The white-haired Daoist Zhen Yang was overjoyed. "That's great! Mr. Xia is indeed a straightforward person! There are a few questions that have been bothering me. The first one is … "
Daoist Zhen Yang shook his head and said, "Today, there are pheasants and rabbits in the same cage. There are thirty-five heads and ninety-four legs. How many pheasants and rabbits are there?"
Xia Ruofei had a strange look on his face. He couldn't tell! This thick-browed Daoist Zhen Yang was actually a math enthusiast! No matter how scholarly his question was, it didn't change the fact that it was a math problem! Wasn't this the original chicken and rabbit in the same cage problem?
Old Taoist Zhen Yang's words could be translated into modern words: "There is a chicken and a rabbit in the same cage. From the top, there are thirty-five heads, and from the bottom, there are ninety-four legs. How many chickens and rabbits are there?
In ancient times, this might have been a very clever math problem, but in this day and age, a junior high school student could easily solve it. All it took was a binary linear equation. How could this be called a problem?
After Daoist Zhen Yang answered the question, he smiled and said, "Mr. Xia, you have fifteen minutes to answer this question."
As soon as he finished speaking, the little Daoist boy Qing Feng brought in an incense burner that had been prepared beforehand. There was a freshly lit incense stick in the burner.
Xia Ruofei didn't know whether to laugh or cry. "Daoist Zhen Yang, there's no need to trouble yourself. I've already solved this problem."
Daoist Zhen Yang raised an eyebrow. "Mr. Xia, you're so fast? Tell me, what's the answer? "
Xia Ruofei smiled. "Twenty-three pheasants and twelve rabbits, correct?"
Of course, Daoist Zhen Yang wasn't really troubled by the problem. The question he gave Xia Ruofei was actually a test.
Xia Ruofei believed that if the other exploration team members, including Ling Qingxue, entered this scenario, Daoist Zhen Yang would have used the exact same tone to ask them the question.
When Xia Ruofei gave the answer, Daoist Zhen Yang couldn't help but raise his eyebrows. "That is indeed the answer to this question …"
"Does that mean I've solved this problem?" Xia Ruofei asked with a smile.
"Wait!" Old Daoist Zhen Yang said, "I would like to know what method Patron Xia used to calculate the answer in such a short period of time."
Xia Ruofei thought, A binary linear equation! Why can't I just solve it? "
However, Daoist Zhen Yang definitely didn't know how to solve a binary linear equation. As Xia Ruofei was thinking, he was thinking. Xia Ruofei Zhen Yang. He Was Daoist Zhen Yang... he Xia Ruofei Zhen Yang was....
Daoist Zhen Yang. My Daoist Daoist's, Zhen Yang.... Taoist priest, there are thirty-five heads, which means that there are thirty-five chickens and rabbits in total, right? "
. Daoist Zhen Yang nodded. He didn't say anything because it was basically nonsense.
Xia Ruofei Zhen Yang smiled and continued. "If you ask the chickens and rabbits to raise both their feet, then there should be 70 fewer feet, right? Out of the 94 feet, there are only 24 feet left. Because the chickens only have two feet, when they raise both their feet, the remaining 24 feet on the ground belong to the rabbits. Every rabbit had raised two feet, so they were standing on two feet. The twenty-four feet naturally corresponded to the twelve rabbits. There are a total of 35 chickens and rabbits. Since there are 12 rabbits, there are 23 chickens. Isn't the answer obvious? "
Daoist Zhen Yang was stunned. He didn't expect the answer to be so simple.
After a while, he said with a strange expression, "Why do the chickens and rabbits raise their feet so obediently? Also, the chickens raise both their feet. What kind of posture is that? "
Xia Ruofei Zhen Yang almost burst out laughing. He held back his laughter and said, "Daoist Zhen Yang, that's not important. It's just a hypothesis! The point is that this is the fastest way to get the answer, isn't it? "
Daoist Zhen Yang thought about it and said, "Mr. Xia is very talented! This solution is very ingenious. I am impressed! "
"So, does this mean that I have solved this problem?" Xia Ruofei Zhen Yang asked with a smile.
"Of course!" Daoist Zhen Yang said. "I have one more question. I hope that Mr. Xia can enlighten me."
"Please ask!"
Daoist Zhen Yang pondered for a moment and said, "There are things that are unknown. When you count three, two are left. When you count five, three are left. When you count seven, two are left. How many are there? "
Great! It was another classic ancient math problem, and it was also from Sun Tzu Arithmetical Classic.
