The journey of the only child of a peasant family to take the imperial examination

The next day, after class, Zhang Pingan came to the Chengnan Chess Academy again. As expected, the old man from yesterday was already waiting. Seeing Zhang Pingan coming, he stroked his beard and said happily, "Boy, you really keep your word. I've been waiting for you for more than half an hour. Come on, sit down and let me set up the pieces."

Zhang Ping'an followed his instructions and walked over to sit down with a smile. The two began to play chess again. After two quarters of an hour, the old man looked at his white piece that was once again trapped, shook his head and sighed, "Young people are really formidable!"

The old man had a bit of a reputation in the South City Chess Academy. When the two of them were playing, there were already three or two people watching nearby. Seeing Zhang Ping'an's black pieces silently eating up the old man's white pieces step by step, and finally trapping him to death, they couldn't help but clap their hands and shout "Good!"

The cheers attracted others to stop and watch. A middle-aged man stepped forward and praised, "Young man, you are a great chess player. Would you like to play a game with me?"

"Yes," Zhang Ping'an nodded. The old man stood up and gave up his seat, but he did not leave. Instead, he watched the game with relish like everyone else.

The middle-aged man's chess skills were obviously better than the old man's, and his style of play was fierce. Every move he made was fast and accurate. Zhang Ping'an had to concentrate and calculate quickly in his mind. The two of them moved back and forth, and both made moves quickly. Such a game made the people around them excited, but no one would point fingers at them. This was the basic rule of watching chess.

Half an hour passed, and the middle-aged man gradually lost the upper hand and made moves slower and slower. Anyone with a discerning eye could see the final outcome of the game.

Another quarter of an hour passed, and the middle-aged man shook his head and said: "Your skills are excellent, and I am willing to admit that I am inferior to you!"

Zhang Ping'an bowed his hands and said modestly: "Thank you for the courtesy, senior!"

The people watching the game began to talk: "This game is really exciting to watch. The back and forth fighting is so intense. Let's have another round."

Zhang Ping'an shook his head and smiled, "It's getting late today, it's time to go home, kid. Come back tomorrow."

On the second day, Zhang Ping'an came to the Chengnan Chess Academy again. After ten days, almost everyone who came to the Chengnan Chess Academy had played chess with Zhang Ping'an, and Zhang Ping'an's reputation in the Chengnan Chess Academy grew.

Zhang Pingan guessed that he might be able to wait for the person he wanted to wait for in the next two days.

On the eleventh day, Zhang Pingan came to the Chengnan Chess Academy again. The boss led him into the side room and said with a smile, "Young man, there is a master who wants to play chess with you."

Zhang Pingan felt something in his heart, and when he opened the door, it was indeed Mr. Fan.

Mr. Fan didn't say much while playing chess. He just made a gesture of invitation to Zhang Ping'an, and started to move the pieces after Zhang Ping'an sat down.

Zhang Ping'an knew that Mr. Fan was also proficient in mathematics, so he was extremely alert from the moment the first move was made. Mr. Fan also did not underestimate his opponent just because he was young. The two of them played back and forth, and the game lasted for more than an hour.

Seeing his black piece trapped and unable to move, Zhang Pingan bowed and said with a wry smile: "Senior, your chess skills are truly superb. I admit defeat."

Mr. Fan finally relaxed, stroked his beard and smiled faintly: "You are the second person who can play chess with me for so long. You are a respectable opponent."

"I don't deserve it," Zhang Ping'an said modestly.

"I heard from Mr. Bao Weng that you integrate mathematics into your chess playing?" Mr. Fan asked slowly after picking up the teacup and taking two sips of tea.

"Yes, kid, I have some experience in mathematics. In fact, mathematics can be applied in many places in chess," Zhang Pingan said neither humbly nor arrogantly.

"Oh? I'd like to hear more about it," Mr. Fan made a gesture of listening attentively.

"The Go board is 19 by 19, which means there are 361 possible options for each move. This number increases rapidly when considering multi-move combinations. Combinatorial mathematics can help analyze the possibilities of these combinations and find the optimal path. At the same time, by counting the number of pieces on both sides, we can assess the balance of the situation and determine whether we have an advantage. The Go board can also be viewed as a graph, and the connections between pieces can be viewed as edges in the graph. Using graph theory, we can analyze the connectivity of the pieces, attack paths, and defensive strategies."

After listening to this, Mr. Fan nodded and said: "It's great that you can have this understanding at such a young age."

Zhang Pingan said calmly: "There are always people better than you, and there are still many things I need to learn."

"Where are you studying now? Do you have any academic achievements?" Mr. Fan was indeed curious about this young man, but he didn't know how knowledgeable he was.

"I'm currently studying at Qingsong Academy. I just finished the provincial examination in April this year and was lucky enough to pass the exam as a Tongsheng," Zhang Pingan replied respectfully.

"Madam Jun, what is the meaning of your sexual desire?"

Zhang Ping'an was startled when he heard this. This was such a coincidence. It happened to be the topic Master Lin had talked about. "The word 'Jun Furen' comes from the last sentence of 'The Analects of Confucius, Ji Shi, Chapter 16'. Foreigners call it 'Jun Furen'. The second half, 'Yang Huo's desire', comes from another chapter, 'The Analects of Confucius, Yang Huo, Chapter 17'. Yang Huo wanted to see Confucius, but Confucius didn't see him. The first half, 'Jun Furen', talks about how the wives of both small and large monarchs are honored as Jun Furen. Women follow their husbands. The husband is the minister who guards the land for the emperor. Whether the country is big or small, the responsibilities are the same, so the respect is the same. This is a way of observing etiquette and order. The second half, 'Yang Huo's desire', refers to Yang Huo accompanying the ministers in governing the country, violating etiquette and disrupting the government. This is a way of not observing etiquette. So put it together, the opening sentence is that the saints observe etiquette and do not do impolite things."

After hearing this, Mr. Fan nodded with satisfaction and praised: "Your knowledge is quite good."

Zhang Ping'an just breathed a sigh of relief when he saw Mr. Fan's face suddenly turned cold and asked, "Do you know me?"

He didn't say he knew him when he came in just now. If he said he knew him now, it would seem that he had bad intentions. But if he said he didn't know him and his lie was exposed one day, it would make him look even more mean-spirited. Zhang Ping'an hesitated for a moment before bowing and saying honestly, "I was fortunate enough to attend your lectures at the county school, Mr. Fan."

After hearing this answer, Mr. Fan smiled again and said, "Actually, I recognized you the moment I saw you. I have a very good memory. I never forget anyone I've met once."

Zhang Ping'an was ashamed, fortunately he didn't lie.

"Then I guess you've been waiting for me at the chess academy for the past ten days. Many people want to get close to me, but you're the only one so young, so knowledgeable, and so proficient in both mathematics and chess. I'm willing to be your mentor. If you have any questions later, you can ask me during our game." Mr. Fan said calmly, then stood up and left, saying as he walked, "Today's game was a very enjoyable one!"

Zhang Ping'an stayed in the chess room and calmed down for a while. Playing chess with Mr. Fan was not an easy task, but fortunately, hard work paid off!