When they came down from the ladder, both Cao Cao and Yuan Shao were silent. On the way to the next subject, they didn't say a word and looked very worried.

Liu Xuande gave a standard answer to a difficult problem that made thousands of participants feel that it was a difficult problem. There was nothing in the answer that was pretentious and mysterious about destiny, and it was all materialistic argument.

Materialism has a characteristic. Materialism has a strong persuasive power. After reading the Xiongwen, Cao Cao and Yuan Shao were undoubtedly completely convinced. They were completely convinced that it was the fate of the country to be destroyed for three hundred years.

It is true that the Han Dynasty has been established for four hundred years and its roots have been deeply rooted. It is true that natural and man-made disasters have piled up and it has reached a critical moment.

As for the method of saving the land, both Cao Cao and Yuan Shao thought it was useful and could really save the country. But when they thought about it more deeply, they had to use the method of equally dividing the land to capture all the land owned by the rich and powerful.

Dividing the people among tens of thousands of people, Cao Cao thought to himself, if this is true, many of his farm properties will be gone, the foundation will be weakened, and in an instant, he will be the same as the head of Guizhou.

When the country is in crisis, it is necessary to seize the land of the rich to find peace. However, if you take the land of the rich, your family's foundation will be greatly damaged. Whether it is for the family or for the country, Cao Cao is in a dilemma, and Yuan Shao is also in a dilemma, so the two of them remain silent.

While walking on the road, the clever Cao Cao and the clever Yuan Shao stopped at the same time. They both thought of a way to have both ends at the same time.

The best way to achieve both ends is to save the country and save the country by letting others save it, and then use other people's fields to distribute to the people, leaving your own fields untouched. In this way, the country's affairs will be restored, and the foundation of your own family will not be harmed.

Neither Cao Cao nor Yuan Shao realized that if they thought this way, other powerful families would also think the same way, and all powerful families in the world would also think the same way.

The method of dividing fields is a magic medicine that can directly bring a dynasty back to life no matter how declining it is in its last years. However, this task is arduous and has a long way to go, unless the powerful family is willing to sacrifice their own interests to benefit the whole society, but this is tantamount to letting the powerful family

He took his own life. It is impossible for a powerful person from a wealthy family to have such courage, nor to have such awareness.

Cao Cao and Yuan Shao walked around the city wall for a while and arrived at the posting area of ​​the [Numerical] subject.

They didn't know how to count before, but after experiencing the difficulties in the exam, Cao Cao and Yuan Shao felt a headache when they thought of the word "count".

I squeezed closer and looked up. On the densely packed examination papers posted on the city wall, there were almost all large blanks. This was obviously in contrast to the densely packed Confucian classics subjects.

Both Cao Cao and Yuan Shao knew how well they did in the exam, and knew that they did poorly in the exam, so they gave up the idea of ​​looking for test papers.

At a high place, there was a huge piece of cloth hanging. The examination questions and answers were clearly written on the cloth. Cao Cao read the examination questions and answers from the beginning.

There was a volume of calculations, and the basic four arithmetic calculations were not difficult. He glanced at them and skipped them, forgetting to read them again. When he saw the difficult problem, Cao Cao stared at it for a long time, frowned and pondered, and was puzzled by the solution.

One question asked, [There are three thousand nine hundred and thirty soldiers, and the whole army is one hundred and eight thousand five hundred. I want to ask, what fraction of the whole army is this army?]

Regarding this question, Cao Cao calculated it silently and found that it did not match the answer.

He thought his answer was wrong, so he asked Yuan Shao next to him. Yuan Shao also calculated it silently and said, "It is indeed wrong."

Yuan Shao was wrong so easily, and Cao Cao was not so sure.

He asked Yuan Shao again what fraction the calculation was, and Yuan Shao gave him a number.

When Cao Cao heard that Yuan Shao's calculation was different from his own, he fell silent.

In order to check who was right, Cao Cao and Yuan Shao walked far away, found an open space, squatted on the ground and picked up branches to calculate carefully.

After a long time, the two finally figured out that the answer was correct, but that they had made a mistake. The question was really difficult, and it was still difficult to solve the difficult question afterwards.

After that, when he looked forward again, another question followed, which Cao Cao and Yuan Shao could not understand.

The question is, [Ten men and ten women. If men and women match each other, how many ways can they be combined?

If there is no distinction between men and women matching each other, how many combinations can there be?】

The first question of this question is that there are a hundred ways for men and women to match each other, which is not difficult to understand.

But for the second question, the answer gives one hundred and ninety ways to make the combination, and the answer also gives the algorithm, which is, twenty multiplied by nineteen and then divided by two.

Both Cao Cao and Yuan Shao answered this question wrong, and neither of them understood the answer clearly.

As a last resort, the two of them immersed themselves in the calculation.

Going aside, Cao Cao and Yuan Shao found small stones, grass roots, firewood sticks and other objects to replace people. First, they started with four people, matching them in pairs. The number was small, and it was easy to match them one by one. After a while, Cao Cao and Yuan Shao pulled

You see, among the four people, if you choose two or two people to match each other, there are six ways to match them.

Adding more numbers, making five, there was another tug, and the numbers were counted, and there were ten.

Add another six...

Tim Zuoqi...

The number is getting bigger and bigger, and the combination is getting more and more complicated.

At this time, Cao Cao glanced at the numbers written on the ground.

He remembered what was written on the answer sheet, twenty times nineteen, divided by two, that is the answer.

