Liu Chen couldn't help but clap his hands and exclaimed: "It seems that some students have discovered this rule, very good, interested students can verify it by themselves, and there is also such a law for three-digit numbers." Pen Fun Pavilion wWw. ｂiquge。 ｉｎfo”

There was a deliberate pause for five seconds, and sure enough, He Qian shouted, "495." ”

"Correct. Liu Chen said expressionlessly, looking at the excited and proud look on this kid's face, he knew that he had come to be interested, and he had fallen into the game of guiding him, and he didn't praise him at all.

The other students were still in a fog and didn't know what was going on.

In fact, starting from this question, we can also ask a question, that is, in addition to the three-digit and four-digit numbers, are there any five-digit, six-digit, and seven-digit numbers? I can tell you that this phenomenon is called a digital black hole, also known as the Kaprekar constant. ”

After the first small question was finished, He Qian was attracted by Liu Chen's lecture, and this knowledge was not something that those teachers could tell.

Liu Chen didn't care about the reactions of his classmates and continued to talk directly.

"Start with any positive integer and repeat the following operation: if the number is even, divide it by 2, and if the number is odd, expand it to 3 times and add 1, what is the pattern?"

He Qian was like a human brain computer, and soon shouted: "In the end, it will always become 4,2,1,4,2,1,... of the cycle. ”

Obviously, this kind of demolition makes him very fun, and I can know immediately what you say, and see what else you have to say.

Xue Song said worriedly: "Liu Chen said that these things are difficult for He Qian, this is simply to give him a chance to perform." ”

Ling'er knew Liu Chen's personality very well, frowning and pondering.

Yuan Zheng smiled and said: "Heh, I think it's very interesting, listen patiently, even if it is on the spot, this Liu Chen junior should not be more than capable of this, after all, Zhuo Ling can take the initiative to invite over." He can't be a mediocre person. ”

Watch with your hands on your chest.

On the surface, Liu Chen was indeed being tricked by He Qian.

"Is it that for all the numbers, the sequence always ends up being 4,2. What about 1 cycle?"

He Qian frowned again, and shouted after a moment: "This is not simple!"

It looks like Liu Chen is going to be despised again.

He continued indifferently: "This problem can be said to be a huge hole, at first glance, the problem is very simple, and there are many breakthroughs. So many mathematicians jumped into it, but they didn't know that it was easy to get in and difficult to get out, and many mathematicians didn't figure out the problem until they died. There are countless mathematicians who have been recruited, and from such a simple problem, the Collatz conjecture, the Syracuse problem, the Kakutani problem, the Hasse algorithm, the Ulam problem, and so on. ”

The average child simply does not know that such a simple question is indeed the most complex one.

"Nonsense, numbers within a thousand are in line with this law!"

He Qian's voice was very disdainful, and with his knowledge, he naturally did not find this kind of pediatric problem difficult.

Liu Chen smiled, "Then what if the number symbol within 10,000 doesn't match?"

He Qian gritted his teeth and tried desperately, and it only took a few minutes before he shouted: "All satisfied." ”

This kid is really powerful, he definitely doesn't count every number. For children in the second year of junior high school, it is not easy to master the methodology on their own, and it is just like Gauss's existence.

"So what if the numbers within 100 million don't match?"

The other students seemed to understand what they didn't understand, but they relished it and thought it was amazing.

He Qian didn't want to admit defeat, so he gritted his teeth and tried all kinds of ways.

Liu Chen directly poured a basin of cold water down, "In number theory, as long as the seemingly simple propositions that are generalized to infinite numbers are very difficult to prove, because you can't use exhaustive methods to prove them one by one." This is the case with the famous Riemann conjecture, Fermat's theorem, Goldbach's conjecture, as well as with the 3x+1 problem, which until now mathematicians have not proven. 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 top ten most famous people on this planet, at least much more powerful than the well-known Chen Jingrun and Hua Luogeng. ”

The students suddenly exploded into a pot of porridge, and the problem that sounded so simple actually solved the famous mathematicians who could surpass those in the textbooks. For these children, it is simply opening up another world, a surge of enthusiasm, and the classmates who usually claim to be smarter can't wait to take out a pen and paper to check it, fantasizing that they can solve the problem and become famous...... And so on, young people are always impulsive and naïve and full of fantasies.

Liu Chen's speech is extremely simple for these students, and even the students who are sitting here are very bad at math and have been failing can easily understand these questions, but they are very different, and the impact on them can be imagined.

"Is what you say?" Hmph, who do you think you are?" He Qian obviously couldn't accept the defeat of being stumped, but he couldn't do anything about such a huge number.

Liu Chen ignored him and continued: "A number is the same when it is read forward and backward, so we call it a palindrome number. Take a random number and add it backwards until you get a palindrome number. What is the palindromic number of 67?"

"Two steps are out, 484, the level of kindergarten. ”

"What about 69?"

"4884, this is the level of elementary school students, we are junior high school students. ”

In the face of such a demonic student, I'm afraid any teacher will collapse, fortunately, Liu Chen is not an ordinary teacher, not only has a high level of mathematics, but also has a strong mentality, the most important thing is that he has seen a lot of examples of this kind of interesting mathematics, and it is not a problem to abuse this kid, and said coldly: "What about 89?"

He Qian was silent for a while.

He Qian couldn't help but break out in a cold sweat on his forehead, this sudden increase in difficulty made him collapse again, and the endless numbers could not be calculated one by one, why was it helpless to claim such a simple calculation just now, in a series of confrontations, the classmates all spontaneously looked at him, felt a pressure on their backs, and were hot.

Yuan Zheng saw it clearly on the side, and laughed in a low voice: "Classmate Liu Chen is really smart, from shallow to deep, give He Qian confidence, and then hit his arrogance, maybe it can really be useful." ”

"This number is not a palindrome at all!" He Qian, who had calculated eighteen steps and still had no results, was on the verge of collapse in his heart, it was almost a super-super big number.

"Is there really not?" said Liu Chen. (To be continued.) )