With the arrival of the second day, the game also went on as usual.

Chen Yanxuan was brought into the examination room again, and when he saw today's test questions, Chen Yanxuan obviously felt that it was more difficult than yesterday's questions, and heard the sighs of the people around him.

Chen Yanxuan blocked these voices, and then concentrated on the topic.

The first question goes like this:

2n coins, n aluminum (A), n copper (B). Taking the positive integer k < 2n, we group all consecutive coins of the same type from left to right, group them according to the method of the least total group, and move all the groups from the kth coin from the left to the far left, and ask which ks can make the final leftmost number of n coins of the same material. Example: k=5n=8.BBAAABBA->AAABBBBA > BBBBAAAAA

Chen Yanxuan thought for twenty minutes, and inspiration suddenly popped into his mind,

"Congratulations to my brother for his knowledge of the high school math competition +0.02%..."

Half an hour later, Chen Yanxuan glanced at the clock on the wall, and estimated the remaining time in his heart.

Immediately looked at the second question, with the idea of the first question in front, the second question, Chen Yanxuan also quickly solved it, and soon, it was the third question.

Proof that the existence of a normal number c has the following properties: for any integer n>1 and the set of n points on the plane SS is not less than 1, then there is a straight line separating S so that the distance from each point in S to the straight line is not less than cn-1/3 (we call the line separation point set S if a line segment with two points in S as the endpoint intersects)

Note: If it is proved that the estimation cn- is weaker than cn-1/3, the score will be given appropriately according to the value of a>1/3.

Seeing the conditions of this question, Chen Yanxuan frowned, he was not proficient in this kind of proof question, but he still did it hard.

"Ding, congratulations to my brother for reaching 75% proficiency in math knowledge in high school, gaining skills, brainstorming!"

Hearing Xiaohong's words, seeing that he had just obtained the skill, when Chen Yanxuan looked at this question again, the whole person's feeling was instantly different.

Chen Yanxuan immediately had an idea for this question, picked up the pen and did it, and when he was done, Chen Yanxuan looked up at his watch and found that four hours had passed.

At this time, Chen Yanxuan did not choose to hand in the papers, but used this half hour to carefully check this set of test papers several times and spent the last half hour.

The invigilator said, "Please put down the pen in your hand, stop answering the questions, and wait for the paper to be collected!"

Many of the students sighed and said, "It's finally over!"

When Chen Yanxuan walked out of the examination room and found Han Mengtian, most of the students were already waiting around Han Mengtian, and after the students came out, Han Mengtian said: "Students, after the exam, the test results will come out tomorrow, and today the teacher invites you to go out for a good meal." The

students were excited and said, "Thank you, teacher." The

group found a restaurant, ordered some dishes, sat down to eat, and at this meal, Han Mengtian didn't talk about the competition with his classmates, just chatted.

After eating, the group returned to the hotel, washed up, and went to bed early.

Nothing was said all night.

Early the next morning, Chen Yanxuan and his classmates finished breakfast and couldn't wait to go to the competition venue to know their results.

Han Mengtian saw that the students were already full, so he led them to the venue.

The host announced: "Now for the third event of the conference, announce the results of the competition, please look at the big screen!" I

saw the names and scores of the students who won the third prize on the big screen start scrolling.

"I turned out to be only the third prize!" Li Nuo on the side found his name and said in disappointment. "I only scored 46 points."

Lu Ang said comfortingly: "The question is very difficult this time, it is good to get forty-six points, and besides, we don't only rely on mathematics to eat!" "

The rankings on the big screen are scrolled from bottom to top, and when it rolls to the second prize, Lu Ang's name appears on it.

"Lu Ang 65

points second prize" The big screen continued to scroll, and soon,

the name of the first prize appeared, and the second name came out was "Chu Yun 76 points first prize" Chen Yanxuan couldn't help but sigh that the score line of the first prize was drawn at 75 points

, and Chu Yun just crossed the line, but he couldn't participate in the national competition.

While sighing, the scores on the big screen continue to slide.

.......

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