Early Monday morning, Lan Jie met Zhang Yutong at the gate of Yangzhong, and the two walked into the campus together.

Zhang Yutong, who is 1.68 meters tall, asked: "Lan Jie, you seem to have grown taller again?

"It's still 185. ”

"Lanjie, you have long legs, you are tall, and you envy people with long legs. ”

"Zhang Yutong, your legs are not short. ”

"The standard for leg length is that there are legs from the head down. Based on this standard, I am a short-legged girl. ”

"Zhang Yutong, the thing you said is an octopus. ”

"The octopus is handsome, and I love the octopus so much. ”

"Even more handsome than an octopus is Eight, who doesn't even have a head. ”

"Poof, you're funny!"

The two talked and laughed, and in a blink of an eye they arrived in front of the teaching building.

Zhang Yutong suddenly stopped smiling, she said in a slightly deep voice: "Within this month, I will transfer to Class 13." ”

"Class 13 is an international class. ”

"Well, the international class. ”

A few days ago, Zhang Yutong said that she was studying IELTS, and now she said that she is about to transfer to the international class, step by step, reasonable, and logical, so Lan Jie is not surprised.

"Before you change shifts, about a wave?"

"Okay, let's talk about it. ”

Lan Jie and Zhang Yutong came to the second and third class classrooms, each in their own seat, and each in their own book.

History classes are dispensable for science students, and the history of the exam is super simple, just write and write.

Rather than wasting 45 precious minutes in history lesson, Ranger learned an equation, N2+6H++6e-+(18-24)ATP→2NH3+(18-24)ADP+(18-24)Pi.

The total reaction formula of nitrogen fixation is widely found in the microbial world, and biological phenomena are expressed through chemical equations, and the relationship between biology and chemistry is extraordinary.

Chemistry and physics have been bound together for a long time, physics and mathematics are all related, mathematics, physics and chemistry are all related, but there are only three places to be a person. People are people, tools are tools, we should distinguish clearly, and we must not mess up ethics and ruin discipline.

The tools are gone, the people are coming.

History class is over, and math class is here.

Whether it's a liberal arts class, a science class, or an international class, you have to learn mathematics.

Mathematics teacher Han Daxian is young and teaches well, he has two packs of cigarettes a day, and is known as "Han Daxian".

More and more young teachers are entering prestigious high schools, and their performance is excellent, and they are highly praised, and Han Daxian is one of them.

Teachers who teach math are certainly smart people.

Being smart may be one of the reasons for the lack of hair, but it's not the main reason.

Lan Jie now knows that Mr. Han is an Aa man.

In this math class, Han Daxian's first three sentences were: "I heard that a certain teacher taught calculus? I heard that my teaching progress is very conservative? I heard that some people don't care about my Han feelings at all?"

is full of Xingshi's questioning style, and no one in the audience dares to answer.

At this time, only the students who scored full marks in the mathematics test dared to respond bravely: "There is no superstructure or overclass, only whether you are willing to learn." Our second and third classes are all students who love learning, Mr. Han, you teach us, teach us!"

"Since Rangier has made a strong call for knowledge on your behalf, then I will teach you. Since a certain teacher has taught calculus, I will talk about supplementary knowledge. Lan Jie, did a certain teacher talk about Taylor?" Han Daxian skillfully picked up a piece of chalk and habitually sent it to his mouth.

Lan Jie replied truthfully: "She hasn't talked about Taylor yet, and this kind of difficult teaching content, of course, needs Teacher Han to guide us personally." ”

"That's true, I'm going to focus this lesson on Taylor unfolding. ”

Han Daxian immediately entered the teaching session, and under his careful teaching, most of the students in the class did not understand Taylor's unfolding.

"The class was very productive, out of class. ”

Han Daxian was afraid of the chalk ash on his hand and went to the smoking area downstairs.

Lan Jie chased down with his notebook, he respectfully handed over the notebook, and humbly asked for advice: "Teacher Han, I have done a math problem, please review and correct it." ”

"I'm very strange, the better the grades, the more diligent and inquisitive, the worse the grades, the more willing to degenerate, why is this?" Han Daxian took the notebook and flipped to a certain page.

Ranger replied, "Because it's fun." ”

"Are you happy, Lanjie?"

"Super happy. ”

"It would be nice for every student to be as happy as you are. ”

Han Daxian quickly examined the math problem that Lan Jie had done.

The question is: in a gambling game, one side wins 6 games first. However, when Pierre won four games and Edmond won three, the game was aborted. How should the stakes be distributed?

This question is based on real events in history, hundreds of years ago, a French gambler recounted his personal experience of gambling and turned to Pascal, the big man at the time.

Pascal felt that there was something wrong with this gamble, so he wrote to his friend --- another big man, Fermat, saying that he wanted to learn from each other and have fun.

Then there is the "staking distribution theory".

Fermat's solution was that if Pierre and Edmond resumed gambling, they would bet up to four more rounds to decide the winner.

Fermat listed 16 permutations of the possible outcome of the last four games: Pierre was the winner if he won 2 or more games, which happened 11 times, and Edmund was the winner if he won 3 or more games, which happened 5 times. Therefore, the ratio of the bet is Pierre: Edmond = 11:5.

The mathematical genius Fermat simplified the complex, and he was brilliant at translating the problem into classical generalizations.

Ranger used Fermat's solution, and he found the result at 11:5.

"Lan Jie, no problem, you have already found the correct answer, why are you still coming to me? So you are here to receive the little red flower? The little red flower is not under my control, you go to a certain teacher to get the little red flower. ”

"I'm ashamed to say that among so many probability methods, I can only make classical generalizations, which is really embarrassing. Teacher Han, can you teach me other methods?"

