Chapter 1790: The victory of mathematics

The white-haired old Taoist Zhen Yang showed joy when he heard the words, and said: "Great! Xia Jushi is really happy! There are several problems that have plagued the poor Tao, the first problem is..."
Speaking of this, the old true Yang shook his head and said, "Today, there are pheasant rabbits in the same cage. There are thirty-five heads on the top and ninety-four legs on the bottom. What are the pheasant rabbits?
After hearing it, Xia Ruofei suddenly showed a strange look, she couldn't tell! This true Yang Dao with thick eyebrows and big eyes is still a math lover! Even if his question is written up, it will not change the nature of a math problem! Isn't this the problem of the original chicken and rabbit cage?
Those few words of Zhenyang Old Tao, translated into modern words: There are chickens and rabbits in the same cage, there are 35 heads on the top, and 94 feet on the bottom. Ask how many chickens and rabbits each have. only?
Perhaps this was a very clever mathematical problem in ancient times, but in this era, a junior high school student can easily solve it, and it can be solved by formulating a linear equation in two unknowns. This is also called a problem?
After Zhen Yang finished talking about this question, with a smile on his face, he said: "Ju Shi Xia, you can have a stick of incense to answer this question."
As soon as his words fell, Xiao Dao Tong Qingfeng had already brought in an incense burner that had already been prepared, and a newly lit incense was inserted in the incense burner.
Xia Ruofei couldn't laugh or cry, and said directly: "Zhenyang Daochang, don't have to be so troublesome, I have solved this question."
The old true Yang raised his eyebrows and said, "The layman is so fast? Then tell me, what is the answer?"
Xia Ruofei smiled slightly and said, "23 chickens and 12 rabbits, right?"
True Yang Lao Dao naturally couldn't really be trapped by the problem. The question he asked Xia Ruofei was actually a test.
Xia Ruofei believed that if other expedition members including Ling Qingxue would also enter this scene, the old true Yang Dao would also use the same tone and tone to throw the problem to them.
As soon as Xia Ruofei said this answer, Old Zhen Yang couldn't help raising his eyebrows, and said, "This is indeed the answer to this question..."
"So, I have solved this problem?" Xia Ruofei asked with a smile.
"Wait!" Zhen Yang said, "I want to know what method Xia Jushi used to calculate in such a short time?"
Xia Ruofei said in his heart: "A linear equation in two unknowns! Isn't it just a direct calculation?"
But Zhenyang Lao Dao definitely doesn’t understand binary linear equations. When Xia Ruofei was considering how to change the solution to an easy-to-understand method, he suddenly thought of an interesting problem-solving method he had seen on the Internet before. It seems ridiculous, but it can be calculated quickly.
So Xia Ruofei smiled and said: "My method is very simple! Daoist, with 35 heads, it means that there are 35 chickens and rabbits in total, right?"
Old Zhenyang nodded, and did not speak, because it was basically nonsense.
Xia Ruofei smiled and continued: "Let the chicken and the rabbit raise both feet, then there should be 70 feet missing, right? Of the 94 feet, there are 24 feet left. Because the chicken has only two feet, after they are lifted up, the remaining 24 feet on the ground are all rabbits. And each rabbit has raised two feet, so they all stand on two feet Twenty-four feet naturally correspond to twelve rabbits. There are thirty-five chickens and rabbits. If the number of rabbits is twelve, the chicken will naturally be twenty-three. Doesn’t the answer come out?"
Old Zhenyang was dumbfounded, he didn't expect the answer to be so simple.
After a while, he said with a weird look: "How can this chicken and rabbit lift their feet obediently? Also, when the chickens both feet are lifted, what kind of posture is this..."
Xia Ruofei almost burst out laughing, he squeezed a smile and said: "Dao Master, this is not important, it is just an assumption! The point is that this method can get the answer the fastest, right?"
The old true yang thought for a while, and said: "Xia Jushi is very talented! This problem-solving method is very ingenious, and the poor Dao admire it!"
"So, this question is solved next?" Xia Ruofei asked with a smile.
"Of course!" said the old true Yang Dao, "the poor Dao still has a problem here, and I hope that Lay Xia will give him any advice."