This problem could be translated into modern words. "There is a pile of things. When you count three, two are left. When you count five, three are left. When you count seven, two are left. When you count seven, two are left. How many are left?"
Xia Ruofei Zhen Yang had a faint smile on his face. There was a trap in this problem. The trap was that the answer to this problem was not unique. To be precise, it should be a series of numbers with a difference of 3 * 5 * 7. If an ancient person who had not learned much mathematics was faced with this problem, they would be able to get the answer by trying the numbers one by one. However, they might have neglected the fact that there were many, many answers to this problem. If they could only give one answer, it would most likely not be correct.
After Daoist Zhen Yang asked the question, he looked at Xia Ruofei Zhen Yang with a smile.
Xia Ruofei Zhen Yang also looked relaxed. After thinking for a while, he said, "Mr. Daoist, the answer to this problem is not unique. There should be at least 23 items in this pile, then 128 items, then 233 items, and so on. If you add 105 to each answer, you will get a new answer. Therefore, there are countless answers. "
Xia Ruofei Zhen Yang's answer, if expressed in mathematical terms, was 23 + 105n, where n was an integer greater than or equal to 1.
Xia Ruofei Zhen Yang's answer was very precise. It could be said that it was watertight. Even if Daoist Zhen Yang wanted to find a loophole, he would not be able to.
Therefore, he only pondered for a while before nodding and saying, "Mr. Daoist Zhen Yang is very talented! This problem is solved! "
This time, Daoist Zhen Yang did not even have the mood to ask Xia Ruofei to explain the calculation method. He immediately decided that Xia Ruofei Zhen Yang had solved the problem.
Soon, Daoist Zhen Yang said, "I have one last question. I hope that Mr. Daoist Zhen Yang can also solve this problem for me!"
Xia Ruofei Zhen Yang secretly sighed in relief. He was afraid that this basic mathematics problem would never end. Although it was not difficult for him at all, it was still a waste of time.
Moreover, the test on the first floor of the tower was to test one's foundation in mathematics. This was really unexpected.
Fortunately, the person who set up these tests was not too bad. There were only three questions in total.
Therefore, Xia Ruofei Zhen Yang only had one thought in mind, and that was to finish it quickly!
When he heard Daoist Zhen Yang's words, he quickly said, "Please go ahead, Mr. Zhen Yang!"
Daoist Zhen Yang said seriously, "The last question is quite difficult. However, I can only give Mr. Daoist Zhen Yang the time it takes to burn a stick of incense. I hope that Mr. Daoist Zhen Yang can continue to work hard and solve all the problems in one go!"
Xia Ruofei Zhen Yang nodded with a smile and said, "Please go ahead, Mr. Zhen Yang. I am all ears!"
Daoist Zhen Yang said, "Today, there are twenty trees. You can plant four trees in each row. Question: How do you plant sixteen rows of trees?"
Xia Ruofei Zhen Yang was slightly stunned. This time, Daoist Zhen Yang really did come up with a world-class mathematical problem! However, the sixteen-row problem was not very challenging. As early as the sixteenth century, mathematicians from ancient Greece, Rome, and Egypt had already completed the sixteen-row diagrams. They were widely used in the decorative patterns of some elegant buildings in the West.
However, Xia Ruofei Zhen Yang thought about it again. This arcane realm had existed for at least a few thousand years. At that time, the sixteen-row diagrams must not have been created. Therefore, this problem was very difficult. If Xia Ruofei Zhen Yang did not know the answer in advance, he would not be able to figure out the correct solution in the time it took to burn a stick of incense.
Fortunately, Xia Ruofei Zhen Yang was very knowledgeable and had seen this classic mathematical problem before.
Therefore, after hearing the question, Xia Ruofei Zhen Yang was very confident that he would be able to pass this test.
He smiled and said, "Mr. Zhen Yang, can you give me a pen and paper?"
Daoist Zhen Yang thought that Xia Ruofei Zhen Yang needed to figure it out. This was normal. Many people used enough paper to fill a room to solve this problem, but they might not be able to solve it.
Therefore, Xia Ruofei Zhen Yang could not figure it out directly in his mind. He still had to use a pen and paper.
Daoist Zhen Yang smiled and nodded. He motioned for Qing Feng to bring him a pen and paper. He also specifically asked Qing Feng to grind the ink for Xia Ruofei.
Xia Ruofei Zhen Yang came to the table, spread the paper flat on the table, and pressed it with a paperweight. Then, he picked up the weasel hair brush, dipped it in the ink, and began to draw on the paper.
