The unveiling ceremony was held in front of the newly built multimedia staircase classroom of Sishui No. 1 Middle School. The county magistrate and the leaders of the county education bureau all participated. The specifications were quite high. Originally, a small classroom at Sishui No. 1 Middle School could not invite these big figures from the county to participate. The reason why they came was because one of them attended, that is, the donor of the multimedia staircase classroom, the boss of Mammoth Technology, a famous domestic mathematician, and the youngest professor-level researcher in China.

The county magistrate shook hands with Liu Meng cordially and said sincerely: "Professor Liu, Sishui No. 1 Middle School is very grateful for your generous donation. It would be a great blessing to have a few more talents like you in this county."

The county education director, principal and others also gave a compliment. Liu Meng's class teacher also interrupted and said, "Liu Meng performed differently in the class at the beginning, and I could see that he will definitely be extraordinary in the future. As expected."

Liu Meng wanted to laugh in his heart. This class teacher is really interesting. In fact, Liu Meng was not very popular with the class teacher in the class at the beginning. Perhaps because he was too maverick and was a student with good grades but not very obedient. He just kept reading and was not as good as a teacher in class. Such students came out of the class, and as a teacher, he had no sense of accomplishment at all, so he definitely didn't like it so much.

The principal was obviously a little unhappy with the head teacher Li Dejin, thinking that there was no place for you to speak in this situation. Before the two leaders could say a few words, I had not even had time to speak, so you went up to mix and understand the rules. You smiled and said with a hurried smile: "The students are all looking forward to it. Mr. Liu should start your speech soon. I will wait and see to learn. Maybe I can make progress."

Liu Meng nodded to the few people and walked to the podium.

"I think many of the students who are sitting here may hate mathematics. They will have a headache when they see the piles of formulas. However, those who really like to study mathematics usually think mathematics is fun. So where is mathematics interesting and where is the beauty of mathematics? I will first use a few arithmetic problems suitable for both young and old, leading everyone to explore a corner of the mathematical world in various forms such as theorems, interesting questions and even unsolved mysteries. Many problems contain profound mathematical knowledge, which touches various fields of mathematics. I hope that students who have failed in mathematics since childhood can like to take a fun subject, mathematics."

"The first small problem is that the number black hole 6174, choose any four-digit number. Of course, the numbers cannot be the same. Arrange all numbers from large to small, and then arrange all numbers from small to large, subtract the former by the large number and the latter by the small number to get a new number. Repeat the above operation on the newly obtained number, and within 7 steps, 6174 will inevitably be obtained. Isn't it very interesting? This may not be intuitive to understand. Okay, let me give an example below, for example, select the four-digit number 6767:7766-6677=1089; 98

10-0189=9621; 9621-1269=8352; 8532-2358=6174; 7641-1467=6174…6174 This ‘black hole’ is called the kaprekar constant. For three-digit numbers, there is also a digital black hole 495. Students may try these interesting phenomena after class. In fact, starting from this question, we can also ask a question, that is, in addition to the three-digit numbers, four-digit numbers have digital black holes, so are there five-digit numbers, six-digit numbers, and seven-digit numbers?"

After finishing the first small question, everyone present was attracted by Liu Meng's speech. This knowledge was not something that high school teachers could tell. In fact, the teachers of Sishui No. 1 Middle School were roughly divided into two categories. The first was those who graduated from high school or junior college in the early years. However, the number of years of teaching was too high, and there was also a staffing. The teaching level was imagined. They had rich experience, but their vision was far from enough. The second was young teachers who had just graduated from ordinary undergraduates. When they were in high school, they were almost all the same type of teachers who studied hard but did not have good grades. Some even repeated the courses for several years before they got into the most general undergraduate. After four years of school, they transformed into high school teachers. With this level, how high can you expect their teaching level to be? Just read the subject according to the text.

Liu Meng remembers it very clearly that English teachers, mathematics teachers, and biology teachers in high school all belong to the first situation, and physics teachers belong to the second situation, among which physics teachers are the most fun. The young man who just graduated was still tender and read the subject according to the text in class. Many times he checked the questions on the blackboard and made mistakes often, which made the students below boo. The young man was persistent and stood by himself and could usually find out what he was wrong. Such a teacher had insufficient experience and poor talent. What kind of good students could he teach? Therefore, in the class where Liu Meng was in at that time, all the students who had better grades rely on self-study. The students who listened carefully to the teacher's class were just very average.

After listening to the first question, the students had a loud discussion. They all felt that mathematics was really fun. Liu Meng waited for a while before starting to talk about the second question.