"Say Chief, please!"
The old true Yang pondered for a moment, and then he said: "There are things that don't know the number, two out of three or three, three out of five or five, and two out of seven or seven. How about things?"
Got it! It is another classic ancient math problem, and it also comes from it.
This question is translated into modern words: there is a pile of things, three and three numbers will eventually be left two, five and five numbers will finally be left three, and seven seven numbers will finally be left two. Find this pile of items quantity.
There was always a faint smile on Xia Ruofei's face. There was a trap in this question. The trap was: The answer to this question is not unique. To be precise, it should be an arithmetic sequence with a difference of 357. If the ancients who have not learned much mathematics face this question, they can get the answer in a number test, but they may have overlooked this question. There are many answers. If only one is mentioned, it is probably not counted. correct.
After Zhen Yang finished asking the question, he looked at Xia Ruofei with a smile.
And Xia Ruofei also had a relaxed look, and after a little thought, he said: "Dao Master, the answer to this question is not the only one. There should be at least 23 items in this pile, then 128, and then maybe 233. One, and so on, add 105 to each answer to get a new answer, so there are countless answers."
Xia Ruofei's answer is expressed in mathematics, that is, n is an integer greater than or equal to 1.
Xia Ruofei's answer is very rigorous, it can be said that it is not leaking, even if the old way of True Yang is looking for flaws, it is impossible to find.
Therefore, he just pondered for a moment, then nodded and said, "Senior wise man! This question has been solved!"
This time, Zhenyang Old Dao didn't even have any interest in asking Xia Ruofei to talk about the calculation method, and directly judged that Xia Ruofei had successfully solved the problem.
Soon, Zhenyang Lao Dao went on to say: "There is one last question, I hope Jushi Xia can also help Lao Dao!"
Xia Ruofei secretly breathed a sigh of relief. He was afraid that this basic math problem would never end. Although it was not difficult for him, it was a waste of time.
Moreover, the test of the first floor of the tower, the test of mathematics, is really unexpected.
Fortunately, the power of setting these levels is not too horrible and interesting, only three questions are arranged in total.
Therefore, Xia Ruofei has only one idea at this time, and that is to end it quickly!
He listened to the words of the old true Yang Dao, and said quickly: "Dao Master, please say!"
The old true Yang said with a serious face: "The last question is quite difficult, but I still can only give Jushi Xia a stick of incense. I hope Jushi Xia can make persistent efforts to solve all the problems in one go!" Weichang
Xia Ruofei smiled and nodded, and said, "Dao Master, please speak, please listen to me!"
The old true Yang said: "There are twenty trees today, and four trees are planted in each row. Ask: How can I plant 16 rows of trees?"
Xia Ruofei was stunned when he heard the words, this time Zhenyang Old Dao really came up with a worldwide mathematical problem! However, his sixteenth row is not very challenging, because as early as the sixteenth century, mathematicians from ancient Greece, ancient Rome, and ancient Egypt completed the sixteen-row map, and it was widely used in some Western countries. Among the decorative patterns of elegant buildings.
However, Xia Ruofei thought about it, this mystery has existed for at least a few thousand years. At that time, the sixteen-line map must not have been born, so this question is very difficult. If Xia Ruofei didn't know the answer in advance, the time for a stick of incense would definitely not Come out the correct drawing.
Fortunately, Xia Ruofei usually dabbles extensively and has really seen this classic mathematical problem.
Therefore, after Xia Ruofei listened to the topic, he was determined to know that he would be able to pass this level.
He smiled and said, "Zhenyang Daoist, can you give me paper and pen?"
The old true Yang Tao thought that Xia Ruofei needed a deduction. This is also normal. Many people can fill a room with paper to solve this problem, but it may not be able to solve it.
Therefore, it is impossible for Xia Ruofei to deduce it directly in his head, he still needs to use pen and paper.
The old true yang smiled and nodded, and motioned to Dao Tong Qingfeng to take the paper and pen, and specifically asked Qingfeng to study the ink for Xia Ruofei.
Xia Ruofei came to the table, flattened the paper on the table and pressed it with a paperweight. Then he picked up the wolf pen, dipped the ink in the inkstone, and began to draw directly on the paper.
