I Just Want to Be a Quiet Top Student

　　 "Oh, I'm going, my mind is broken!"

　　 Doing math problems is the same as writing a novel, with a smooth thinking that changes ten days a day, but if one breaks ten days, one change.

　　 At the critical moment when Shen Qi was about to solve the first geometry problem, he was interrupted by the vice chairman.

　　 "This uncle is really annoying." Shen Qi had to reorganize his thoughts, which took him five extra minutes.

　　 The entire blank paper was written during the verification process, and Shen Qi finally found the value of sinψ.

　　 The answer surprised him. Sinψ is 1/2, which is a 30-degree angle.

　　 Take a ruler and measure it, it seems to be 30 degrees.

　　Verified by Lobachevsky's mapping method, it turned out to be 30 degrees.

　　 "I'm stupid, I'm really stupid..." Shen Qi realized a low-level mistake. He was confused by the complicated geometric pattern. It took nearly an hour for the forward derivation.

　　 If you use Lobachevsky's mapping method to directly calculate the degree of ψ, and then verify that the ψ angle is 30 degrees, you can save at least half of the time.

　　 Of course, Lobachevsky’s drawing method certainly cannot be drawn on the examination paper. Drawing on the draft paper is no problem.

　　 Having a conclusion to verify the conclusion is easier than deriving an unknown number.

　　 This is a game, a mathematical game between the questioner and the answerer.

　　 Fighting is the best training, and exams are the best review.

　　 Although there is systematic assistance, Shen Qi also gained a new understanding of mathematics in the extremely difficult semi-finals.

　　 There must be a deeper relationship between hypothesis and proof. Truth or fallacy is not as simple and contradictory as it seems on the surface. Fallacy may be a reverse of truth.

　　 Shen Qi was distracted. He thought a lot and thought for several minutes. It seemed that his math level was still too low, and he couldn't understand many questions.

　　 "There are two hours left for the exam, please take the time to answer the questions." An invigilator said to all the players.

　　 "In two hours, there are two questions left." Shen Qi recovered and went to the next question.

　　 This semi-final examination paper is the one with the least questions he has ever done, with only three questions.

　　 is also the most difficult one. The first question with the lowest score took Shen Qi an hour.

　　 The second question is an algebra question, the question surface is like this:

1

　　1-1

　　1-2-1

　　1-3-3-1

　　1-4-6-4-1

　　1-5-10-10-5-1

　　1. Please calculate the sum of all the numbers in line 1024. (5 points)

　　2, and prove that any number in line 4201 is a fraction or a negative number. (15 points)

　　 In fact, many high school students know this digital triangle. No one knows the Yang Hui triangle. Middle school students who have participated in the Mathematical Union and Olympiad competitions all know the regularity of the Yang Hui triangle.

　　 Shen Qi certainly understands this digital triangle. This digital triangle is called Yanghui Triangle in China and "Pascal Triangle" in the West. It is named after two mathematicians in China and the West.

The regularity of the 　　 Yanghui triangle is not difficult to be observed. Each number in the triangle is the sum of the two numbers immediately above it.

　　 and so on, Shen Qi quickly calculated that the sum of all the numbers in row 1024 was 1,278,324.

　　 The first question of the second question is simply a sub-question, so the score is not high, only 5 points.

　　The hard part is the second question, with a score of 15 points.

　　 The positive derivation applies to any number in line 4201 that is a fraction or a negative number. This is a headache. I can’t write, I can’t find a clue at all.

　　 Shen Qi wants to reverse the calculation. The content of the second question requires a proof, which must be based on a formula, theorem or inference.

　　 "Bernoulli's permutation and combination or probability theory? No, it doesn't look like it."

　　 "The expansion of Veda's three special types of equations? Nor is it."

　　 "Playing this kind of pure digital game, Fermat is a top master, yes, it should be Fermat, he and Pascal are good friends, and the two often write letters, and this question is based on Pascal's triangle."

"This guy Fermat put forward hundreds of hypotheses in his life. 99% of the hypotheses were proved to be valid by later generations. He is called the'king of amateur mathematics', but I never believe that Fermat's mathematics I'm an amateur class."

　　 "Big head, Fermat's 273 hypotheses, I have only studied 70 at most, which one is it? Has it touched my blind spot in mathematics?"

　　 Shen Qi put down the ballpoint pen, closed his eyes and rested, racking his brains to find a way.

The vice chairman swayed and swayed behind Shen Qi again. He smiled triumphantly and was very satisfied with Shen Qi's current state: "Young man, even if you can solve the first geometric problem and are familiar with the law of Yang Hui's triangle, you can How? My second question is more difficult than your imagination, right?"

At this moment, Shen Qi suddenly opened his eyes, his eyes gleaming: "I thought, this is Fermat's (1+a) inference! He said that this inference is definitely valid, and there is no need to prove it, but 100 years after his death, his French compatriots proved this inference."

　　The train of thought is coming, the train of thought is coming!

　　 Shen Qi's inspiration is like spring water, he picks up the ballpoint pen and prepares to solve the problem.

　　 Just as he was about to write, Shen Qi inexplicably felt a chill from his back, the same as before.

　　 Shen Qi glanced back, UU reading www.uukanshu. com was very upset: "Fuck, it's you again! Are you passing by again?"

　　 The vice chairman pretended to be calm: "The examination room is so big. As an invigilator, I occasionally pass by." After that, he left with his hand.

　　 "Uncle, you are really annoying!" Shen Qi calmed down as quickly as possible and entered the proof process of the second question of the second question.

Ten minutes later, Shen Qi wrote out the entire proof process of the second question, which was verified by the inference of the expenses horse (1+a). This proof is completely valid. Any number in line 4201 is a fraction or a negative number. .

　　 "Both the first and second questions have been solved, and I got 35 points."

　　 Shen Qi, who had broken two consecutive questions, was very confident, and he started to do the last one.

　　The vice chairman is a person who can't stop himself. After a lap, he walked around behind the other players to observe in secret.

　　 "He Tao, this young man can't do it. Except for understanding Yang Hui's triangle, he can't write anything at all."

"Luo Ming, from Nangang Foreign Languages ​​School, after all, he is a student of a prestigious school. This young man is okay. The first geometry question is answered correctly, but the second question of the second question is obviously wrong. Young man, you are quite the opposite. Directional error."

　　...

　　 The vice-chairman visually observed that the player with the fastest progress and the highest accuracy rate in the entire examination room was Shen Qi. He couldn't help it. He couldn't help it, so he touched Shen Qi again and observed it secretly.

　　Shen Qi suddenly turned around, he was about to collapse: "Uncle, don't do this, why do you have to go with me?"

　　The vice-chairman is still innocent: "I wrote this test paper. I'll take a look. Isn't it okay not to speak?"

　　 "Fuck, did you write this paper?" Shen Qi never expected that the expert in his mind was actually this wretched uncle.