"Lan Jie, you have such good math scores, and you have scored full marks in every exam, but you have always maintained a humble attitude, which is worthy of praise. ”

Jingle bell.

Jingle bell.

Infinite good scenery.

Eye exercises inspiring music sounded.

Han Daxian said, "You don't go back to the classroom to do exercises?"

Lan Jie, who has a strong desire for knowledge, is reluctant to leave: "If I didn't learn knowledge from Mr. Han, I couldn't feel at ease when I left." ”

In Lan Jie's body, Han Daxian seemed to see his own peerless appearance when he was young, and he admired from the bottom of his heart: "Excellent." ”

Lan Jieli started doing eye exercises on the spot, and Han Daxian drew triangles.

The eye exercises are over, and Han Daxian's triangle is finished.

"Using Pascal's triangle, you can find the number of combinations that take out r pieces out of n items at once, and you're good to go. Han Daxian returned the notebook to Lan Jie, and he said: "My next class is the second class, Lan Jie, you can understand this triangle yourself, there are other problems in mathematics that you don't understand, come to me at any time." ”

"Thank you, Mr. Han, thank you!"

"It is the duty of the people's teachers to preach and teach and solve doubts, you asked the questions you should ask, and I did the work I should do, so Lan Jie, you don't have to thank me, if you want to thank the party and the government. Let's go, see you tomorrow. ”

"Teacher Han will see you every day!"

Lan Jie paid attention to the salute and watched Teacher Han leave.

Teacher Han, what a commendable people's teacher, I really want to send a pennant to Teacher Han.

During my father's business trip, I am really grateful that I can accept your guidance from Mr. Han.

Lan Jie returned to the classroom of Class 2 and 3 and devoted himself to studying the authentic works of Teacher Han.

1

11

121

1331

14641

15101051

......

"The fifth row of the triangle deduces the gambler's victory, yes, 11:5!"

Drawing inferences, Lan Jie continued to deduce.

1615201561

172135352171

18285670562881

......

#include

#include

int arr[n+1][m]=2*n-1；

......

Pascal's triangle is actually the Yang Hui triangle, and the numbers in any row of the triangle can be found through known laws.

The rules are fixed, the usage is ever-changing, and this is the charm and evil spirit of mathematics, those who love her are willing to eat, and those who hate her feel the fear of being dominated all day long.

If r takes a value of 2 or more, it must be ten draws. If r takes 1, according to my preliminary calculation results, the single draw has a short return period, the market is effective, and the working capital turnover is flexible, and the single draw is not a loss! ’

Don't itch your hands, don't have a fluke mentality, this is not a vulgar and superficial game of kryptonite, but a rigorous and serious scientific research, and this time you must accumulate 117 medals.

Langeres has set a medium- and long-term plan and strictly implements it in its daily study life.

In spring, the sprouts are unearthed.

In summer, lotus flowers flutter.

Autumn leaves are shaken by the wind.

In winter, all herbs wear filial piety.

The four words are combined into one word, which is not half a cent.

The summer and the cold come to kill the knife, and cut off all the men, women and children in the world.

Time flies, time flies.

Gossip aside, long story short.

Dozens of minutes have passed in a blink of an eye.

Physical education classes are always scheduled at the end of the morning, and classes 2 and 3 are still in physical education classes with classes 2 and 5.

"In this class, push the shot put, count the grades, and after that, you will move freely, and if you don't pass, you will continue to practice the shot put. The boys are here, the girls are there. ”

Mr. Wei was in charge of the boys, and he pronounced the names one by one according to the strokes of the surname: "Ding Haoze!"

"Here!"

"Start putting the shot put!"

"Good!"

Sou!

Click!

"Eight meters one, pass!"

"Next, Ma Haoran! Eight meters, pass!"

"Wang Mingxuan, nine meters nine, pass!"

"Wang Junze, seven meters three, but! Do it again! Seven meters five, but not! Wang Junze, you go to the side to practice, next!"

"Lanjie!"

"Here!"

"Start putting the shot put!"

"Good!"

Sou!

Click!

"Fifteen meters eight! over! over! over, over!"

Teacher Wei is very happy, he knows that Lan Jie is strong in sports, but he didn't expect Lan Jie to be so strong!

"Li Zihan, five meters six! I read that right? Yes, that's right, five meters six, Li Zihan, you are not even as good as a girl!"

Teacher Wei was suddenly irritable, he had never seen such a weak sophomore boy.

Li Zihan was ashamed: "Teacher Wei, I'm ...... Do I push one more time?"

Teacher Wei reprimanded: "Push a ghost! Li Zihan, you pushed three times in a row, five meters six is your best result, go next!"

As the saying goes, if you don't lose your strength, you lose your kidneys. Li Zihan, who is 1.62 meters tall, is a relatively short breed among the sophomore boys, and sports events, especially those with explosive strength, are Li Zihan's shortcomings.

Li Zihan stepped aside and deeply reviewed his own shortcomings.

The boy pushes the 5-kilogram shot put, and eight meters is the passing line.

To be reasonable, it is not easy to reach the eight-meter passing mark.

"Du Yuxuan, nine meters one, pass!"

"Chen Zixuan, eight meters three, pass!"

"Wu Zihan, ten meters four, good!"

This......

These classmates have all passed!

These classmates are Lan Jie's fan brothers, and a few of them follow Lan Jie to play football, and they don't want to worship Lan Jie.

Li Zihan has to admit that it is beneficial to do more exercise on weekdays.

"Chen Haoran, nine meters, pass!"

"Yang Kewei, twelve meters one, excellent!"

Wow, Yang Kewei from Class 5 threw more than 12 meters, he is so good!

And Lan Jie's dog actually threw more than fifteen meters, Lan Jie is a pervert.

Li Zihan finally realized that the reason why he couldn't get along with Lan Jie was because he wasn't perverted enough.