It was Qin Ke who pretended to support Chi Jiamu and said: "Be careful, beauty, you are so beautiful, it would be a pity if you break your face. By the way, let's go clubbing together after the exam, my buddy likes you the most

Such a beautiful woman with plastic surgery. Haha!”

Chi Jiamu broke away from his hand and shrank into a ball in fear.

Others who didn't know about it thought the three of them were friends. Seeing Quan Wenyan's face turned ugly and Chi Jiamu's face pale and trembling, they realized something was wrong. However, Qin Ke had already walked away. Quan Wenyan could only clench his fists and say something in his heart.

He cursed so loudly 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 at all.

Chi Jiamu also came back to his senses, glanced at Quan Wenyan with disappointment and even contempt, kept a distance from him, and refused to leave together anymore. It seemed that the friendship boat that was not very strong in the first place had capsized. Of course, it could also be

I'm afraid of being affected again.

This minor incident did not attract much attention, but it had a greater impact on the mentality of Quan Wenyan and Chi Jiamu, especially when they walked into the examination room and saw the ferocious look from Qin Ke sitting in the first row.

My whole body was shaken violently, and I quickly returned to my seat.

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

Qin Ke winked at him from time to time, but 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 after the three invigilators read out the rules of the examination room, they began to distribute the test papers.

Quan Wenyan felt that his brain was in chaos, and even the hand holding the pen was shaking. After a while, he managed to calm down and started to read the test paper.

Qin Ke has long since turned his attention from this small role back to the test paper. It is important to attack the opponent psychologically, but more importantly, it is more important to ensure that his own performance is impeccable!

As Lao Zheng said, the test paper is divided into the main paper and the additional paper. The main paper has a total of twenty-five questions, fifteen fill-in-the-blank questions, and ten comprehensive questions, totaling 250 points, while the additional paper has two large questions worth 50 points.

, the total score of the rolled noodles is 300 points.

Qin Ke glanced at the fill-in-the-blank questions. It seemed that the answer process for the fill-in-the-blank questions did not need to be written, and it was also worth 10 points like the comprehensive questions. It seemed that these fill-in-the-blank questions should be prioritized, but Qin Ke keenly discovered that the fill-in-the-blank questions involved geometry.

Functions, sequence, probability and other knowledge are no easier than the big questions. There are also many hidden pitfalls, and it is very easy to make mistakes. Candidates who really want to take advantage of the problem and answer the questions by filling in the blanks may end up in a big somersault.

Of course, for Qin Ke, fill-in-the-blank questions are real score-earning questions. With his current mathematics level of "High School Mathematical Olympiad (provincial semi-finals)", the answer can emerge after reading the questions almost once.

It only took him about two minutes to complete fifteen fill-in-the-blank questions, heading towards ten comprehensive questions.

The first big question is the stumbling block, which is a more difficult compound proof question of array column addition inequality in the high school Mathematical Olympiad preliminary level.

"1. Let a0, a1, a2,... be any infinite positive real number sequence. Verify: the inequality 1an is greater than 2^1/n*an-1." (Note, n-1 is the subscript of a)"

But for Qin Ke, he only had time to yawn before he thought of the method of proof, which is proof by contradiction.

Qin Ke is also very skilled in using the method of proof by contradiction. 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, thus leading to a new conclusion, and this

If the conclusion either contradicts the known conditions given in the question, or contradicts the conclusion that is known to be true, then it can prove that the conclusion of the original proposition is correct.

In this proof question, Qin Ke used the proof by contradiction method plus Bernoulli's inequality, supplemented by mathematical induction method. It only took about three minutes to write the three steps of counter hypothesis, reductio ad absurdum 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 candidates left and right from the corner of his eye, he saw that Quan Wenyan, including Quan Wenyan, was still struggling with the previous fill-in-the-blank questions. Qin Ke moved forward to the second big question in a comfortable mood.

The next nine big questions include three solution 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 questions. He solved them without any lag, look at it.

The clock on the wall showed that less than half an hour had passed.

He just hurriedly read through the previous main volume and stopped checking when he saw that he didn't miss any questions.

He has absolute confidence in his answers and there is no way he can make mistakes.

Okay, let's continue to solve the two additional big questions. I hope they are a little difficult, otherwise it will be too boring.

Qin Ke yawned, regained his consciousness and opened the second supplementary volume, which was also the additional volume.

According to Lao Zheng, the two big questions in the additional volume will be at the quasi-provincial level in difficulty and will not be inferior to the three big questions that Lao Zheng handed down last time. Qin Ke still has some expectations.

It's not difficult, how can he increase the points to ensure the first place?

"Additional question 1: Excuse me, how many numbers can be selected at most from the 13 numbers 1, 2,...,13, so that the difference between every two numbers selected is neither equal to 5 nor equal to 8

?”

Qin Ke's eyes widened, couldn't it? Such a coincidence?

Why do you say clever?

Because some time ago when he gave Ning Qingyun an example to explain Mathematical Olympiad skills, he used a similar question as an example (from system knowledge).

"Example: To solve the problem, there are 13 children holding hands and forming a circle. Now we need to select a few children from them so that they are not adjacent to each other. How many qualified children can be selected 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 this solved example question for children holding hands.

When it comes to the "reduction" method, anyone who has 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, the problem to be solved is reduced to a type of problem that has been solved or is relatively easy to solve through a certain transformation process, so that the original problem can be solved more simply.

Hungarian mathematician Rosa Peter has a vivid joke in her famous book "Infinite Playthings: The Exploration and Journey of Mathematics" (published by Dalian University of Technology Press in 2018), which can vividly describe what "chemistry" is.

"Return":

If 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 should you do if the conditions change and the kettle is filled in advance?

Normal person: Just light the fire and put it on the gas stove.

Mathematician: First pour out the water in the kettle and repeat the previous steps.

What the mathematician does in this joke is to "reduction", turning the new problem after the conditions have changed back into the original familiar problem.

Of course, this is only one application of reduction. Reduction also reduces complex problems into simple ones, general situations into special situations, etc.
Chapter completed!