White-robed Minister

Chapter 70 0068 [Master Yu's Unexpected Gain]

Chapter 70 0068 [Mr. Yu's Unexpected Gain] (Fifth update, please subscribe)

"Xu Lai greets the young lady."

"May Scholar Xu be blessed with good fortune."

If we don't count peeking through the latticed window, this was their second meeting, and they were still a bit awkward with each other.

"Whether you're an official or a householder, you must master mathematics. I'll give you a math problem, and you'll each have to solve it." Yu Jing took out counting rods and placed them on the table, then picked up a brush and began writing the math problem.

There are three bundles of high-quality rice and two bundles of medium-quality rice, totaling thirty-nine bushels; and two bundles of high-quality rice and three bundles of medium-quality rice, totaling thirty-six bushels.

How many grains are in each of the upper and middle bundles of rice?

Xu Lai's first reaction was not to carefully examine the question, but to speculate on Yu Jing's purpose.

He called me to his house and asked me to make a physics force gauge for him. He also called his daughter over to do math problems together.

His actions are perplexing.

What exactly is Mr. Yu trying to do?

Why did you call your daughter here? Are you trying to recruit me as your son-in-law? But there's no need to beat around the bush. A few subtle questions would have sufficed.

It's so weird to do math problems together.

In fact, Yu Jing's actions were purely driven by the mindset of an old-fashioned straight man.

He wanted to foster a relationship between his disciple and his daughter, but felt that playing together in private was against propriety. So he decided to have the young boy and girl do exercises together in his presence, so they could quickly become familiar with each other.

In Yu Jing's view, reading together, doing exercises together, and discussing academic matters together are the easiest ways to become close. And it doesn't overstep the bounds of propriety.

Simply perfect!

Pianpian had already guessed her father's thoughts and felt extremely helpless. She disliked math and this way of interacting. Especially with her father present, she felt extremely awkward and embarrassed.

"Take your time with the calculations," Yu Jing said, sitting down to drink tea.

Looking at the young couple in front of him, he felt they were a perfect match, a handsome man and a beautiful woman, a match made in heaven.

Moreover, Yu Jing was very proud of his arrangement, which he considered the most polite and elegant way to date.

This time, let them do arithmetic problems together; next time, let them discuss the Classic of Filial Piety. Surely, my daughter and my disciple will soon develop feelings for each other. Then, we can discuss marriage, and everything will fall into place naturally.

The old father is really worried sick!

However, Xu Sanlang was completely at a loss at this moment.

The problem, which could be solved with a linear equation in two variables, was naturally very simple for Xu Lai. The problem was that Yu Jing had placed counting rods on the table, clearly indicating that he was to use them to solve the problem.

Xu Lai had no idea how to use counting rods.

He subconsciously turned his head to look at Pianpian, only to see her first arrange two rows of counting rods on the table. Then she changed the second row of counting rods, and then moved the counting rods around again—this process seemed to have gone wrong, and Pianpian arranged the counting rods again next to her.

Finally, Pianpian replied, "A bundle of top-grade rice is nine dou, and a bundle of medium-grade rice is six dou."

Yu Jing was quite satisfied with his daughter's calculation speed, but Xu Lai's performance made him frown.

Xu Lai told the truth: "Sir, I have never learned how to use counting rods."

"I see," Yu Jing said with a smile, relieved. "Pianpian, you teach Xu Sanlang how to use it."

Pianpian, upon learning that Xu Lai didn't know this skill, couldn't help but feel a little smug. Always eager to teach, she said, "There are two ways to arrange counting rods: horizontally and vertically. Let's talk about the horizontal way first. One rod placed horizontally is 1, and one rod placed vertically is 5. Like this, three horizontally and one vertically, what is that?"

It's a base-5 system.

Xu Lai said, "It's 8."

"Then I'll teach you how to do addition using counting rods," Pianpian continued her earnest teaching.

Yu Jing sat beside him, watching with a maternal smile on his face, everything was under his control.

At this moment, Xu Lai really had no other thoughts on his mind.

For him, counting rods were a novelty. Although relatively outdated, they were still a skill, and Xu Lai was wholeheartedly learning them.

Fifteen minutes later.

Pianpian asked in surprise, "You really understood? Don't I need to explain it again?"

"Okay, I understand." Xu Lai nodded.

Pianpian expressed extreme skepticism about this, wondering how someone could learn everything so quickly after just one lesson on counting rods.

When she first started learning, it was very simple, but later her mind became completely confused.

"Then I'll teach you how to solve that problem using counting rods!" Pianpian really didn't believe it and jumped straight to the advanced mode.

Xu Lai watched her rearrange the items, and this time he was finally able to understand them.

Pianpian was actually using counting rods to arrange two linear equations in two variables. Then she multiplied each equation by 2 and 3 respectively, subtracted one variable to get the solution for the other variable. She then substituted the solution into one of the equations to find the solution for the other variable.

It's no different from solving systems of equations in modern mathematics, only the way it's presented is different.

Pianpian asked, "Did you understand?"

"Understood." Xu Lai nodded.

"You really understand? Then you try it." Pianpian became increasingly skeptical.

Because she deliberately didn't explain, but just kept moving the counting rods, harboring the intention of making things difficult for Xu Lai.

Xu Lai picked up the counting rods and began to lay them out, then moved swiftly. His movement was exactly the same as Pianpian's, but much faster, at least half the time.

Pianpian was speechless for a moment and couldn't help but look at Xu.

Is there really a genius in the world who can learn everything by heart?

Pianpian recalled how her mother had repeatedly taught her how to solve similar problems a while ago. It had completely baffled her; she had learned the basics at the time, but couldn't understand the process. It wasn't until later, through reflection, that she finally grasped the concept.

