A Difficult Problem

Gan Lun then took out the question and read it aloud, "In the second year of Hongxuan, Wu County was merged into Guanlin, and the yamen officials were reorganized. In the first year of their reorganization, they received their original salary, and in the second year, they received two-thirds of their original salary. After entering Guanlin, they received their original salary in the first year; in the second year, their salary was twenty; and after that, their original salary increased by half a percent each year. Question: If a certain person's hourly salary was sixteen in the second year, what would their salary be after four years in Guanlin?"

After he finished reading the question, everyone was surprised and exclaimed, "Oh, it's this question! Wow, amazing! You can even solve this question. Your student is truly remarkable, Lord Gan!"

This question is a difficult problem accumulated by the Ministry of Revenue, and everyone is familiar with it.

At that time, the Great Jin. After the war, less than one in ten people survived, and the national treasury was also very empty.

In order to reduce expenses, the imperial court decided to merge two or three counties into one large county. As a result, the number of official positions in the government offices will be reduced, and officials will be reassigned based on their performance.

Because the imperial court was unable to pay salaries, the salaries of officials who were willing to be reassigned were reduced for the first two years; after the economy of the Great Jin recovered and the national treasury was full, the salaries were increased year by year to make up for the initial salary arrears.

To determine the necessary increase in salary for officials to make up for their previous arrears, and to ascertain how much the court would need to pay officials' salaries and whether the national treasury could afford it, the emperor ordered officials from the Ministry of Revenue to calculate the figures. If the Ministry of Revenue could not afford it, the increase would have to be adjusted and the compensation period extended.

It would be easy to calculate the salary of a single official; by adding and subtracting, everyone could arrive at the answer.

But this isn't just one official; it's local officials across the country, and each official's salary level is different. Therefore, a calculation method is needed.

At the time, the officials in the Ministry of Revenue had no idea how to formulate an equation to calculate it. In the end, they had to resort to a brute-force method, calculating it one by one from province to county to official, exhausting the entire Ministry of Revenue staff to the point of near death, before finally managing to calculate the data and submit it to the emperor.

After that, this problem became an unsolvable puzzle for the Ministry of Revenue. Every new official in the Ministry of Revenue, who prided himself on his mathematical skills, would try to solve it, but they all failed miserably.

"Oh dear, when I first joined the Ministry of Revenue, I was so obsessed with solving this problem that I couldn't eat or sleep, and I almost went mad. In the end, my wife scolded me and told me to go live with a math scholar, and only then did I forget about it," an official said.

Everyone burst into laughter upon hearing this.

Almost everyone has had the same experience.

"Enough with the chit-chat, everyone. Since Lord Gan says he's solved it, hurry up, Lord Gan, tell us how you solved it!" someone urged.

Gan Lun immediately put his newfound knowledge to use, relaying Zhao Ruxi's words. "This is a problem of reducing staff and increasing efficiency, belonging to the categories of 'sequence general term' and 'function maximum/minimum value model' problems."

Everyone: "..." They understood each word individually, but what did it mean when put together? They didn't understand!

"Lord Gan, can't you speak like a human being? I can't understand you!" someone shouted.

"You don't understand, do you?" Gan Lun asked with a smile, stroking his beard.

Everyone nodded.

Gan Lun glanced sideways at Guo Jitong: "Lord Guo is skilled in mathematics, so he must have understood. Why don't Lord Guo explain it to everyone?"

Guo Jitong's expression was not good. He chuckled awkwardly and cupped his hands in a gesture of respect, saying, "I am ashamed and do not deserve the title of 'amazing.' I am also ignorant, and I would be Lord Gan enlighten me."

Qi Xugu quickly tried to smooth things over. "Lord Gan, stop keeping us in suspense and tell us quickly."

Gan Lun, aware of Qi Xugu's predicament, stopped targeting Guo Jitong, turned his gaze away, and recounted the problem-solving approach Zhao Ruxi had given him.

When Zhao Ruxi spoke to Gan Lun, she tried to use the Great Jin Mathematical System to explain things whenever possible, and for things that couldn't be explained, she directly told Gan Lun which theories from the Empress Shengyao's Mathematical System she had used.

Gan Lun's memory was decent, and he managed to explain most of Zhao Ruxi's solution.

The Ministry of Revenue is not like other government offices; those require people to roll up their sleeves and get things done. Most of the staff are quite proficient in mathematics, and few get in solely through family connections or by currying favor.

From the part of what they understood, everyone could tell that Gan Lun's line of reasoning was correct. However, when it came to the part about the theory in the Empress Shengyao's mathematical book, everyone was scratching their heads in confusion.

Just as everyone was about to grab Gan Lun and question him closely, Qi Xugu grabbed Gan Lun's arm. "Brother Gan, come inside with me, I have something to tell you."

He waved to everyone again. "I know you all still have many questions for Lord Gan. But it's getting late, and some of you are going to the auction hosted by the Fifth Highness, right? Hurry back and pack your things, get ready to leave the office. Lord Gan isn't going anywhere; you'll have plenty of time to ask him questions later."

As he spoke, he pulled Gan Lun into the inner room.

The officials outside had no choice but to disperse.

Gan Lun was pulled into the house by Qi Xugu, still feeling quite unhappy.

Although Zhao Ruxi's problem-solving theories include some that he doesn't understand and can't explain clearly to everyone, he's not here to teach students, but to show off his students. He can simply say, "That's what the students told me, I don't understand it either," and be completely irresponsible.

Since everyone here is proficient in mathematics, they can understand the whole picture from a single point. Even if they don't understand some parts, they can still sense whether the general idea is correct.

That's exactly the effect he wanted.

Although he couldn't reveal Zhao Ruxi's name, he could still pave the way for her and spread her fame.

The awl, nestled in the bag, emerges from the depths.

He believed that Zhao Ruxi's mathematical talent could not be hidden.

Once her reputation as a painter advances further, and she becomes a master painter and a celebrity, her talent will no longer need to be hidden. What he did for her today will not be entirely useless.

Therefore, he was extremely unwilling when Qi Xugu interrupted him from showing off his students.

Qi Xugu didn't care whether he wanted to or not, and asked, "Can you really understand Empress Shengyao's mathematics book?"

"I don't understand." Gan Lun shook his head vigorously.

Qi Xugu: "..."

He glared at Gan Lun: "Then how did you apply the theory you used to solve the problem?"

"That was solved by my student."

"Which student are you? Tell me. If you don't, I'll assume you understand it yourself but don't want to tell everyone. Tomorrow after court, I'll report to the Emperor that you've understood Empress Shengyao's mathematics book but are keeping it to yourself and unwilling to teach others. By then, when the Emperor issues an imperial edict, it will be too late to say you don't understand," Qi Xugu threatened.

This time it was Gan Lun's turn to widen his eyes. "You... you... how dare you act like such a scoundrel?"

"Hmph, wasn't that what you forced me to do?"

Qi Xugu, as expected of someone capable of serving Ministry of Revenue, immediately fell silent after saying this and began to play the victim card.

"Old Gan, we've been colleagues in the Ministry of Revenue for decades, spending more time together than family. You know my struggles."