Since its establishment, Yuzhou University has developed into a first-class university in China with significant advantages in mechanical and electrical engineering, energy, materials, biotechnology, natural sciences and other disciplines.

Walking into the campus, it is easy to see the eight-character school motto engraved on the stone wall: hard-working, thrifty, diligent and patriotic.

After thousands of choices, he found the most beautiful senior sister to ask for directions, and Ding Sheng finally found the independent admissions office with twists and turns.

Generally speaking, the independent enrollment of colleges and universities adopts the principle of "secondary school recommendation is the mainstay, supplemented by student self-recommendation".

Although Linzhou and Chongqing are close neighbors, they actually belong to two different provincial-level administrative regions in terms of administrative planning, so Linzhou Middle School did not get a recommended place this year.

"Won the first prize of the National Physics Competition for Middle School Students and the first prize of the National Chemistry Competition for Middle School Students for three consecutive years......"

Due to the high requirements for self-recommendation, and Ding Sheng is one of the few candidates who have successfully recommended himself, the teacher in charge of issuing the admission ticket in the admissions office out of curiosity, he specially checked his self-recommendation materials and couldn't help but nod his head in surprise.

The weight of the awards in the national competition for middle school students may not be enough to impress Yuzhou University, but winning the first prize three times in a row is very intriguing.

In other words, this student has been beating high school students across the country in competitions since at least the beginning of high school.

Terrible.

In fact, Ding Sheng is already very low-key, the truth is that he did not participate in the national competition at all in the third year of high school, and he has dominated the country for three consecutive years since the third year of junior high school.

That's right, if he didn't have two brushes, how could he be an inventor in Marvel, where technology is at its peak.

"This is your admission ticket, the examination room is in the arc classroom where you go out and turn right and go straight, come on. ”

In recent years, the battle for excellent students between colleges and universities has intensified, and part of the reason why the school set up independent enrollment is to lock in the source of students in advance.

Independent enrollment is divided into written test and interview, mainly to examine the candidate's knowledge accumulation, the flexibility of the test questions is higher than that of the college entrance examination, and the knowledge involved will be wider.

There are generally no more than two written test subjects, which is very friendly, especially for students with serious biases, participating in independent enrollment is indeed a way out, provided that you are strong enough in the biased subjects.

This year, Yuzhou University has only one part of the written test for independent admissions, which lasts for one hour and has a total of 20 questions with a total of 100 points.

Because geometric drawing will be involved in the exam questions, compasses and rulers are also distributed in the exam room.

1. Find the least positive integer R so that 4725R is the smallest square number.

—21

Ding Sheng only silently calculated this question in his head for two seconds before filling in the answer.

2. In 1900, mathematician (_________) proposed 23 unsolved problems at the International Congress of Mathematics in Paris.

—David Hilbert

Ding Sheng expressed doubts about the difficulty of this exam question, isn't it common sense?

3. Write down any of the 23 unsolved questions in the above question that have not been completely solved so far.

- The impossibility of solving a general seventh-degree algebraic equation with a combination of two-variable continuous functions.

This question is beyond the curriculum for ordinary high school students, but fortunately, Ding Sheng is not ordinary at all, the twenty-three unsolved problems proposed by David Hilbert one hundred and ten years ago have only been completely solved over the years, and only nine have been completely solved over the years, and one is written randomly from the remaining fourteen, and this question is finished.

In fact, in this unsolved problem written by Ding Sheng, there is a branch problem about "the root of the seventh-dimensional equation x7+ax3+bx2+cx+1=0 depends on three parameters a, b, c;x=x(a, b, c), can this function be expressed by a two-variable function?", after eight years of study by Marvel, he can also solve it.

It can be proven, but it is not necessary.

The following questions are also very simple, Ding Sheng chopped melons and vegetables all the way, and soon the soldiers came to the city and killed the last finale.

20. Ruler gauge drawing regular seventeen sides.

Alas...

Fall into clichés.

Ding Sheng can say that when he saw that the examination room had its own compass and ruler, he guessed that there would be this question? Can it be more novel?

The first person to discover that he could draw a regular seventeen-sided shape with a ruler and gauge was Gauss, the prince of mathematics, and the drawing process was quite complicated, so complicated that most of them couldn't even understand the drawing teaching videos on the Internet.

Looking at the time, there are still forty minutes before the exam ends, and Ding Sheng is also itchy, so let's draw it reluctantly.

Regular seventeen-sided .jpg

Thirty minutes into the exam, Ding Sheng raised his hand to hand in the paper.

The invigilator nodded in understanding.

This time, most of the independent enrollment examination questions of Yuzhou University are particularly difficult, and it is meaningless to be forced to stay in the examination room if they can't do it, and it is a relief to hand in the papers early.

Sure enough, after someone took the lead in handing in the papers, seven or eight candidates with numb scalps followed up and handed in the papers and left.

The rest of the candidates are also holding on to their status, and most of the questions on the test paper are still blank.

After Ding Sheng left the examination room, he walked around the school for a while and looked at the campus beauties before leaving.

As for the afternoon interview, he was not ready to go.

Originally, this time to participate in independent enrollment is to go through the motions, the written test has been played so well, if the interview is mixed up again, then the fact that I am very good will not leak the news?

If you say that you want to hold on, you must hold on.

On the way back to the hotel, Ding Sheng bought two large boxes, packed all the equipment, called a taxi to the bus station, and bought a ticket to go home.

The two places are only 100 kilometers apart, so why not just take a taxi back to the neighboring state?

No money.

When I arrived in the neighboring state, I called a taxi to pull the equipment to the old distillery, and after everything was put out, it finally had the appearance of a laboratory.

And Ding Sheng finally hovered on the verge of bankruptcy.

For the rest of the time, he was chemically purifying silicon raw materials, and he was busy until eight o'clock in the evening, walking home, just like the illusion of taking the last train back from Yuzhou City.

"Son, how did you do on the exam?"

Of course, Ding Sheng's parents knew that he went to Yuzhou to take the exam, otherwise just one night of not returning home would be enough to be hit by a phone call.

"So-so. ”

"It's okay, even if you don't make the cut, we believe in your ability. ”。

Ding's mother specially checked it, even if the university's independent enrollment is selected, it does not mean that you will be admitted, candidates still need to take the college entrance examination, but they can enjoy the preferential policy of the school's score reduction admission.

At this juncture, sensible parents should give priority to encouragement, supplemented by enlightenment, and no matter what, they can't put pressure on their children.

......

Comprehensive Research Laboratory of Mechanical Engineering and Applied Science, Yuzhou University.

"Lao Yang, the exam questions this time were only finalized by the two of us this morning, but we are afraid that the leakage of the exam questions will make people fish in troubled waters, and now someone has scored a full score, what do you think?" said an old man.

Another white-haired old man in a simple shirt and heavy glasses held an exam paper in his hand and smiled very kindly.

"If you want me to say, let's start first. ”