Xu Lai, his thirst for knowledge at that moment blazing, as if he had received a new and exciting toy, said to Yu Jing, "Sir, could you give me an even more difficult one?"

Yu Jing got up, picked up his pen, and posed another question, which also turned out to be a problem involving two linear variables.

This disappointed Xu Lai somewhat.

What he really wanted to know was how to express a quadratic equation in two variables using counting rods. But he didn't know what the square was called in ancient times, so he could only ask Yu Jing to give him an even more difficult one.

Left with no other option, Xu Lai could only fiddle with the counting rods and quickly solved the problem.

Pianpian was speechless. She thought to herself: He must have studied this before, otherwise he wouldn't have been able to calculate it so quickly.

Yu Jing's thoughts were exactly the same as her daughter's: "You really haven't learned how to use counting rods?"

"I'm a beginner," Xu said.

Yu Jing had seen many geniuses, and he himself had a photographic memory. He immediately stopped doubting Xu Lai and praised him, "You learn very quickly."

Xu Lai said, "Sir, this method is too cumbersome. Moreover, if a mistake is made in the middle, it is difficult to know which step was wrong, and we have to start all over again. Just now, I have figured out a method that can solve this problem."

Yu Jing thought he had misheard; for thousands of years, there had been no other way to solve this kind of problem except by using counting rods.

This disciple before me can comprehend a new method in a short time?

"What new method is it? Tell me," Yu Jing said calmly.

Xu Lai picked up his pen and said, "I used to eavesdrop on the village school teacher's lectures and felt that arithmetic should be written faster, so I created some arithmetic symbols myself."

0, 1, 2, 3 — Xu Lai wrote down a bunch of modern numbers and wrote zero, one, two, three next to them —

Yu Jing didn't say anything.

The ancients were not fools; in the actual production process, craftsmen had already created simplified symbols.

However, the symbols popular among artisans in different regions are also different.

Until the Southern Song Dynasty, the numerical symbols in the Jiangnan region were gradually standardized during the Yuan and Ming Dynasties and spread throughout the country until the Qing Dynasty—when they were finally replaced by Arabic numerals.

Xu Lai didn't set anything, y, but directly used the original problem's Zhonghe and Shanghe, abbreviated to Zhonghe and Shanghe as unknowns.

Write out the equations and quickly calculate the results.

Yu Jing picked up the paper, remained silent for a long time without saying a word.

He was well-versed in the I Ching and the principles of Yin and Yang. While he might not be considered a mathematician, he certainly possessed a profound understanding of mathematics.

He could tell how powerful this method was.

First, you don't need counting rods; all you need is paper and pen, or you can draw on the ground if you don't have paper and pen. You can calculate anytime, anywhere.

Secondly, the steps are clear, with each step written on paper. In contrast, counting rods need to be moved, and it is difficult to know which step was wrong after the movement.

Third, it is easy to learn and understand, which facilitates the rapid dissemination of mathematical knowledge and allows for the mass training of relevant personnel!

Finally, Yu Jing spoke up: "Write down your method in detail. I will submit it to the court so that it can be promoted in the Three Departments first."

"Disciple obeys!" Xu Lai bowed and said.

Yu Jing asked, "Is there anything else?"

Xu Lai said, "There is another type of vertical calculation, which can be used for addition, subtraction, multiplication, and division. For example, multiplying several million by several million, a long string of numbers, although it is slow to calculate, can be done without counting rods and an abacus."

"Write it down for me." Yu Jing was already in work mode and had no time to think about his children.

Xu Lai immediately wrote down two sets of numbers and set them up in a multiplication table. Because the numbers were too large, the multiplication table was a long string, but he still managed to get the result in the end.

After listing all the vertical equations for the four arithmetic operations, Xu Lai simply came up with a system of two quadratic equations in two variables.

Upon seeing the system of two quadratic equations, Yu Jing's pupils constricted sharply.

Such complex mathematical calculations were impossible to solve using counting rods. Yu Jing's friend Jia Xian (a great mathematician) had made limited progress in his research over half his life, but Xu Sanlang actually provided another approach, although it was just a clever solution to a special problem.

Yu Jing stared at Xu for a long time, and couldn't help but wonder: What kind of monster did I take as my disciple?

He only asked his daughter to teach Xu Lai how to use counting rods, so how did he inexplicably create so many things?

Could there really be such a wise person as Confucius described in this world?

"Husband, young lady, Xu Sanlang, Madam, please come in for dinner!" a maid called from outside the study.

Yu Jing gathered his thoughts and smiled, "Let's eat first."

Pianpian, however, remained standing there, still reading what Xu Lai had written. She could now understand vertical calculations and was studying the system of equations.

Yu Jing walked out of the study, turned back and said, "Sixth Sister, let's eat first, then we'll look at it."

"oh."

Pianpian was momentarily dazed, and subconsciously followed him out.

She hurried after her father, and as she passed Xu Lai, she couldn't help but turn her head to look at his profile, thinking: What's wrong with his brain?

He's incredibly smart.

Madam Lin was already standing at the entrance of the dining room, inviting everyone to come and sit down.

During the meal, Madam Lin inquired about Sanlang's well-being and took the opportunity to ask, "Who lives in Sanlang's family?"

Xu Lai replied, "Both parents are alive. My eldest brother died two years ago while serving in the military, falling into the river from the plank road. My sister-in-law has remarried and has a niece. My second brother and sister-in-law are loving and harmonious, and they have a son who is over one year old."

Mrs. Lin sighed, "I feel sorry for your little niece. She lost her parents at such a young age."