Su Hao calmly replied: "The student has only heard about Mr. Wu's talents for a long time, but he does not know how much knowledge Mr. Wu is proficient in, so he cannot tell whether he has the knowledge that Mr. Wu can appreciate. The student wants to ask Wu
Sir, I have a question to ask. Mr. Wu just needs to say whether you can or can’t, without wasting your time. What do you think?”
The students sitting below looked at Su Hao and Wu Zhicheng with wide eyes. Su Hao's words sounded polite, but there was a sharp edge hidden in them. Su Hao's request was simple: I will give you a question.
You do it, you just need to say yes or no. As a young man who only got the last place in the scholar examination, saying this to a learned scholar is simply a naked provocation.
"If I can, what will you do? If I can't, what will you do?" Wu Zhicheng asked, holding back his anger. A young man can be calm and calm under his own derogation, but if he is provoked by someone else's words,
If he jumped up, wouldn't he fall down first? Thinking of this, he decided not to explode yet.
Su Hao said: "If sir can do it, then the student will immediately hide his face and leave, because this is the only way the student can show it to the teacher to see. If sir can't..."
"Then I will resign immediately as an evangelist, go home and study behind closed doors, and no longer mislead others." Wu Zhicheng was forced into a corner by Su Hao, and he had to say harsh words. He thought to himself, if Su Hao's question is about being upright and upright
If Su Hao had to find an unpopular question to test him, Fang Mengjin would have scolded Su Hao for being shameless, so he didn't have to worry about it.
Su Hao said: "That's not necessary. There are specialties in the arts. It's normal for Mr. Wu to encounter things he doesn't understand occasionally. Students just hope to get an opportunity to ask Mr. Wu for advice."
"No need to talk much, just tell me your problem." Wu Zhicheng said.
Su Hao said: "This problem is a problem our workshop encountered during the project. Today we want to make 150 pieces of bamboo utensils. Each piece requires one bamboo pole each of 4 feet, 2 feet 6 inches and 1 feet 7 feet. We currently have a number of 1 feet long bamboos.
I want to ask how to cut the materials so that the amount of long bamboo can be minimized, and how much is the minimum?"
"this……"
As soon as Su Hao finished asking the question, the expressions of everyone in the room changed. The question sounded very clear, but everyone knew that they could not solve such a question at all.
A 1-foot-long piece of bamboo can be cut into two 4-foot pieces, and the remaining part can be cut into one 1-foot-7-inch piece. This will leave a 3-inch bamboo head. By changing the cutting method, it can be cut into one 4-foot piece.
, 1 piece of 2 feet 6 inches, 2 pieces of 1 foot 7 inches, so there is no waste. The problem is that the required quantity is 150 pieces of each of the three sizes, which requires a combination of various cutting methods. As for how to combine
is the best. In everyone's mind, there is no better way except to test them one by one.
Obviously, when Su Hao raised such a question, he did not ask Wu Zhicheng to use experimental methods to solve it. However, Wu Zhicheng didn't know how to solve it yet. If you want to say that this problem is unpopular, it seems unreasonable. Similar to such a problem
, it is entirely possible to encounter it in daily life.
The weather in the middle of April on the lunar calendar was so hot that everyone was sweating, but Wu Zhicheng felt that his vest was covered with cold sweat. As a proud and arrogant scholar, the most unbearable thing was to be defeated by others in knowledge. Wu Zhicheng is like this
There have been times in my life when I was asked questions by others, but never like this. I obviously think this is a very simple question, but I can't even figure it out.
"Su Hao, this is an arithmetic problem, but I can't remember which book has formulas for it. You asked this question, can you solve it?" Fang Mengjin could hear from Wu Zhicheng's breathing next to him. Seeing that he was in embarrassment, he broke the silence and asked Su Hao. Fang Mengjin didn't bet anything with Su Hao, so it was very appropriate for him to ask the question.
When Su Hao came up with the problem, he did not expect Wu Zhicheng to be able to solve it. You must know that this is a linear programming problem, hundreds of years ahead of this era. Even in the West, the linear programming problem was raised in 200 Later, at the beginning of the 19th century, the first person to raise this problem was the famous French mathematician Fourier. However, even with Fourier's level, he could not find a good solution. He had to wait until another time. It took more than 100 years, and it was not until the 1950s that the corresponding algorithm was developed.
Su Hao used such a question to test Wu Zhicheng. To put it bluntly, he was using a golden finger to bully the ancients. Then again, time-travelers don't use golden fingers, so how dare they say that they came from time-travel?
Seeing Wu Zhicheng's old face turning red, Su Hao smiled slightly and said to Fang Meng Jin: "Master Fang, there is no way to solve this problem in our Ming Dynasty knowledge. However, the Yi people have the art of matrix and can solve this problem."
"Can Brother Su know this technique?" Fang Mengjin asked.
"Know a thing or two." Su Hao said unceremoniously.
Fang Mengjin said: "How about asking Brother Su to demonstrate it to me?"
"Yes." Su Hao folded his arms and asked the students, "Which brother can lend me some blank paper?"
"I have it!"
"Use mine!"