A square quickly appeared on the paper. Xia Ruofei Zhen Yang marked the four vertices black. Then, he accurately pointed two dots on each side.
After Xia Ruofei Zhen Yang entered the Golden Core Stage, his physical fitness had been improved. Moreover, he had strong mental strength and was very good at precise control. Therefore, he did not need a ruler at all. The square he drew was very accurate. Every line was straight, as if it had been printed.
Then, Xia Ruofei Zhen Yang connected the two dots on each side to the two dots on the opposite side and the dots on the next side clockwise.
Another 24 straight lines were drawn without a single mistake.
In this way, an octagon was formed inside the square.
Xia Ruofei smiled and marked every vertex of the regular octagon formed by the intersecting lines inside the octagon in black.
Before Old Taoist Zhen Yang could react, Xia Ruofei placed the brush on the inkstone and said with a smile, "Taoist Zhen Yang, I'm done!"
Old Taoist Zhen Yang had thought that Xia Ruofei was just making a draft or doing some calculations. He never expected that Xia Ruofei would immediately start answering the questions and finish them in such a short time. What a joke!
Xia Ruofei was given an incense stick's worth of time to think and answer each question, but Xia Ruofei was able to solve the answers without thinking. Not to mention an incense stick's worth of time for each question, even after answering the first three questions, the incense stick's worth of time had only burned a little!
That's it?
Old Taoist Zhen Yang found it hard to believe, but when he saw the picture Xia Ruofei had drawn, he immediately knew that Xia Ruofei had solved the problem.
Even those cultivators who were proficient in calculations would find it difficult to solve this problem. Those who could solve it in an incense stick's worth of time were few and far between.
However, Xia Ruofei had finished answering the question in less than ten seconds, and he had written down the answer without hesitation. It was as if he didn't even need to think to complete it.
"Taoist Zhen Yang, is my answer correct?" Xia Ruofei asked.
Old Taoist Zhen Yang snapped out of his daze and smiled bitterly. "Yes …"
Xia Ruofei Zhen Yang grinned and said, "In that case, I've helped you …"
"Of course!" Old Taoist Zhen Yang said. "Master Xia is indeed very intelligent. I admire you!"
"You're too kind! You're too kind! " Xia Ruofei Zhen Yang said with a smile. "Actually, the 16 lines aren't that difficult. I can even come up with 18 or even 20 lines!"
"What?" Old Taoist Zhen Yang's eyes widened when he heard this. "Master Xia, are you serious?"
Xia Ruofei Zhen Yang smiled and nodded. "Of course it's true! However, Taoist Zhen Yang's question only asked me to draw the 16 lines of arrangement, so I answered according to the requirements. "
"Yes, yes, yes! I'm not denying Master Xia's answer, "Old Taoist Zhen Yang said quickly. Old Daoist Zhen Yang hurriedly said, "However, if Patron Xia doesn't mind, can you also draw the 18 lines and 20 lines of diagrams you mentioned?"
At this point, Daoist Zhen Yang hurriedly added, "This can also be included in the answer to the last question. If the answer is better, then our True Yang Temple will give you a more generous gift as a token of our appreciation! Master Xia, what do you think? Draw another picture? "
This was equivalent to an additional question. If you answered correctly, you'd get points, but if you answered incorrectly, you wouldn't get points deducted.
As someone who had gone through nine years of compulsory education, Xia Ruofei Zhen Yang was very familiar with this pattern, so he wasn't surprised.
However, when he was a student, Xia Ruofei Zhen Yang was too lazy to study additional questions.
Today, when he heard that he'd get a better reward if he could draw more lines of arrangement, his eyes lit up.
Obviously, this meant that the higher the quality of the answer, the better the reward!
How could Xia Ruofei Zhen Yang reject this kind of benefit that was delivered to his doorstep?
Moreover, this might be a difficult question for other cultivators, but for Xia Ruofei Zhen Yang, it was a freebie question!
Because of this question, in the 18th century, the mathematician Gauss had already guessed that there could be 18 lines of arrangement. However, until his death, he didn't produce an official diagram. It wasn't until the 19th century, when the interesting American mathematician Lloyd completed Gauss' conjecture and drew 18 lines of arrangement. At the end of the 20th century, with the rapid development of computer technology, two experts successfully completed 20 lines of arrangement with the help of computers.
Xia Ruofei Zhen Yang had seen these two diagrams before and remembered them in his heart.
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