On November 1, the day before Lan Jie participated in the rematch, the theoretical results of the semi-final were announced.

Lan Jie, 30 points!

Li Zihan, 27 points!

Wu Zihan, 22 points!

Chen Zixuan, 16 points!

……

21 points is the entry line, and players with a theoretical score greater than or equal to 21 points are eligible to participate in the experimental examination of the semi-finals.

There are three contestants in Lan Jie's class who were shortlisted for the competition experiment, and there are more than 20 people in the entire sheep competition team.

More than 70% of the contestants were kicked out of the competition team by Tong Yuanhong.

Oh no, I was invited out of the competition team by Tong Yuanhong.

Oh no, it was they who quit the competition team on their own initiative.

The remaining 20 or so players are the most elite physics masters in the sheep, and the physics masters were told to participate in the experimental examination of the physical competition semi-finals on the morning of November 3.

"Hey......" Wu Zihan sighed, so irritable.

Lan Jie asked Wu Zihan: "Zihan, why is this so?"

Wu Zihan said extremely sadly: "There is a high probability that I will not be able to get the provincial one." ”

Ranger encouraged: "If the game is not over, never give up. ”

"Brother Jie, you are kind enough to comfort me, I am very grateful. But as you know, my theoretical score is too low, and it is difficult to turn it around by experiments. ”

"Zihan, you have a chance to turn the tables, please be optimistic. To give a vivid example, Evergrande lost 0-3 away to Perth Glory and will most likely be eliminated. However, Evergrande is reckless and reckless at home, and it is reckless to force it into the AFC Champions League final, making the impossible possible!"

"Evergrande has reached the finals, and it is not that he will be beaten by others. Those players who made it to the final but finished runners-up might as well not make it to the final. ”

"Zihan, you're too pessimistic, aren't you! Can you come up with the spirit of the second middle school that my life is up to me?"

"Hey, don't talk about it, I'm in a bad state now, I don't want to affect Brother Jie, I'll go find a quiet place and be alone. ”

The depressed Wu Zihan faced the wall and reflected, while Li Zihan was quite calm.

In recent months, Lan Jie has clearly felt that Li Zihan has made rapid progress by a huge margin.

Li Zihan's progress is also a spur to Lan Jie.

On the morning of November 2, Lan Jie came to the test center to participate in the semi-finals.

Ding Ding Ding!

The semi-finals begin!

There are a total of 6 questions, each question is worth 7 points, and the answering time is 5 hours.

Although the scores of the six-way math competition are the same, the difficulty is different.

Questions 1, 3 and 4 were not that difficult, and Lan Jie quickly found the answers.

21 points in hand!

However, 21 points is certainly useless.

According to the previous data of the competition, at least 30 points are needed to win the provincial first and advance to the national final.

The difficulty of the second question is significantly higher than that of questions 1, 3 and 4.

Question 2 (7 marks): Knowing that the difference between any two adjacent internal angles of a convex n-sided is 20°, try to find the maximum value of n.

'It's combinatorial geometry, it's hard, it's hard!'

There are several types of math problems that Ranger is reluctant to face, and one of them is combinatorial geometry.

Combinatorial geometry is a new discipline that integrates combinatorial problems into geometric problems, and its research object is the combination of geometric elements.

This kind of question is cleverly conceived, and the difficulty with this kind of problem is that there is no uniform rule to follow.

There is no fixed pattern for combinatorial geometry. Topics without routines are particularly difficult.

Don't panic, take it one step at a time, and first determine whether n is odd or even. ’

Although this problem has certain geometric properties, it mainly relies on algebraic methods to find clues to solve the problem. The most crucial role is logical thinking and analytical thinking.

Logic?

Analyse?

Who have I, Applejack been afraid of!

With the support of strict logic, Lanjie carefully analyzed.

The clues are becoming more and more obvious, n is an even number!

So what is the range of n?

Keep analyzing!

Let the largest of the n inner angles be x, then all the inner angles should include at least another angle x-20°, and any two adjacent angles in all the inner angles are not the same, and the sum should not exceed 2x-20°, that is, the average should not exceed x-10°.

'Ask for it!'

'n is less than 36!'

'And because n is an even number, n is less than or equal to 34!'

Ranger initially got the answer of 34, the battle is not over, and the reasonableness of 34 still needs to be verified.

Let there be only two values x and x-20° in the inner angles of the convex 34-sided polygon, and they appear alternately, each half of which is 17 (2x-20°) = 32×180°, and x=3050°/17M+B to M+1≥M+B.

'This is bigger than the sign, and it almost killed me!'

Lan Jie crossed out the wrong verification process on the test paper and wrote new content in the blank space.

'This time it should be stable, right?'

After the revisions were completed, Ranger checked the paper again.

Ding Ding Ding!

Submit the papers.