The brown-haired invigilator looked at the time. Four hours had passed since the exam started, and there were only less than 55 minutes left. It was good to be able to finish one question in such a small amount of time.

At this time, another candidate raised a sign asking for help. The brown-haired invigilator was no longer interested in seeing Qin Ke's situation and walked away quickly.

Liang Shaoping saw Qin Ke starting to answer the questions from a distance. He was relieved and felt inexplicably motivated to do the questions.

Persist, keep on keeping on!

If Teacher Qin doesn’t hand in the paper, I will never hand it in either!

Qin Ke didn't pay any attention to the outside world. He didn't even pay attention to whether others had handed in their papers.

The tip of his pen scratched out numbers and mathematical symbols on the paper at a rhythmic and even speed. Lines of regular handwriting extended and combined into complete steps to solve the problem.

If the brown-haired invigilator was still there, he would be surprised to find that Qin Ke used five methods for the first question, and none of the solutions exceeded ten lines!

This is a threshold question that stumps most of the candidates. In the eyes of Qin Ke, who has created his own Olympiad theory at this time, it is like dough that can be kneaded at will, and like a peeled banana, with no secrets at all.

, you can stutter as much as you want. (I originally wanted to use the common "what" without "what", but after thinking about it, it is too easy to be 404, dear readers, please replace this metaphor in your mind)

In about eight minutes, Qin Ke completed five solutions to the first question, each of which was a completely different way of solving the problem. Among them, both the thinking of Lagrange's mean value theorem and Leib's thinking were used.

The connotation of Nitz's formula is all based on the way of thinking of college mathematics, but it uses all the knowledge points of high school mathematics.

He is like a superb chef who uses the simplest ingredients to cook the most delicious and gorgeous top-notch meals.

After solving the first big question, Qin Ke went to the second, third, fourth, and fifth questions non-stop...

The following questions were difficult and easy, but Qin Ke took the "master key" in his hand and easily played them into eighteen shapes. In less than forty minutes, Qin Ke had finished writing the answer sheet and put it down.

Pen.

Uh... I'm a little embarrassed. Although each question uses five solutions, because the steps do not exceed ten lines, it can be written on one answer sheet.

It was useless to ask the teacher for two more answer sheets.

Qin Ke checked it over and found that there was nothing wrong. He looked at the time and saw that it was almost time to hand in the papers, so he simply did not bother the invigilator to collect the papers in advance without raising a sign.

While eating biscuits, he pondered a very important question.

——What would be a good name for this original mathematical theory system of my own?

…

Finally, Qin Ke came up with the most satisfying name when the bell rang at the end of the exam.

He decided to refer to Beethoven's approach and name his theory "Zhi Ning Qingjun". Of course, the official name is "Qin Ke Zhi Ning Qingjun's new high school Olympic mathematics thinking theory system".

This set of theories is scientific, concise, and easy to understand. It is better and more advanced than what he taught to the Mathematical Olympiad training team before. It can improve high school students' interest in learning Mathematical Olympiad and problem-solving skills to a considerable extent, but if you want to really be able to

To master its essence, one must have at least Ning Qingyun's level of talent in science.

"It seems necessary to hold another crash course tonight." Qin Ke thought, and then the paper collecting teacher came. Qin Ke picked up his stationery and ID, and let the paper collecting teacher put away the rest of the test papers and answer sheets.

seal.

Sometimes fate is very strange. The person who came to collect Qin Ke's papers happened to be the brown-haired invigilator.

The first thing he saw were Qin Ke's two blank answer sheets without writing on them, and he said "ha" in his heart, but the blank answer sheets had to be taken away as well. As soon as he collected the two blank answer sheets,

I saw Qin Ke’s first answer sheet.

The answers are densely written on it.

At a glance, I can see that I have answered all five questions, but I don’t know whether they are correct or not.

Hmm? Proof one? Proof two...proof five? What the hell is this? Five different proof methods?

Is it true or false? But each method of proof is too short, right? It doesn’t exceed ten lines!

The brown-haired invigilator looked at the calm Qin Ke in surprise and confusion, and couldn't help but look at the name column on the answer sheet, and saw that it was written in Chinese and English: "Qin Ke Qin Ke".

He silently remembered the name, and then sealed Qin Ke's paper.

…

"Teacher Qin!" Liang Shaoping chased after Qin Ke and asked curiously: "Why did you answer the question in the last hour? Have you finished it all?"

"It's done." Qin Ke didn't brag about his five methods. He smiled and said: "Four hours before the exam, I happened to have inspiration and thought of a new method system for solving problems. I called everyone in the evening and I shared it.

one time."

Liang Shaoping was startled, and then gave a thumbs up in amazement: "Teacher Qin is awesome. He finished five difficult questions in one hour! And he is still thinking about new problem-solving methods! Today's questions are better than the selection papers we usually do.

It’s still difficult, I only solved two and a half questions! Looking forward to Teacher Qin’s sharing in the evening!”

"Don't worry, you might be able to answer three or even four questions tomorrow. Let's go." Qin Ke smiled and met Deng Hongguo, Ning Qingjun and the other three team members at the exit of the examination room, and returned to the hotel together.

The DAY1 exam was over. Deng Hongguo didn't want to ask everyone how they did. He just encouraged everyone to persevere. There will be DAY2 exam tomorrow.

