During arithmetic class, Fu Lin and I stepped into the classroom, and the Confucian disciples all looked at us with wide eyes, they must have thought that we were in the wrong place. I walked to the front of the stage, cleared my throat, stabilized my momentum, and said, "In today's arithmetic class, you three teachers are entangled in public affairs, and I will take the class." ”

The disciples in the audience all looked surprised and discussed. I just wanted to open my mouth to let the disciples be quiet, but suddenly there was silence in the classroom, their eyes turned to the door, and Zhang Liang's voice sounded slowly: "Yun'er, it's very punctual." ”

I glanced at him for some reason, what is he doing here when he is not in the library? Is he here to tear down the stage or to press the scene?

He walked up to me and said lightly: "Yun'er is in class for the first time, so I naturally want to come to audit and see if I can really do it." ”

Then he turned to his disciples and said, "You third master will take a few arithmetic classes on your behalf, if you think that the third master has something bad in her class, you can sue me." ”

The disciples did not express any objection to Zhang Liang's explanation, but they still seemed to have difficulty understanding why I would substitute for the teacher, and when they looked at me, it was obvious that they were not the inquisitive eyes that students should have, but a casual look waiting to see a good show.

Zhang Liang waved his sleeves leisurely, sat at the end of the classroom, smiled elegantly, and also looked like he was waiting to see a good show......

Since the disciples are very optimistic about my appearance, I won't say anything more and go straight to the question.

First Fu Lin read the question: "I don't know the number of things today, the remaining two of the three or three numbers, the remaining three of the five or five numbers, and the remaining two of the seven and seven numbers.

This is so familiar, it seems to be the residual theorem, right? The impression should be from "Sun Tzu's Arithmetic", did the Qin Dynasty have this algorithm? Regarding the residual theorem, I still came into contact with it in high school, but it has long been returned to the teacher, but fortunately, I don't have to rack my brains myself, it really saves a lot of effort.

It was my turn to read the question: "My question is very simple, suppose the government catches two thieves who are involved in the theft, but the evidence obtained is not very accurate, and the sentence for both may depend on their confessions to the theft." The two thieves were held separately to prevent them from colluding in confessions. The two thieves were sentenced to five years' imprisonment if they both confessed to the crime, and if they did not confess, they might be sentenced to one year each for a lesser offence because of insufficient evidence, and if one confessed and the other did not, the confessor would be released immediately, and those who did not confess would be sentenced to 10 years' imprisonment. What is the best option for the two thieves to get the least punishment?"

The disciples looked at each other, whispered, and were a little confused, Zimu stood up and questioned: "Third Master, you don't need to think about this kind of question to know the answer, do you still need it?"

"It seems that this kind of simple question can not be more difficult than our smartest classmate Zi Mu, but now is the time to do the question, Zi Mu please keep quiet and don't affect the thinking of other disciples. ”

Zimu has always been high-flying, as if he was very good, but my words made the other disciples listen to it very relieved, and they all snickered.

Zi Mu sat down stupidly, and it didn't take long to hand in the answer, still looking proud.

Halfway through the class, I asked the students to hand in their answers. Fu Lin and I each counted the number of correct answers, and Fu Lin announced the answers first.

"The answer is twenty-three, where the remaining one of the three or three numbers is placed at seventy, the remaining one of the five or five numbers is placed at twenty-one, the remaining one of the seven or seven numbers is placed at fifteen, and the above one hundred and sixteen is subtracted by one hundred and five, that is, the ......" She explained the specific solution in detail, to be honest, I really didn't understand it, the mathematical calculations that were already dizzy, and the explanations of those tongue-twisting written ancient Chinese sentences, my whole brain was a mess. I had to pretend to nod my head in agreement, indicating that I was listening, indicating that I understood... His mind has drifted far away.

In fact, when it comes to the remainder theorem, although it was recorded for the first time in the "Sun Tzu Sutra", it is not impossible that the Qin Dynasty had a clear calculation method. Because I remember that there is another legend about this concept, which is Han Xin's soldiers.

It is said that Han Shin's method of calculating the number of soldiers is very special. He first ordered the soldiers to line up in a line of three, then a row of five, then a row of seven. He knew the total number of soldiers by simply recording the number of soldiers left in the last row of three rows.

Now it seems that the credibility of this legend is still high, and maybe the soldiers in history are really good at mathematics. If Han Shin had lived in modern times, perhaps his math mind would have been able to mix up with the work of a math teacher. I remembered the last time I met Han Xin on the street of Songhai, he was carrying a sword, his face was cold, and he looked cool and imposing. His mind suddenly flashed to the scene of his expressionless poker face holding a teaching stick to class, and he couldn't help but laugh. I didn't think about it too much, and I didn't notice that Fu Lin had finished speaking.

"Senior sister?!"

"Huh?" I came back to my senses.

"I'm done. ”

"Oh, good. I smiled, walked up to the center of the room, and announced, "Only one person of mine got this question right." ”

"Huh, how is that possible?" the disciples were incredulous.

I disagreed, and continued: "This person is Ziming. ”

There was an uproar in the classroom.

"Ah?!Ziming!"

"He's not!"

I unfolded Tianming's answer sheet to face everyone, and the answers to two questions were written on it, both of which were just three words: I don't know.

Immediately, the disciples burst into laughter.

I raised my voice and said, "Yes, I just don't know!" There is no absolute answer to this question, and there is no absolute best solution. ”

The disciples looked at me inexplicably, as if I was talking nonsense.