Several students scrambled to hand over the paper. Su Hao thanked him and took the paper. Another student took out a pen and ink and wanted to hand it to Su Hao. Su Hao waved his hand, took out a few pieces of charcoal from his sleeve and said with a smile. : "I'm ashamed, I'm used to using this as a pen when doing arithmetic."
Isn't this nonsense? No one can solve matrix problems with a brush. Su Hao took a simple charcoal pen and began to write the formula on the paper. Everyone gathered around to watch. Although Wu Zhicheng couldn't save face, he still I wanted to know what method Su Hao used to solve this problem, so I stood aside and watched.
"Brother Su, what you wrote is the counting method of the Yi people, right?" Fang Mengjin looked at the string of Arabic numerals written by Su Hao and couldn't help but ask.
"Exactly." Su Hao said, "This counting method, called Arabic numerals, was actually invented by the Tianzhu people and passed to Folangji by the Tianfang people. The Tianfang we are talking about is called Arabic in the Folangji language. In fact, Arabic numerals had been introduced to China during the Southern Song Dynasty, but no one used them."
"Did you also learn this from Fo Langji?" Fang Mengjin asked.
"Yes, the Flemish missionary I met is very knowledgeable and told me a lot."
While Su Hao was talking, he was still writing equations on his hand. He used the simplex method to solve linear programming problems. The steps of this method are quite troublesome, but it only involves simple addition, subtraction, multiplication and division, so the calculations are easy. It was pretty fast. After a while, Su Hao listed the final formula. He pointed at the result and said to everyone:
"Look, everyone, this is the result of the calculation. Let's assume that the 4-foot bamboo pole is A, the 2-foot-6-inch bamboo pole is B, and the 1-foot-7-inch bamboo pole is C.
Take 21 long bamboo roots and cut them into 2 A and 1 C, you can get 42 A and 21 C; take 45 long bamboo roots and cut them into 1 A and 2 B, you can get 45 A and 90 B; take 60 long bamboo roots and cut them into
1 A, 1 B, 2 C, you can get 60 A, 60 B, 120 C; take 3 long bamboos, cut off 1 A and 3 C, you can get 3 A, 9 C.
The total cost of the above is 129 long bamboos, and you can get 150 bamboos each of A, B, and C. This is the most economical method."
Everyone looked at each other. As students of the academy, they usually have to learn some arithmetic, which is called mathematical arts in the academy, including Fangtian, Libu, Difference, Shaoguang, Shanggong, Junshu, Yingxu, Equation, and Hook.
Stocks and other contents. Students who felt that they were good at mathematics immediately began to check the numbers calculated by Su Hao. The result was of course no problem at all. As for whether 129 long bamboos is the optimal result, we can't say
Verification, but when they tried to use other combination methods to cut, the values obtained were all greater than 129.
"Brother Riqian, look at Su Hao's result..." Fang Mengjin turned to look at Wu Zhicheng, asking for his opinion.
As a great scholar, Wu Zhicheng also had some attainments in mathematical arts. Su Hao used the simplex method to solve this planning problem. He stood aside and watched carefully, and vaguely understood some ideas. Because of this, he became more
He felt shocked. You must know that this is a brand-new field that he has never seen before, or even thought about. In this world, there is such a wonderful algorithm that can solve such a difficult problem with simple addition, addition and subtraction.
Just reduce it and it will be solved.
"Mr. Su, I sit in a well and look at the sky. I have forgotten the ancient saying that there is no end to learning. I am really ashamed. I made some disrespectful remarks about Mr. Su earlier. Please forgive me. Mr. Su, please accept my bow."
Wu Zhicheng is arrogant, but at the same time he is also a responsible person. Once he realizes his mistakes, he will immediately admit them and does not shy away from apologizing to young people like Su Hao in front of all the students.
Seeing that Wu Zhicheng was so humble, Su Hao dared to accept his great gift, so he quickly bowed and returned the gift, saying: "Mr. Wu has embarrassed the student. The student just learned some strange and cunning tricks from the barbarians. How can he compare with the great talent of Mr. Wu?"
Compare."
"Master Su, I am very envious of your Yi people's math skills. I wonder if Mr. Su would be willing to teach me his skills?" After Wu Zhicheng apologized, he immediately shamelessly wanted to learn from Su Hao. This is who he is.
This kind of old intellectual has the character of hearing something in the morning and dying in the evening. When he sees something he doesn't understand, he doesn't even have the patience to wait for a few days.
Su Hao said: "Sir, if you have a question, students should tell you everything they know. However, Mr. Wu, this is not the time to teach the art of mathematics. The most important thing is to dig a well. The student dared to ask the teacher to borrow it."
Give me some disciples to help me."
"Easy to say, easy to say." Wu Zhicheng nodded repeatedly. He walked up to the podium, looked at the students in the entire lecture hall, and said loudly: "Dear students, Mr. Su Hao has been appointed by Mr. Han of the county to be responsible for the well digging affairs of the county. Su
The Young Master would like to hire some students in my academy to help him survey the well location. Who among you is willing to participate?"
Before he finished speaking, all the students in the room raised their right hands in unison, like a forest.