As the captain, Qin Ke had a good relationship with the team members, so naturally he didn't have so many worries, so he asked each person privately how they had answered the questions.

The best answerer was naturally his cabbage Ning Qingyun, who answered all five questions, followed by Wang Changai, Sun Bingfei, and Wei Yuyuan who answered four questions each, and Liang Shaoping who answered two questions each.

Half of the questions were asked, but neither Sun Bingfei nor Liang Shaoping answered the threshold questions, so 7 points would actually be deducted.

After the evening, Qin Ke called several team members to his room. Deng Hongguo heard that Qin Ke had a new method of solving questions and came to listen curiously.

Qin Ke asked the hotel for a small whiteboard and an erasable pen. Then he looked around at the anxious and expectant eyes of everyone and said with a smile: "My theoretical method system was only summarized in the afternoon, and there are probably still some differences.

If it is too perfect, it will take a long time to really master it, but it doesn't matter. Today I have basically figured out the direction and ideas of IMO questions. I use my new theoretical method system for IMO.

, I’ll give you a special training session.”

Qin Ke looked at his little cabbage and said with a smile: "This theory is called 'Zhi Ning Qingjun', and its full name is 'Qin Ke Zhi Ning Qingjun's new high school Olympic mathematics thinking theory system', ha,

Don't laugh."

At first, everyone could hold it in, but when he heard what he said, they all laughed: "Teacher Qin, can you please stop stuffing dog food for us? It's too sweet and we can't stand it!"

Ning Qingyun's face turned red when she was told that, and she couldn't help but roll her eyes at him: "Why do you want to involve me?"

"Because this is based on the Mathematical Olympiad skills I have taught you for more than half a year." Qin Ke smiled and patted the small whiteboard: "Okay, from now to ten o'clock in the evening, three hours, you guys

Whether you can do three questions or more tomorrow depends on how much you can absorb tonight!"

…

The DAY2 exam came as scheduled, but because there was no opening ceremony, the time was advanced to 9:00, and the end time was accordingly advanced to 14:00.

It was still the original examination room, with the same biscuits, chocolates and small bottles of mineral water.

Liang Shaoping walked into the examination room excitedly. Qin Ke next to him patted him on the shoulder: "Shaoping, don't be too excited. Stay calm so that you can think calmly."

"I'm sorry, Teacher Qin." Liang Shaoping said embarrassedly: "I thought about your 'Zhi Ning Qingjun' theory all night last night and almost didn't fall asleep. If I could have heard this a day earlier, I could have done it yesterday

Here comes the first threshold question."

"And today, don't worry, you should do better than most people today."

"Well! Thank you, Teacher Qin!" Liang Shaoping returned to his seat full of energy.

As soon as Qin Ke sat down, Hill from the American team came over and said in English: "QIN, what happened to you yesterday? You handed in a blank paper?" There was some suppressed anger in his voice.

Qin Ke smiled and said: "No, I finished it, I just didn't hand it in in advance."

Hill's anger disappeared immediately, and he gave Qin Ke a deep look: "In this IMO, only you and Yevgeny of the Bear Country can be called my strong rivals. I hope your performance today can make

I'm impressed." After saying that, he turned around and returned to his seat.

"Want to be impressed? Yes, I will grant your wish." Qin Ke smiled softly and learned to turn his pen like Hill, huh? It's a bit difficult. This kid's pen turning level is so high. How many years has he practiced?

The melodious bell rang again, and the test papers were distributed to all candidates in advance.

Qin Ke scanned the next question,

The first threshold question is a big geometry question:

"1. In the acute triangle ABC, AB is greater than AC. Let ⊙O be its circumcircle, H be its vertical center, F be the vertical foot raised by the vertex A, M be the midpoint of side BC, Q is

A point on ⊙O makes ∠HQA=90 degrees. K is a point on ⊙O such that ∠HKQ=90 degrees. It is known that points A, B, C, K and Q are different from each other and are arranged in this order.

⊙O above. Prove: The circumcircle of triangle KQH is tangent to the circumcircle of triangle FKM."

It is indeed quite difficult. It is worthy of being called DAY2. The simplest question is equivalent to yesterday's first threshold question, and today's threshold question is even more difficult.

It is just used to continue to improve my own mathematical theory system "Zhi Ning Qingyun"!

Qin Ke thought briefly and used his new theoretical system to see the intention of the question maker. He only needed to make a few auxiliary lines to transform the question into proof that the four points E, K, D, H are coaxial, Q, M

, the three points H are collinear, and HA·FH=HD·HG.

It took Qin Ke about ten minutes to complete the five methods of verification, and each method also had no more than ten steps.

Now holding the New Mathematical Olympiad theoretical system in his hand, he is like killing a chicken with a sledgehammer, relaxed and happy.

Among the next four big questions, the only one was more difficult, and it only took Qin Ke about fifteen minutes to complete the five solutions.

In less than an hour, Qin Ke completed the entire paper.

He checked it and found that there was no problem, then he raised the "HELP" sign and prepared to hand in the papers and leave.

The one who came to collect the papers was the brown-haired teacher. He came here specially from a distance. The other invigilator who was about to go over looked at him strangely, but the brown-haired teacher ignored him and hurriedly came to the Qin Dynasty.
Chapter completed!