I justified myself by saying, "This problem is an unsolvable game. The reason why there is no solution depends on whether these two people are gentlemen or villains. Mencius said: The gentleman is in righteousness, and the villain is in profit. We knew at a glance that not confessing was the best solution, and both sides were only imprisoned for one year, and most of the disciples also made this choice. But the premise of this outcome is that neither side is treacherous. If the two of them are thieves who follow the chivalrous demeanor to rob the rich and help the poor, and pay attention to a righteous word, they will naturally be able to choose not to confess with one heart and reach the best plan. However, if they are villains who only care about their own interests and do not trust each other, they will take a greater risk if they choose not to confess, and if the other party confesses, they will be imprisoned for ten years. So, to be on the safe side, they will choose a compromise to prevent the other party from betraying. Instead of making the best choice, both of them chose to confess, and both were sentenced to five years in prison. ”

"Third Master, this is an arithmetic class, did you say the wrong content?" Zimu provoked trouble again.

"Then Zimu, why don't you tell me what arithmetic is?"

"There are nine numbers in the Zhou metric system, and the flow of nine numbers is the "Nine Chapters". Nine numbers: Fangtian, corn, differential, Shaoguang, business, average loss, equation, lack of win, side; ”

"Arithmetic does contain these contents, but what is the ultimate purpose of learning arithmetic? In the end, it still provides effective numbers to help us solve problems and make better decisions in life......" I wanted to explain more clearly, and suddenly found that it was really a headache to explain abstract mathematics to the ancients, and I suddenly felt a little short of words.

At this time, Zhang Liang got up and echoed: "The husband calculates, the longitude and latitude of heaven and earth, the head of the masses, the origin and end of the five constants, the parents of yin and yang, the building number of the stars, the surface and the inside of the three lights, the quasi-level of the five elements, the beginning of the end of the four hours, the ancestor of all things, the outline of the six arts; the gathering and dispersion of the group of people, the rise and fall of the two qis, the overlapping fortune of pushing the cold and the summer, and the difference between the distance and the distance; the subtle Zhaoji of the Heavenly Dao, the length of the geographical vertical and horizontal; the location of the gods, the talisman of success or failure; the principle of poor morality, and the love of life. ”

I breathed a sigh of relief, Zhang Liang's most authoritative summary saved me a lot of laborious explanations. He smiled at me and motioned for me to continue.

"So what I'm going to talk to you about today is about the game of numbers. This kind of game is also preserved in "The Art of War", and there is also the story of Tian Ji's horse race, which also reflects this game very well. In order to give you a better understanding of the use of this game, we will make a game as a demonstration. I glanced at Zhang Liang, walked up to him, and continued, "First of all, I and you Third Master will demonstrate this game. He and I each showed one side of the coin, heads or tails. If we are all positives, then if he wins, he will add 3 points, and if we are all negatives, he will add 1 point and I will deduct 1 point, and in the rest of the cases, I will deduct 2 points if I win, and he will deduct 2 points. If you don't dispute the fairness of this game, I'll bet three sets and eight games with you three masters to see who has the better chance of winning, how about it?"

The disciples' eyes were blazing, and they all suddenly came to their senses, and their heads were like rattles, and they all stood up together and gathered around. In this scene, why did I suddenly feel like a crowd gambling......

Zhang Liang did not refuse, but smiled leisurely, with a clear look in his eyes, after three sets, they are all under my control, and I win.

"The Third Master lost ...... again"

"I actually lost three times. ”

"Third Master, you're too lucky! Tianming frowned, anxious for Zhang Liang.

Zhang Liang smiled slyly, but didn't mind, but said in a word: "Yun'er, I'm afraid I will never win this bet." ”

He really saw the way, so although I won in three sets, it was a narrow victory.

This is an unfair game proposed by the mathematician Nash, as long as I play heads and tails according to a certain probability, no matter how the opponent adjusts his strategy, he will not be able to turn the tables, and the opponent can only deal with the best countermeasures and try to lose a few points. And he understood the law from the beginning and used the best countermeasures. Mou Sheng's brain really has a talent for game theory, which simply means considering the predictive behavior and actual behavior of individuals in the game, and studying their optimization strategies. And people like Zhang Liang are best at decision-making.

As a liberal arts student, I know some of the skin of game theory, or thanks to "A Beautiful Mind", a movie about the mathematician Nash, because I liked this movie too much, I was also moved by Nash's fate, and I patiently studied the small cases in game theory, and then I thought of using it to fool Confucian disciples.

"Third Master try again?" the disciples agitated on the side.

"Third Master, it won't be a deliberate loss to the Third Master, right? "Tianming is really not big or small, 'fairy tales are unscrupulous'.

I glared at Tianming. Zhang Liang shook his head and said with a smile: "Which disciple is interested in playing against the third master, you can give it a try." ”

As soon as he said this, the disciples were eager to try. Of course, Zhang Liang couldn't win against me, let alone these disciples, but as a result, they were even more persistent in defeating me, and they were dragged by them after class.

Zhang Liang actually thought that I was not popular enough, so he added fuel to the fire and said: "Whoever came up with a way to win the third master, all my subject exams will be exempted, and I will be counted as excellent." However, the third master deliberately humbly let you lose is not counted, you have to distinguish carefully. "After speaking, in the blink of an eye, people don't know where they have gone. Poor me was surrounded by the disciples and couldn't get through, and I was inexplicably stabbed upside down, I was depressed and abnormal, he was too black!