Yi Cheng is the only lone seedling in Mingfeng Middle School, and it is gone when it dies.

He was placed in the same classroom as Yan Ziqi for the exam.

Coincidentally, Ziqi sat next to him.

It's a tough opponent.

Although he didn't have much money, Yi Cheng still wanted to treat himself to a treat.

Yan Ziqi smiled at him and signaled that he didn't need to be so nervous.

At 8 o'clock in the morning, the first trial officially began.

8 fill-in-the-blank questions, each worth 8 points, for a total score of 64 points.

3 major questions, question 9 is worth 16 points, and questions 10 and 11 are both worth 20 points. The total score is 56 points.

A total of 120 points.

There are only two levels of 8 and 0 points for fill-in-the-blank questions;

Question 9 is divided into 4 points, and if you think correctly, you can get 4 points, 8 points, and 12 points;

Questions 10 and 11 are 5 points, and you can get 5 points, 10 points, and 15 points if you think correctly.

The scope of knowledge involved in the first test does not exceed the teaching requirements and content stipulated in the "Mathematics Syllabus for Full-time General Senior High Schools" of the Ministry of Education, but the requirements of the method have been improved.

The second test is in line with international standards, and some content beyond the syllabus has been added, mainly examining plane geometry, algebra, elementary number theory and combinations.

Yi Cheng got the test paper and began to answer the questions seriously.

The first attempt starts at 8 a.m. and ends at 9:20 a.m., for a total of 1 hour and 20 minutes.

After doing two fill-in-the-blank questions, he suddenly realized that something was wrong.

For example, the previous question:

1. In the sequence {an}, a1=1, n+1 term: a(n+1)=(1/16)*[1+4an+(1+24an)^(1/2)]

Ask for an.

That's too easy, isn't it?

Yi Cheng was taken aback the moment he saw the question, it was not so simple that it didn't look like a high school joint question, just like the practice question he usually did.

You only need to construct a new number series so that the new number column (1+24an)^(1/2) can be neatly rooted.

Then use the new sequence to build the old one.

It took Yi Cheng less than 2 minutes to finish:

The answer is an=[2^(2n-1)+3*2^(n-1)+1]/[3*2^(2n-1)]

What to do?

Yi Cheng suspects that he has obtained a fake test paper.

If the questioner is so watery, then he won't be able to win against Yan Ziqi.

Let's have a few dishes that can be played a little bit......

Yi Cheng shook his head as he did the question.

Disappointed.

It's so disappointing.

8 fill-in-the-blank questions, none of which can be played.

In less than 20 minutes, he solved them one by one.

Uncomfortable.

It's really uncomfortable.

It's as uncomfortable as a high school student doing elementary school math problems, and he can mentally calculate the answers to a few geometry problems without having to type a draft.

And the people who produce the math papers are too sloppy, how can you draw geometric figures so standardly?

Just look at it visually and you'll know that this angle is 75 degrees, right?

It was only for the sake of insurance that he did a little mental calculation.

The answer is 75 degrees.

Even those who don't know how to count can be right.

In this way, it will be even more difficult to close the score difference.

Oh, it's heart-wrenching.

It took less than 20 minutes to solve the previous fill-in-the-blank questions, and Yicheng came to the 3 big questions in the back.

Let's hope these big questions can be argued.

Yi Cheng took a deep breath and began to work on the 9th question, which is the first big question, which is worth 16 points.

This is an interval function consisting of a logarithmic function and an exponential function, and the value of x is divided into two segments between 0 to 17 and 17 to infinity.

Then you need to solve another equation based on this interval function.

It's not difficult, it's not that hard.

Yi Cheng said that this is a paper tiger, and it is not as good as Ran Bingqing's Veda question.

Even if you don't have to do the math, you can roughly deduce the answer from the number 17.

17 is a number that is so special that anyone with some attainment in mathematics will maintain a high degree of sensitivity to it.