Thinking of this, I tried this method. There were four people, and two by two, it should be, four times three, divided by two, there are... six types.

Cao Cao compared it again and found that the four people he had just counted matched each other in twos and twos, and there were really six types.

(Huh?) Cao Cao was shocked in his heart.

Immediately afterwards, Cao Cao calculated two out of five and applied the formula to calculate, which was ten.

Take two out of six, fifteen.

At this point, the smaller numbers that I checked one by one with my bare hands all match up.

When Cao Cao added twenty to the calculation, it turned out to be one hundred and ninety.

Cao Cao vaguely understood but was a little puzzled. He somewhat knew how the answer was calculated.

Cao Cao casually thought about it. If two of the ten thousand people were matched, it would be ten thousand times nine thousand nine hundred and ninety-nine, divided by two. This must be the case.

For Cao Cao, this was an extremely special experience. This was an arithmetic where the key was not calculation. There were only twenty people, so the number was not large. However, if the method was not used correctly, it would be extremely difficult. Cao Cao had the intuition to understand the fundamentals of arithmetic.

The feeling of essence.

Cao Cao called Yuan Shao to move forward and read the test questions again. Yuan Shao was squatting on the ground. When he raised his head, he was still frowning and puzzled. Yuan Shao hadn't figured it out yet.

This chapter is not over yet, please click on the next page to continue reading! It can be said that among the multi-subject examinations conducted in Luoyang City, counting is the subject with the highest content of knowledge. In other subjects, there are many people who can answer them.

Counting one subject, thousands of people were almost wiped out.

There is another question: [A bag contains clay pills of the same size and weight, ten white and five black. If you take one pill, what is the probability that it will be black?]

Cao Cao answered correctly, maybe one-third, while Yuan Shao's answer was half and half black and white.

Facing the answer hanging on the wall, Yuan Shao was indignant. He said, "The pill is in the bag. It doesn't matter whether it is black or white. If you just take it, how can it be that it is black or white but not fifty-five?"

Seeing that Yuan Shao did not understand the meaning of the question, Cao Cao kindly explained it to Yuan Shao, but Yuan Shao was not interested and did not want to listen more.

This is still a question of medium difficulty. Yuan Shao is already impatient and unwilling to study it in detail.

Further down, there are questions about arithmetic series. Cao Cao did not answer many of them correctly during the exam. Now that he has seen the answers and the method of solving the problems, Cao Cao thought carefully and learned a lot.

When it came to the sequence questions, Cao Cao could at least understand the questions and understand the answers.

Later, when it came to difficult questions, Cao Cao had already thought about them and understood them.

When asked about Pythagorean, Cao Cao only answered "Pythagorean three strands, four strings and five".

I went to see the answer, but the answer said that as long as the hook square plus the stock square is equal to the string square, it can become Pythagorean.

Cao Cao was greatly surprised. He immediately thought about a few numbers in his mind and started counting silently.

According to the answer, as long as the hook square and the strand square are equal to the string square, it will become Pythagorean. Cao Cao took the length of the hook as one and the length of the strand as one to calculate the string square.

Pythagorean and Pythagorean are both one, and the sum of Pythagorean and Pythagorean is two.

Later, Cao Cao silently calculated what the string was and which number had exactly two powers.

This calculation was incredible. As he continued to calculate, Cao Cao discovered that there seemed to be something wrong with this number. Why was the calculation inaccurate...

Inadvertently, Cao Cao started to think deeply about irrational numbers.

After frowning and thinking for a long time, it was not accurate anyway. Cao Cao could only sigh and put it down for the time being, and gave up. He was very unwilling to do so.

In order to verify whether Liu Xuande's Pythagorean formula is correct or not, Cao Cao spent time here.

Since hooking one and one cannot work, then hook one and two, hook three and so on.

Finally, inadvertently, Cao Cao randomly made up a few numbers, using the hook five, the stock twelve, and the string thirteen to calculate. Once added, it happened to be right, and Cao Cao's eyes lit up.

Cao Cao's eyes lit up and he was eager for proof. He looked around and caught sight of Yuan Shao's sleeve. Cao Cao pulled Yuan Shao's sleeve and cut off Yuan Shao's sleeve with a swipe of his knife.

Yuan Shao's arm lit up. He looked down at his cut sleeves and glared at Cao Cao, "What are you doing?"

Cao Cao chuckled and said, "I'm going to do a Pythagorean..."

Yuan Shao cursed angrily, "Then tear your own clothes off! What more could you do than tear me off!"

Yuan Shao was so angry that his teeth itched.

After that, Cao Cao used a wooden stick as a ruler and cut five, twelve, and thirteen strips of cloth in three lengths, and put the strips together. When the strips were aligned, they formed an angle like a high wall standing on the ground, not straight.

Leap, Pythagorean has obviously become.

Cao Cao smiled happily.

Sure enough, the method of forming Pythagorean not only hooks three strands, four strings and five strings, but also other methods. Ancient craftsmanship is all wrong!

When Cao Cao saw the fundamental meaning of Pythagorean, Liu Bei appeared in his mind, and he was particularly impressed by the profoundness of Liu Bei's knowledge.

——

It took a long time for Cao Cao to finish counting the answers in the paper. Especially the last part of the calculation paper, which involved squares covering balls and balls covering squares. It was such a mess that Cao Cao couldn't even read the answers.

Understand.
To be continued...