Black Tech Scholar

They only speak? "

Liao Yuanbai looked at Liu Wei with a half-smile, "Are you trying to create panic? Let alone them, can the two of us make any mathematical guesses? At that time, it will not be a test of imagination, the big deal is the score of the final additional question Just don’t. It’s impossible for the previous questions to have such problems. Only the last additional question, we can’t do it, do you think others can do it?”

"That's right!" Liu Wei nodded, he felt that what Liao Yuanbai said was quite reasonable.But the wait is still hard to bear, especially after Liao Yuanbai said the mathematics conjecture of the exam.He still comforted himself in his heart that such strange questions should not appear in the International Mathematical Olympiad.

When the results came out, the teacher who led the team took all the students to see the results.Hua Guo's team made it to the final without any surprise. No.1 is Huaguo's team. In the Mathematical Olympiad competition, Liao Yuanbai sits firmly at No.1 with a full score plus a full score for additional questions, as stable as an old dog.Immediately after the second place is the millennium second Liu Wei. He was deducted five points for the additional questions, and his total score was only 115 points.

No.3 is a player from Lighthouse Country, and his strength is also very strong.The next one is Mao Xiongguo's contestants, but several contestants from Huaguo's test scores are not bad, with a high average score.Sitting firmly on the throne of No. 1, as for physics... Hua Guo also entered the final with No. [-] result.

The teacher who led the team breathed a sigh of relief. When he saw the results of Liao Yuanbai and Liu Wei, he relaxed.Anyway, this time the first prize should be taken away.As for the throne of champion... the teacher who leads the team doesn't know whether Hua Guo's players will be able to get it.Although Hua Guo's players are very strong, players from other countries are not weak.Liao Yuanbai was able to lead this time with a full score of 120, but as for the final, no one knows what the final will be like.

With such achievements, the teacher who led the team invited everyone to have a big meal at the Chinese restaurant outside Mills University, which is regarded as a reward for everyone's efforts.

After drinking and eating, the teacher who led the team cleared his throat and said, "Students, we have entered the finals. Tomorrow, the students in the Mathematical Olympiad will participate in the competition. I hope you will show your true skills and don't let the outside look down on us. After cheering up, the teacher who led the team brought the students back to the dormitory.

The small towns in the Lighthouse Country are fairly safe at night, especially in prestigious schools like Mills University.Liao Yuanbai and Liu Wei walked out of the dormitory, walked for a while and then talked for a while.

This final exam is different from all the previous exams. It lasts seven hours from nine o'clock in the morning to two o'clock in the afternoon.Time is enough to tell how difficult this final topic is.Liu Wei touched Liao Yuanbai with his elbow, and said in a low voice, "You won't be right, are you really going to take the math conjecture test?" Don't be fooled by your crow's mouth."

"I just said it casually." Liao Yuanbai comforted Liu Wei. He could see that Liu Wei was a little nervous. It can be solved. Therefore, I think that although the possibility of taking a mathematical conjecture is high, it may also be a question with hidden secrets. For example, a topic in topology or geometry."

"Euclidean?" Liu Wei was stunned for a moment, "No way, if it was Euclid, it would be too simple."

The corner of Liao Yuanbai's mouth twitched, "Do you know what you are talking about? Have you never been abused by geometry, and you can say such things easily."

"No, I mean, if you want to take the geometry test, there is a high probability that it will be Euclid, after all, it is the one you have been exposed to the most. And it is impossible to take the test too deep..." Liu Wei's voice It was getting smaller and smaller, after all, he was not sure what the teacher was thinking about.

Liao Yuanbai walked to a chair and sat down.He thought for a while, "I heard something interesting, Weishen, do you want to know about it?"

"What's the matter?" Liu Wei tilted his head and looked at Liao Yuanbai. Obviously, his face was full of wanting to know.

Liao Yuanbai looked at the twinkling stars in the sky, and said with a smile, "I heard that the exam questions this time are given by the mathematics professor of Hilton University, so it looks a little difficult and interesting." Standing up, Liao Yuanbai thought about it Thinking about it, he said to Liu Wei, "Let me warn you again, Weishen, if you dare to turn on the lights to fight at night... I will curse you for failing the exam in the future."

After speaking, Liao Yuanbai walked towards the dormitory with a smile.Liu Wei stomped his feet in the moonlight alone, secretly thinking in his heart, the curse of Liao Yuanbai is too poisonous.

The next day's International Mathematical Olympiad still came. After breakfast, the teacher leading the team led the students participating in the Mathematical Olympiad to the examination room.Because of the road signs, it was not time for the exam when I arrived at the exam room.The teacher leading the team first chatted with the students for a while to let them relax.Then let them enter the examination room. This is the last examination of the International Mathematical Olympiad, and the teacher leading the team can only do their best and obey the destiny.

I can only pray secretly in my heart that the students can get a good grade in the exam.