"The second is the 3x+1 problem. Start with any positive integer and repeat the following operations: If this number is an even number, divide it by 2; if this number is an odd number, expand it to 3 times and then add 1. You will find that the sequence will eventually become a loop of 4, 2, 1, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1... Mathematicians have tried many numbers, and none of them can escape the '421 trap'. But, for all numbers, the sequence will eventually become a loop of 4, 2, 1?"

The students were discussing it all, and some of them had even begun to try to verify it.

Liu Meng continued: "This problem can be said to be a huge pit - at first glance, the problem is very simple and there are many breakthroughs, so many mathematicians jump into it; but they don't know that it is easy to get in and out, and many mathematicians have not solved this problem until they die. There are countless mathematicians who have been involved in it, which can be seen from various alias of the 3x+1 problem: the 3x+1 problem is also called the collatz conjecture, the syracu color problem, the ka pants Tani problem, the has color algorithm, the ulam problem, etc. Later, because the naming dispute was too great, it simply made no one benefit, and it was called the 3x+1 problem directly."

"In number theory, as long as you extend to infinite numbers, it is very difficult to prove, because you can't prove it one by one by one, the famous Riemann conjecture, Fermat's theorem, and the Goldbach's conjecture all belong to this situation, and the same is true for the 3x+1 problem. Until now, mathematicians have not proved it. This law holds true for all numbers. If anyone can prove this problem, then he will be one of the greatest mathematicians, at least one of the most famous top ten people on this earth, at least much better than the well-known Chen Jingrun and Hua Luogeng."

The students suddenly burst into a pot of porridge. What sounds so simple actually solved the famous mathematicians in the textbook. For high school students, especially high school students in a remote town, it was a new world. A stream of passion was pouring out. Students who usually claimed to be smart couldn't wait to take out paper and pen to verify it. They fantasized that they could solve the problem by just one go, became famous, and were admitted to Shuimu University and Yenching University... etc. Young people are always impulsive and naive, full of fantasy.

Liu Meng's speech is extremely simple for these students. Those who are sitting in math are very bad and have failed, can easily understand these problems, but they are very different. The impact on them can be imagined. Liu Meng is very satisfied with this effect, and at the same time he has some ideas. In fact, the younger he is, the greater the chance of solving these global problems. Just like Wiles was in contact with Fermat's theorem in childhood. Teacher Kong came into contact with the Goldbach conjecture and was a little late.

I have thoughts in my childhood. When I have the means to finish college, I am very likely to have new ideas and achieve great success. However, in the early stages of Chinese teaching, I have learned too much difficulty and uninnovative knowledge in high school. Students always do the questions over and over again. Some so-called well-known high schools have to take exams every week and even make up for classes on weekends. The so-called admission rate is indeed dazzling, but what will these suppressed high school students do after entering college?

The suppressed youth hormones exploded, and those missed TV series, movies, and games all need to be remedied, and curiosity and restlessness about the opposite sex also erupted. Entering the university campus, it was like the zoo in spring, just like what Teacher Zhao said, "Spring is here, the season for animals to court and mating..."

College students over 90 years old talk about women all day long, and there are a few who are interested in scientific problems. This is the biggest drawback of Chinese teaching. Whether parents and teachers always like to instill knowledge into their children's minds in advance, what is the use? Relatively speaking, Liu Meng is more optimistic about American teaching methods, which is to let students who are really interested learn more deeply. Most people may misunderstand that American high school mathematics, physics, chemistry, etc. are too simple. This is wrong. Basic teaching in American high school is indeed very simple, but students can take difficult courses by themselves. For example, if you are interested in mathematics, you can take advanced mathematics courses. These advanced courses are advanced mathematics in China's freshman year, and the same is true for other subjects, which is to let the students who are interested in learning more deeply.

Instead of the teaching method of big pot rice like China, everyone is serious about studying the periodic table of elements, various complex chemical reactions, complex organic structure formulas, complex mechanical formulas, complex momentum conservation, and complex mathematical knowledge. But how many people are really interested? How many people really use this knowledge in the next ten years? How many people return all the things they learned to deal with the exam to the teacher within a few years of graduation? It should be the vast majority of people! This is a waste of intelligence of young people in the entire society, which is even more poisonous than the eight-legged essay imperial examination. It is very unscientific and seriously hinders the progress of society.

Liu Meng suddenly felt that this speech was very meaningful, opening up a limited sky for young people. These small mathematical problems can even be understood by junior high school students. The enlightenment should be earlier. Thinking of this, I had some ideas and continued to say: "The next small problem is the quick calculation of special two-digit multiplication. If the ten digits of two two-digit numbers are the same and the single digits are added to 10, then you can immediately say the product of these two numbers. If these two numbers are written as ab and ac respectively, then the first two digits of their product are a and a+1

The product of the last two digits is the product of b and c. For example, the ten-digit numbers of 47 and 43 are the same, and the sum of the single digits is 10, so the first two digits of their product are 4x(4+1)=20, and the last two digits are 7x3=21. That is to say, 47x43=2021. Similarly, 61x69=4209, 86x84=7224, 35x35=1225, etc. So why?" After saying that, Liu Meng raised the essence of this question with a smile.