It is the 17th positive integer, one of the twin primes, the third Fermat prime, the 3rd Pythagorean prime, and the 7th Chan prime......

The number 17 is the number 17 that can form a continuous increasing interval function between the exponential function and the logarithmic function, and becomes an important watershed, which is enough to explain a lot of problems.

Yi Cheng blindly guessed that there is only one solution to the equation to be solved in the range of x, and this solution is 666.

It took him 10 minutes to solve it, and it turned out to be 666.

This number has a deep meaning, and it is not just as simple as expressing pretending to be powerful.

666 is the sum of squares of prime numbers within 17.

Yi Cheng honestly wrote down the problem solving process, otherwise this question will score 0 points.

The second problem is a series of numbers, counting 64x64 squares with 4 colors and adjacent squares of different colors. Find the minimum value of the common edge.

At first glance it looks a bit bluffing.

Yi Cheng thought he was going to ask him to make a four-color certificate, but after doing it for a long time, it turned out that he was just asking for the public side.

These two are not orders of magnitude at all.

The four-color proof has not yet been fully mathematically proven, only the computer proof.

This is also a great advance in human history, through the computer-assisted mathematics, to complete the proof of the great conjecture.

However, this is not acceptable for mathematicians, who need to use concise mathematical formulas, proven by rigorous derivation, so that it is perfect.

Computer?

Hmph, what is this?

Fortunately, Yi Cheng does not have the paranoia of mathematicians, and he is very comfortable accepting computer proofs and using computers as tools to assist himself.

However, this problem is still far from being proven by a computer.

Yi Cheng first drew the squares on the scratch paper, and then used the pen to draw shadows as a distinction.

……

This question was a physical task, and it took 15 minutes for Yi Cheng to finish it.

It's a little harder than before, but it's not that hard.

The last question is a plane geometry, as shown in the figure: (Sorry I can't draw the picture, let's take a look)

It is about two tangent circles, and then two lines are tangent to the major and minor circles at the tangent points of the two circles, and one of the tangents passes through the origin.

The slope of the tangent needs to be found so that the area of the two circles is minimized.

Hey, that's disappointing.

Yi Cheng shook his head, originally thought that the last question would be more difficult, but it was difficult to calculate the complexity after working on it for a long time.

Again, this is a physical job.

Basically, the solution to the questions is manual work.

All you need to do is list the simultaneous equations by stem, and then follow the steps to solve the equations.

It took Yi Cheng 5 minutes to lay out the equations.

This look is even more melancholy.

The maximum number of times is only 2.

It's far worse than Ran Bingqing's private goods.

What to do?

I can only hope that the second test will be a little stronger.

Yi Cheng finished answering the question, spent another ten minutes checking the test paper, and then left the examination room.

Standing up with him was Yan Ziqi, who was sitting next to him.

The two men glanced at each other.

Ziqi lowered her head shyly.

……

Two people turned in their papers at least half an hour early.

The second test starts at 9:40.

There are still 50 minutes left before the start of the second test.

The two men walked out of the classroom and bought an ice cream at a stall outside.

Yi Cheng insisted on treating himself, and Ziqi did not refuse.

Ice cream is a popular Internet celebrity ice cream double yolk egg recently.

Yi Cheng was a little uncomfortable.

What was uncomfortable was that he finished answering the question at the same time as Ziqi.

And why is double yolk egg ice cream so expensive?!

"Just when you've won." Ziqi licked the ice cream and laughed happily.

"No, I'm still going to have a treat after the results come out." Yi Cheng didn't think he would lose.

"That's fine. "When the time comes," Ziqi ruffled her hair to the base of her ears, "why don't we go to the beach?" ”

"Huh?"

"I mean, there are also delicious restaurants by the sea, and you can also play in the water ......"

"Oh. Yes. Yi Cheng nodded.

He turned his head and stared into Ziqi's eyes.

"How...... What's wrong? Ziqi was flustered by him.

"By the way, do you want the answer?"