When the invigilator handed out the papers, Liao Yuanbai looked at the questions.Very good... As expected, it is a question given by the mathematics professor of Hilton University. The first question is linear algebra.What the hell... Liao Yuanbai was about to swear, he took a pen and started writing.

Although it is a topic of linear algebra, it is not too difficult.After finishing the first question, look at the second question.Very good, Liu Wei was right.It was indeed a simple Euclidean geometry problem. After finishing the second problem, Liao Yuanbai started to scold his mother again.He actually started to get a little confused about the third question, and he read it for a long time.His eyes were almost blinded by the question, and he still couldn't understand the question.

Liao Yuanbai took a deep breath, isn't this cheating.This question is simply... Turning his head to look at other people, he found that candidates from other countries were just like him, with a look of bitterness and hatred.

emmmmm, it seems that the mathematics professor at Hilton University played a bit too big.Liao Yuanbai thought so in his heart, and looked at the topic for a while, when he was about to give up this topic, he found something wrong.He glanced at the title again, what the hell?This is... a manifold?

It seems that it should be solved by Li Qun, Liao Yuanbai frowned and thought for a while.

The so-called manifold refers to the space that locally has the property of Euclidean space, which is used to describe geometric shapes in mathematics. ①The Lie group is a relatively simple algebraic structure with only one operation; it is a basic structure that can be used to establish many other algebraic systems.In mathematics, a Liegroup is a real manifold or a complex manifold with a group structure, and the addition and inverse operations in the group are analytic maps in the shape. ②

This math professor is playing too much, right?I'm afraid I don't want everyone to be wiped out.Liao Yuanbai picked up the pen and began to calculate, thinking while calculating, no wonder it takes seven hours to take the exam.Although there are only twelve questions, and there are additional questions together.With this amount of calculation, I'm afraid it will last forever.

It looks like a geometric body, but it can't be calculated no matter what, so it is.Counting you as cunning, Liao Yuanbai hummed a few times and started to do the fourth question below.

The latter questions are pretty good. Although the amount of calculation is huge, they are not as perverted as the first few questions.Liao Yuanbai wrote question No.11 easily, but he hadn't had time to read the last question yet.Many students seem to be stumped by the third question. Some choose to do the following questions first, while some students choose to confront the third question head-on.

The teacher leading the team standing outside the door really couldn't eat, it was already twelve o'clock, and no student had come out yet.These leading teachers were also not allowed in the examination room, and he seemed a little flustered walking around outside.

Even the other team leader outside the court couldn't stand it any longer. This is also the team leader from another country in Asia.He watched Jinghua University's teacher wandering around, squinted his eyes and said in English, "Dude, can we stop swaying like this. You are Huaguo's teacher, so what are you still worried about? Huaguo Mathematics and physics are both strong points, although this time the math test is a bit longer, but if you do poorly in Huaguo, the whole world will not do well in the test."

Having said this, the teacher deliberately paused.He was observing the expression of the teacher leading the team at Jinghua University, and found that the teacher's expression seemed to have improved, so he continued, "So don't worry, it should be the first time you lead the team. When I led the team for the first time, I was not as lucky as you."

The teacher smiled, and the leading teacher froze for a moment.Looking at the teacher, he asked, "Why do you say I'm lucky?"

"When I led the team for the first time, I didn't make it to the finals. Both Mathematical Olympiad and Physics competitions were wiped out in the preliminary stage. Back then, it was still an individual competition system. Regardless of nationality, as long as you can enter the finals, you will be fine." Without a single teammate, I can continue the exam. But the first team I led, the foundation was indeed a bit weak. So...they went home during the qualifiers." Speaking of this, the teacher raised a smile Yi, looking a little proud, said, "It's all right now, at least this year's students can be admitted to the finals. As for the results, I think it's great to be able to enter the finals."

"Thank you." The teacher leading the team took a deep breath, he was indeed comforted.Although still very nervous, at least there is no sense of urgency like before.

After finishing question No.11, Liao Yuanbai shook his weak hands.He rubbed his wrist while looking at the last mention.It doesn't matter if you don't look at him, he is not well at all.

The above title is written as follows: To find such a smallest number n, so that among n people, there must be k people who know each other or l people who do not know each other. ③It looks very short, right? It looks very simple, right?Liao Yuanbai wished he could slap himself and make him crow mouth.

Isn't this so... He actually wanted me to solve this problem. Is this math professor going crazy?Liao Yuanbai's whole body is not well.

This question, is he going to do it or not? !For a while, Liao Yuanbai couldn't pay attention.Do you want to throw a note, the one with words is done, and the one without words is not done.Thinking of this, Liao Yuanbai crumpled the draft paper and gently threw it to his desktop.

The ball of paper kept rolling between the square inches of the desk, and after a while, the ball of paper slowly tried to stop...