Before returning to the college entrance examination, I became popular in the science circle

Chapter 39

The nine team members who participated in the training camp nodded earnestly. This is a problem they want to avoid. They must keep in mind that their opponents are the top high school students in the country, and all of them can be said to be geniuses.Sprint for better results, don't be sloppy at all!
Everyone was a top student in mathematics. As soon as they thought about it, they realized that Lao Zhang had just called the names of nine people, and the remaining one was the god. He couldn't help but quietly glanced at Wu Tong, wanting to see how Lao Zhang would explain their province. Is this trump card confident?

"Don't even look at it. As for Wu Tong, I have nothing to say. You can just keep performing normally. The national competition is not your end. I will give you a small goal. First grab a national team spot and come back!"

With perfect scores in the league, IMO classic puzzles can be solved easily, and the college textbooks have gone to number theory, what else does he have to say!Look at this girl's attitude of treating her performance on the spot as nothing, he doesn't even need to tell her to perform normally and maintain a good attitude!

He even had extravagant hopes that if this girl could enter the national team and win a gold medal with a perfect score in the IMO, their Central Plains Province would be a big hit!
"Does Teacher Xiao Zhang have anything else to arrange?"

"Everyone should practice and reserve everything. There is no need to add more icing on the cake today. As long as you maintain a good attitude, you must rest well and face the competition with plenty of energy! Don't be too excited before the exam. , I can’t sleep, the effect is not worth the loss!” Teacher Xiao Zhang, who is the chief steward of the provincial team, gave instructions on the details.

On the 14th, this year’s Chinese High School Mathematics Olympiad officially kicked off.

"I am here, and I wish all the students great success!" With the enthusiastic encouragement of the two leading teachers, Lao Zhang and Xiao Zhang, all the participating members of the Central Plains Provincial Team, like hundreds of contestants from all over the country, were full of fighting spirit into the examination room.

At [-]:[-], all candidates are in their seats.

Eight O'clock.

The test papers have been distributed and the No. 20 Chinese High School Students Mathematics Olympiad has officially begun.

CMO completely simulates the format of the International Mathematical Olympiad (IMO). The exam is divided into two days, with one test per day, each test time limit of 4.5 hours, and a total of three questions.There is a difference only in the scores. The total score of each CMO question is 21 points, and there are six questions in two days, with a total of 126 points, which is three times that of the IMO. This is to conform to the cognitive habits of the Chinese people. IMO, each question is worth 7 points, and the total score is 42 points.

Four and a half hours is still a long time for an ordinary exam, but compared to the players participating in CMO, it is still tight for time.Although CMO only has three questions per session, these three questions cannot be written casually. For many candidates, it is not too much to give them twice the time.

Especially this year is an odd-numbered year. According to the rules, the questions of Zilai are more difficult than those of even-numbered years.In addition, in the past two years, the Chinese team has won the Olympic Games with great victories, overcoming obstacles, and last year's IMO's hardware and silver medals with a total score of 217 points and winning the No. Brilliant and great results, the difficulty of this year's questions can be imagined.

Many candidates were already blinded as soon as they read the questions after receiving the test paper, and they entered a state of thinking and racking their brains. Only a very small number of them even put pen to paper to deduce the questions.

Wu Tong got the test paper, checked and filled in the information as usual, and glanced roughly. It was still the usual CMO questioning policy, the first question was geometrically proven.There are two small questions in total, and the naked eye can see that it is a given proof question with a lot of engineering.

The difficulty of the questions, she looked at, was not as difficult as the classic IMO questions, but it also surpassed the difficulty of the usual national competition questions. The second major question was already equivalent to the difficulty of the finale of the usual national competition.

However, such difficulty is still not a hurdle for Wu Tong.

Wu Tong read the questions carefully, brainstorming began in his mind, and his sharp thoughts were running like a white horse, sparking inspiration.Her thoughts expanded, directions emerged like water, and her pen began to deduce on the draft paper.

Let Q and R be the midpoints of OB and OC respectively.

Connect EQ, MQ···
Therefore △EQM=MRF, so EM=FM,

In the same way, EN=FN can be obtained,

So EM·FN=EN·FM
The first question was solved, and the second question continued to develop smoothly. This question is more complicated. Wu Tong wrote a whole page in the proof process, and finally proved that the result is negative.

As long as the analysis is clear, proof questions are actually much simpler than other calculation questions. There is no need for tedious calculations and it is very enjoyable to perform step-by-step deductions. Wu Tong actually likes doing proof questions.

After sorting out the proof process, Wu Tong copied it onto the test paper and solved the first question.

The second question is a prime number problem. The question is really simple, just one sentence, but the search is also very wide. Find all pairs of prime numbers (p, q)... The difficulty of this question rises sharply. Deduce carefully on the draft paper, and quickly find the direction.

If 2|pq, we might as well set p=2, then 2q=·····
By fermat's little theorem, we get...

In the same way, K<1, a contradiction!That is, there is no satisfactory (p, q) at this time,
In summary, all pairs of prime numbers (p, q) that satisfy the requirements are (2, 3) (3, 2) (2, 5) (5, 2) (5, 5) (5, 313) and (313 , 5).

The second question was solved again, and Wu Tong advanced to the last big question.

This question could not stop Wu Tong from moving forward. The spark of inspiration completely exploded. Wu Tong quickly came up with an ingenious solution. First, he proved a lemma, then used the lemma to derive the satisfying conditions, and finally solved it completely in two steps. For this question, the number of convex m-gons whose vertices belong to P and have exactly two interior angles are acute angles, the answer is quite brilliant.

For Wu Tong, the precautions for this question are the use of those mathematical symbols, which must be written neatly and clearly.

The completion of the transcription of the third question also means that Wu Tong has completed all three questions on the first day of the exam. Wu Tong checked the time and saw that just over an hour had passed. Now Wu Tong has a very clear judgment on his derivation results. .As long as she reads the question correctly, the result cannot be wrong.

It took about ten minutes for Wu Tong to check carefully, which was equivalent to deducing and verifying again in her mind at a faster speed. After confirming that she was correct, she raised her hand and handed in the paper. At this time, the exam time had just passed an hour and a half.

In the examination room, many students were still struggling with the first question. Those who did it quickly were still solving the second question, and almost none of them did the third question.

These academic masters from various schools can be said to be among the top two or three hundred in the country. At this moment, I deeply feel that they are like the poor students in the school. Their brains are blank when they are troubled by the questions, and their brains are almost dry.

At this time, Wu Tong's actions were nothing less than a shock to the examinees who noticed her actions.

How long has it been since someone handed in the paper?
Did they waste too much time, or did someone just get burnt out and give up?

The invigilator was also surprised. It had only been half an hour, right?Is this candidate sure he wants to hand in the paper to end the exam?However, when he came over and saw the neatly written examination papers by Wu Tong, his doubts turned into silence.

Today's kids are really amazing!This year's unprecedentedly difficult exam questions, let him do it, he may not be able to complete the answer sheet so quickly.

With such an exam question, there are still candidates who can complete the answer sheet and hand in the paper three hours in advance. It is estimated that he is another top seedling who can book a place in the national team!
(End of this chapter)