A square soon appeared on the paper, Xia Ruofei marked the four black, and then accurately clicked two points on each side.
After Xia Ruofei entered the Golden Core Stage, his physical fitness has also been comprehensively improved, and he has strong mental power and is very good in fine control. Therefore, he didn't need a ruler at all, the square he drew was quite precise, and each line was straight, just like it was printed.
Then Xia Ruofei connected the two points on each side with the two points on the opposite side and the point away from them on the clockwise side.
There are 24 straight lines again, drawn exactly.
In this way, inside the square, an octagon has been formed.
Xia Ruofei smiled slightly, and marked each of the regular octagons formed by intersecting the inner lines of the octagon in black.
Before Zhenyang Old Dao had even reacted, Xia Ruofei leaned the brush on the inkstone, and then said with a smile: "Zhenyang Daoist, I am done!"
The old true Yang Tao thought that Xia Ruofei was drafting and calculating, but he didn't expect that Xia Ruofei would start answering as soon as he came up, and he would complete it in such a short period of time. This is a joke!
Each question gave Xia Ruofei a stick of incense to think about and answer time, but every time Xia Ruofei came up to solve the answer without thinking, let alone a stick of incense, the first part of the three questions will also be answered. Just burned a head!
Is this done?
The old true Yang Dao was a little unbelievable, but he glanced at the map drawn by Xia Ruofei and immediately knew that Xia Ruofei had already solved this question.
Even those monks who are proficient in mathematics, when faced with this problem, usually fall into the long exam, and there are very few people who can make it in a stick of incense.
However, Xia Ruofei completed the answer in just ten seconds, and wrote the answer without hesitation, as if he could complete it without thinking at all.
"Daoist Zhenyang, am I right to answer this way?" Xia Ruofei asked.
The old true yang came back, with a wry smile on his face, and said, "Yes..."
Xia Ruofei said with a grin: "So, I can help you..."
"Of course!" Zhen Yang said, "Ju Shi Xia is indeed very clever, poor Dao admires it!"
"Where is it! You are too famous!" Xia Ruofei said with a smile, "Actually, the arrangement of these sixteen lines is not very difficult. I can also arrange a map of 18 or even 20 lines!"
"What?" The old true Yang Dao's eyes widened when he heard it, "Jushi Xia, is this really true?"
Xia Ruofei smiled and nodded, and said, "Of course it is true! However, in Daochang's question, only the 16-line arrangement method is required, so I answered as required."
"Yes, yes! The poor Tao did not deny the results of Xia Jushi's answer." Old Zhenyang said quickly, "but if Xia Jushi doesn't mind, can you also draw the 18-line map and the 20-line map you said? come out?"
Speaking of this, the old true Yang Dao quickly added: "This can also be counted in the answer to the last question. If the answer is better, then the gift of thanks to the layman from our Zhenyang View will be more generous! Xia Jushi, how about? Draw another picture?"
This is equivalent to adding extra points for correct answers, and no penalty for incorrect answers.
As Xia Ruofei, who has experienced nine years of compulsory education, he is already familiar with this model, so he is not surprised.
However, Xia Ruofei always didn't bother to study additional questions when he was a student.
And here today, as soon as he heard that he had drawn more lines of graphs, the thank-you gifts would be more generous, and his eyes suddenly brightened.
Obviously, that is to say, the higher the quality of the answer, the greater the reward for the final task!
How could Xia Ruofei refuse this kind of welfare delivered to his door?
What's more, this may be a difficult problem for other monks, but for Xia Ruofei, it's just a sub-question!
Because of the problem of twenty trees, in the 18th century, the mathematician Gauss had already guessed that it would be ranked 18th, but until his death, he did not come up with an official map. Until the 19th century, American interesting mathematics Lloyd completed Gauss’s conjecture and drew an eighteen-line map. By the end of the twentieth century, electronic computer technology was booming. With the help of computers, two masters successfully completed the 20-line map.
Xia Ruofei had read these two maps and remembered them in his heart.
As long as you draw a map that you have already remembered, you can get more generous rewards. Why not?