crucial, and you need to give it your all in 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 these 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 nearly two months of vacation, free to have fun until the start of school in September, when they will enter university and begin their fresh university life.
"Come on, I'll be waiting for your triumphant return and picking up your Professor Li in a while. Starting tomorrow we'll have four days of free time to look around and it won't be a wasted trip to Nur-Sultan!" Before entering the examination room, Professor Cheng patted everyone on the shoulders to encourage and boost morale.
The exam started again, and 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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