I really just want to be a scholar

Chapter 47
It was Qin Ke who pretended to support Chi Jiamu and said: "Be careful, beauty, she is so good-looking, it would be a pity to break her face. By the way, let's go clubbing together after the exam, my buddy likes you the most Such a beauty with plastic surgery. Haha!"

Chi Jiamu broke away from his hand, shrinking into a ball in fright.

Others who didn't know thought the three of them were friends. Seeing Wen Wenyan's ugly face and Chi Jiamu's pale and trembling face, they realized something was wrong, but Qin Ke had already drifted away. He cursed so much that his teeth were almost broken.

But the bastard temperament played by Qin Ke really made him palpitate, and he couldn't muster the courage to fight back.

Chi Jiamu also came back to his senses, looked at the whole text with disappointment and even contempt, kept a distance from him, and refused to go together again, it seemed that the boat of friendship, which was not very strong in the first place, had capsized.Of course, it may also be because he is afraid of being a pond fish that will be affected again.

This small disturbance did not attract much attention, but it had a greater impact on Wen Wenyan and Chi Jiamu's mentality, especially when they walked into the examination room and saw Qin Ke's fierce eyes sitting in the first row, they immediately He trembled all over his body and hurried back to his seat.

Quan Wenyan was even more miserable, because he found that Qin Ke was actually in the same row as him, only two seats away from him.

Qin Ke winked at him from time to time, Quan Wenyan didn't dare to look at him, and kept staring at the blackboard, but this undoubtedly increased his psychological burden and made him a little restless.

Fortunately, the bell rang soon, and the three invigilators began to distribute the test papers after announcing the rules of the test room.

Quan Wenyan only felt that his brain was in a mess, and even the hand holding the pen was trembling. After a while, he managed to calm down and began to read the test paper.

Qin Ke had already shifted his attention from this small role back to the test papers. It was important to beat the opponent psychologically, but what was more important was to ensure that his grades were impeccable!

As Lao Zheng said, the test paper is divided into the main paper and the additional paper. The main paper has 25 questions in total, 250 fill-in-the-blank questions, and 50 comprehensive questions, with a total of 300 points. The total score of rolled noodles is [-] points.

Qin Ke glanced at the fill-in-the-blank questions. It seems that the fill-in-blank questions do not need to write out the solution process, and they are also worth 10 points together with the comprehensive questions. It seems that these fill-in-blank questions should be given priority. Functions, sequence of numbers, probability and other knowledge are not at all simpler than big questions, and there are many hidden pitfalls in them, making it extremely easy to make mistakes. Candidates who really want to pick a trick to answer the blank questions first are afraid of falling into a big somersault.

Of course, for Qin Ke, the fill-in-the-blank questions are the real points-giving questions. With his current "high school Olympiad (provincial rematch)" math level ability, he can almost think of the problem-solving idea after reading the questions. I can figure out the answer.

It only took him about 2 minutes to complete [-] fill-in-the-blank questions and move on to ten comprehensive questions.

The first big problem is a stumbling block, which belongs to the difficult compound proof problem of arrays and inequalities in the high school Olympiad preliminary level.

"1. Let a0, a1, a2, ... be any infinite series of positive real numbers, and prove that the inequality 1+an is greater than 2^1/n*an-1." (Note, n-1 is the subscript of a)"

However, for Qin Ke, he thought of the proof method after just yawning, which is the method of proof by contradiction.

As for the method of counter-evidence, Qin Ke is also very proficient in using it. He puts forward a hypothesis that is contrary to the conclusion of the proposition, and then uses axioms, theorems, definitions, etc. to make a series of correct and rigorous logical reasoning, which leads to a new conclusion, and this If the conclusion either contradicts the known conditions given in the title, or contradicts the conclusion known to be true, then it can prove that the conclusion of the original proposition is correct.

In this proof problem, Qin Ke skillfully used the method of contradiction plus Bernoulli's inequality, supplemented by mathematical induction, and only spent about 3 minutes to complete the three steps of antithesis, reductio absurdity and conclusion, and completed the proof process.

Of course, if you don't think of proof by contradiction, this question will be very difficult.

Glancing at the examinees left and right from the corner of his eye, he saw that everyone including Wen Wenyan was still struggling with the previous fill-in-the-blank questions, and Qin Ke proceeded to the second big question in a good mood.

The following nine major questions have three answer questions and six proof questions, with varying degrees of difficulty, but in Qin Ke's eyes, they are as simple as junior high school math problems. According to the clock on the wall, less than half an hour has passed.

He just glanced through the front papers in a hurry, and stopped checking when he saw that there were no missing questions.

He has absolute confidence in the answers he makes, and it is impossible to make mistakes.

Well, continue to solve the two additional big questions, I hope it will be a little difficult, otherwise it will be too boring.

Qin Ke yawned, and opened up the second secondary volume, which is the additional volume.

According to what Old Zheng said, the two big questions in the additional paper will be of quasi-provincial level of difficulty, and will not be inferior to the three big questions that Old Zheng sent out last time. Qin Ke is still looking forward to it.

It's not difficult, how can he pull points to secure No.1?
"Additional question 1: Excuse me, how many numbers can be selected from the 1 numbers 2, 13, ..., 13, so that the difference between the selected numbers is neither 5 nor 8 ?”

Qin Ke's eyes widened, didn't he?Such a coincidence?
Why do you say coincidence?
Because some time ago when he gave Ning Qingyun an example to explain the Olympiad skills, he took a similar topic as an example (from the system knowledge).

"Example: Solve the problem. Now there are 13 children. They form a circle hand in hand. Now we need to select a few people so that they are not adjacent to each other. How many qualified children can we select at most?"

What?The two questions look only slightly similar?
It doesn't matter, as long as you use the "reduction method", you can reduce the current additional question 1 into the solved children's hand-in-hand example question.

When it comes to the "reduction" method, in fact, people who have participated in the Mathematical Olympiad should be familiar with it. This is a very common problem-solving idea, and its core is "simplification".

To put it simply, it is to attribute the problem to be solved to a kind of problem that has been solved or is relatively easy to solve through a certain transformation process, so as to solve the original problem more simply.

Hungarian mathematician Rosa Peter has a vivid joke in her famous book "Infinite Things: Exploration and Travel in Mathematics" (published by Dalian University of Technology Press in 2018), which can vividly illustrate what "reduction" is. ":
You want to boil water, the steps are to fill the kettle with water, light the gas, and put the kettle on the gas stove.What if conditions changed and the jug was filled earlier?
Normal people: directly ignite and burn on the gas stove.

Mathematician: Pour out the water in the kettle first, and repeat the previous steps.

The mathematician's approach in this joke is "reduction", which turns the new problem after the condition changes back to the original familiar problem.

Of course, this is just one of the applications of reduction, which also reduces complex problems to simple problems, general situations to special situations, and so on.

Qin Ke's use of "return" at this time means to change the new problem after the change of conditions into the original familiar problem.

(End of this chapter)