The students immediately started to think about it, and a very thin student in the front row raised his hand and said, "I know."

Liu Meng was very happy and signaled him to say it. The student was very excited and stood up and said, "The reason behind this quick calculation method is that such a double-digit number can represent bits (10x+y) and (10x+(10-y)). If it is multiplied, it is 100x(x+1)+y(10-y), which holds for any x and y, so it can be calculated as quickly."

Liu Meng exclaimed: "It's true. It seems that this student is very interested in mathematics. He might as well listen to less teachers' lectures and study some difficult and innovative mathematical propositions as soon as possible after learning the content of high school. The achievements he has made must be quite good."

With Liu Meng's approval, these students were very excited, their chests were undulating, and their faces were very proud and proud. Who is Liu Meng? He is the most famous mathematician in China today, no one, even surpasses other well-known mathematicians in China in the past. What a great honor is this? It's no wonder that this student is so excited.

"Illusion square, everyone should have played with it. A third-order fantasy square refers to filling the numbers 1 to 9 into a 3x3 square, so that the sum of the three numbers in each row, each column and two diagonal lines is exactly the same. For example, the first row 8, 1, 6; the second row 3, 5, 7; the third row 4, 9, 2; the sum of the three numbers on each straight line is equal to 15. Students may have heard of the magic square, but they may not know some wonderful properties in the magic square. For example, any third-order fantasy square satisfies, and the sum of the squares of the three digits composed of each row is equal to the inverse of each row. For example, any third-order fantasy square satisfies, and the sum of squares of the three digits composed of each row is equal to the inverse of each row.

The sum of squares of three digits composed of order. For the third-order fantasy square just mentioned, it is satisfactory. The sum of squares of 816, 357, 492 is equal to the sum of squares of 618, 753, 294. As for why this property is there? Interested students can prove it by themselves. Using the knowledge learned in high school, you can prove it. Haha, the most important thing in mathematics is thinking, not a means, so, elementary mathematics may not be worse than advanced mathematics, and even the thinking contained in elementary mathematics is more cleverer than advanced mathematics."

The small math problems that Liu Meng talked about today really made everyone interested. The most important thing is that they are simple problems. However, after Liu Meng said this, he suddenly became high-end and grand. He actually solved such simple problems and became the most powerful mathematician. He was even better than those students who won gold medals in the mathematics of the Olympiad. A brand new and prosperous road appeared in front of him, making these people wait for the boredom and depression of studying, reviewing, exams, and tutoring all day long. He hoped that the students who could get into a key university would feel enlightened.

"The 196 algorithm is the same for reading forward and inverse reading a number. We call it palindrome. Choose a number casually, and add the number you get after writing it in reverse until a palindrome is obtained. For example, if the selected number is 67, you can get a palindrome number in two steps 484:67+76=143,143+341=484. Turning 69 into a palindrome number requires four steps: 69+96=165,165+561=726,726+627=1353,1353+3531=4884. The path to palindrome number of 89 is particularly long. It takes only the first palindrome number to be obtained until the 24th step, 8813200023188."

"Students may think that it is not surprising that they can always get a palindrome number by constantly adding one positive and one inverse, and finally get a palindrome number. This is true. For almost all numbers, if they continue to add according to the rules, the palindrome number will appear sooner or later. However, 196 is a very eye-catching exception. Mathematicians have used computers to calculate more than 300 million digits, but have never produced palindrome number once. Starting from 196, can palindrome number be added? What is the special thing about 196? This is still a mystery. If anyone among you can solve this mystery, it may be able to open up a new branch of number theory."

The seemingly simple and unsolved problems that Liu Meng threw out have made the students extremely imminent. Liu Meng is well aware of these high school children. When the teacher talked about the structure of the benzene ring, he said that if a student could solve similar problems, he would win the Nobel Prize. How excited the students were after hearing this. Now Liu Meng threw these simple and so specific problems to the students. The result is conceivable. The students were excited throughout the whole process, and they wanted to solve one of the problems that Liu Meng mentioned immediately, or all of them were solved.

The only solution

"Classic Number puzzle: Use 1 to 9 to form a nine-digit number, so that the first digit of this number can be divisible by 1, the two-digit number composed of the first two digits can be divisible by 2, the three-digit number composed of the first three digits can be divisible by 3, and so on until the entire nine-digit number can be divisible by 9. You are right, there are really such a fierce number: 381654729. Among them, 38 can be divisible by 2, 381 can be divisible by 3, and until the entire number can be divisible by 9. This number can be deduced step by step by step by step by step by step by step by computer programming. Another interesting fact is that among all the 362880 different nine-digit numbers composed of 1 to 9, 381654729 is the only number that meets the requirements!"

"The number is changing, the number remains unchanged. The twice of 123456789 is 246913578, which is exactly a number composed of 1 to 9. The twice of 246913578 is 493827156, which is exactly a number composed of 1 to 9. Double the 493827156 again, and 987654312 is still composed of numbers 1 to 9. If you double the 987654312 again, you will get a 10-digit number 1975308624. There is still no repeated number in it, which is exactly composed of 10 numbers 0 to 9. If you double the 1975308624, the number will become 3950617248, which is still composed of 0 to 9. So, will this rule continue? Let's verify it yourself later."

Liu Meng talked about several interesting small questions in number theory in succession, and the students off the field were all very interested. Not only that, even the county magistrate, county education director, senior and many teachers who were sitting below were all focused. Some teachers who taught mathematics couldn't help but check according to Liu Meng's idea. The county magistrate sighed: "You all listen to it. Masters are different. We can tell such profound problems in a simple way. We all understand that your teachers should teach. Sometimes my son's homework is only in junior high school. Sometimes I can't understand it. This is the gap. I always like to complicate simple problems and show that I am not stupid enough. A confident genius simplifies the most complex problems and let everyone understand it."

The Education Director, Principal and Teachers nodded quickly and said, "What the county magistrate said is that our education work will definitely improve." Having said that, do you know if these guys are going to improve?

Liu Meng then explained the Goldbach conjecture in a simple and easy-to-understand manner. This is an authentic world-class problem. Liu Meng is a little bit away from solving her, but it has been stuck for more than a year. He tried various experiences over the past year and could not solve it. He could only give up returning to his hometown and instead carry out education work in his hometown. In fact, he really hopes to find inspiration from the thinking of these students. The young people's ideas are wild, so they can open up their thinking. Those famous mathematicians have long been eroded by too many thinking trends.

"If anyone of you has any ideas about the Goldbach conjecture, you can come to me. In the next week, I will be at the Mammoth Technology Company next door. Even if it is unrealistic, it doesn't matter. You can come to me boldly. Dare to think is the first priority." Liu Meng said with a smile.

The students were in an uproar and immediately began to think hard. Liu Meng added: "If any student's ideas inspire me and do love mathematics, I can recommend to Shuimu University to participate in advance admissions."

With a thud, the students were in a bad mood again. You should know that the teaching level of Sishui No. 1 Middle School is not high, especially the teaching staff of English teaching is too poor. No one has been able to get into Shuimu University for three consecutive years. It is a very glorious thing to get into Shuimu University in Sishui City. The entire county town will spread wildly and be particularly respectful.

Liu Meng's words are definitely not bragging. Since he published a paper on twin primes, plus the professor-level researcher who had previously solved the Sitapan conjecture, he is now the first mathematician in China. After his return, Shuimu University has sent him an invitation letter to hire a professor at Shuimu University. The treatment given is even more generous. Liu Meng did not agree directly. Shuimu University instead invited him to be a judge of a prize. According to the contact person, this scholarship is the most valuable award of Shuimu University. Each student can only participate once during college, and there are only ten undergraduates in a year. If Shuimu University is the holy land in the hearts of all Chinese students and is longing for, then this award is the holy land in the hearts of all Shuimu University students and are dreaming about it. It is conceivable that Liu Meng has agreed to be a judge, just two weeks later.

Liu Meng continued: "In fact, thinking is the most important thing when doing mathematics. The so-called thinking is the illusory point of the soul. Simply put, it is to have a unique perspective on the problem. The students of Gauss' story must know that the teacher assigned a question, and the sum of 1 to 100, and all students used this method to add it. However, he thought of using sequences to solve it. Even a person with excellent mental arithmetic is not as fast as Gauss' unique thinking. This is the power of thinking, so thinking is a power that is stronger than ability and knowledge."

"Then the most popular speech is. Finally, I will tell a little story to see which student can get the answer the fastest. The two trains are 200 kilometers apart, each heading towards each other at a speed of 50 kilometers per hour. A fly sets from the front end of one of the trains and flies back and forth between the two trains at a speed of 75 kilometers per hour. The question is: What is the total distance between the flies until the two trains collided? Is there any student able to give the answer in one minute?"

As soon as Liu Meng's question came out, everyone took out paper and pen to calculate it. Although Liu Meng just said that thinking is the most important, when time is tight, the students are still used to starting to calculate. This is the influence of thinking trends. In fact, this question is like a question with 1+2+3 all the way to 100. It is easy to find the entry point.r1152
Chapter completed!