To, the second day of the imperial examination.

The imperial examination scholars were gathered together in the morning light. After hearing that what was going to be tested today, they were, "Numbers".

Counting is probably easy. If you don't know how to write, how can you still count? This is what most scholars think.

When the test started, the first batch of candidates got their papers and when they saw the test questions, there was a huge white silk hanging on two large wooden boards that were merged together. There were densely packed words on the white silk.

When seeing so many words, some people began to notice that something was unusual.

Like the previous subject, the math test also follows the selection from easy to difficult, and the difficulty of the test questions transitions very smoothly.

The first question in the counting test is: [There is a jujube tree, a locust tree, and an elm tree on the bank. How many trees are there in total?]

This is obviously a simple addition. One plus one, plus one, plus one, there are three trees.

Then, the second question asked, "There are five trees behind the house. If two of them are cut down, how many trees are left?"

Subtraction, the simplest subtraction, five minus two, three.

The first question is just the simplest addition and subtraction question, and it is a very small number of addition and subtraction calculations, with no twists and turns. Then, the questions go down to the more difficult addition and subtraction questions.

The most difficult question for addition and subtraction calculations is, [Wu Youbing has 1,683,982 soldiers. In battle, 109,665 died and 16,600 escaped.

Ask, how many troops are left?]

For such a question, the number is large and the calculation is cumbersome. It is obvious that the ability to calculate addition and subtraction of large numbers is tested.

At this point, many candidates cannot understand this question.

In the Zhuozhou Army, there were many soldiers in the army who had never learned arithmetic. However, they were familiar with and could perform simple addition and subtraction calculations. However, these soldiers could only perform calculations on small numbers, and the numbers were in the thousands.

It's difficult to get up, and it's even more difficult when the weight is tens of thousands.

Among the soldiers in Zhuozhou, many of them had no idea what a million was.

Just like the sergeants of the Zhuozhou Army, so are the low-level candidates in the examination room. There are quite a few candidates who can barely read, understand the questions, and recognize the characters clearly, but they cannot calculate numbers as large as millions.

At this point, people who are really proficient in addition and subtraction calculations can be distinguished from those who have only a little knowledge of calculations and can only calculate small numbers.

The most basic calculations are just the four arithmetic operations of addition, subtraction, multiplication and division.

After that, questions on multiplication and division operations followed.

Multiplication and division problems also start with the easiest ones at the beginning, and then gradually increase in difficulty.

This is the second part. The second part eliminates a group of people who know addition and subtraction but do not understand multiplication and division calculations.

The third part, mixed operations of addition, subtraction, multiplication and division.

These first three parts are nothing more than simple questions.

In the sixth exam, when Cao Cao reached this point in the math problem, he didn't feel any difficulty at all.

But then, the difficulty of promotion comes.

The question is, [I have ten dollars, how much will it cost if I take half of it?]

One-half, or division by two, is a fraction.

The question is, [Now I have accumulated hundreds of steps. What is the geometry of the square?]

This is the prescription.

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

This is a problem of pairwise allocation.

The question is, [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?

If you take the pill without putting it away and take another pill, what is the probability that the pill you take is black?】

This is probability.

These questions began to become troublesome. These questions did not require much calculation, but were quite obscure. Cao Cao never relaxed his brows since he started doing these questions.

From now on, the questions will become more difficult.

The title is, [One, two, four, eighty-six], what is the next number?

This is very simple. You can tell at a glance that the next one is thirty-two.

Okay, if you think this is not difficult, then the difficulty of promotion comes.

The title is, [One, two, four, eighty-six... and so on, the number is the tenth number, why?

Number one hundred, why?”

There are two ways to answer this promotion question. One is to multiply one by one and calculate to the hundredth number, but this is time-consuming and laborious. Or, one can be familiar with the sequence and use formulas to calculate.

People who are proficient in the formulas of geometric series can be regarded as numeracy talents, and those who are chosen are numeracy talents.

Cao Cao didn't know how to calculate geometric series, so he counted them one by one for a while. When he had counted more than twenty digits, Cao Cao thought that if he continued to calculate like this, he didn't know how long it would take, so he gave up the problem.

, and moved on to the next question.

In the same examination room, when Yuan Shao reached this point in his calculations, Yuan Shao lost his mind and stared at this question and kept calculating, thus wasting too much time.

There is a story. It is said that when Guiguzi was testing Sun Bin and Pang Juan, he gave five cakes to them and said that you can take up to two cakes at a time. You can take more after eating. Whoever eats more cakes will win.

Who wins.

As a result, Pang Juan went up and grabbed two cakes and ate them with great enthusiasm. Sun Bin, after thinking for a while, took only one cake from the remaining three cakes and started eating it leisurely.

The result can be imagined. Even though Pang Juan wolfed down the two cakes, he did not finish the two cakes. Sun Bin ate one of the cakes in his hand and calmly picked up the remaining two cakes. In this way, Sun Bin got three cakes and Pang Juan got two cakes.

Sun Binsheng.

After this test, Gui Guzi concluded that Pang Juan would never be Sun Bin's rival in the future, and this was indeed the case in the future.

The imperial examination held in Luoyang was the first time for everyone. Everyone had no experience in examinations. Cao Cao had no experience in examinations, and neither did Yuan Shao.

Cao Cao decisively gave up on the questions, while Yuan Shao was obsessed with them. This was certainly because both of them lacked experience in taking exams. However, they both lacked experience. Cao Cao was more clever and decisive, while Yuan Shao lacked consideration and was too straightforward.

Looking at the details, in today's math test, Cao Cao is likely to beat Yuan Shao. This may not be because Cao Cao's math skills are higher than Yuan Shao's, but that Cao Cao is smarter and knows how to take the initiative to give up the questions and do the simple questions first.

If we want to select talents from this test of counting, Cao Cao and Yuan Shao are both equally skilled in counting, and Cao Cao stands out. Is this fair? It seems extremely fair.

Cao Cao, who has a higher score, has a higher score, which explains the problem. Whether it is said that Cao Cao is smarter, that Cao Cao is decisive, or that Cao Cao is cautious, no matter what, if you select talents based on their performance, there is a high probability that they will be successful.

He is a person who is better than others.

Cao Cao encountered another problem.

The title is, [Two, five, ten, seventeen, twenty-six...and so on, ask, what is the hundredth number? 】

Compared with the geometric sequence with obvious regularity, this sequence is one level more difficult.

Cao Cao frowned and thought for a long time. He had some inspiration, but he couldn't figure out the pattern. He struggled for a long time and counted on his fingers. Finally, inspiration suddenly came. Cao Cao suddenly understood that this sequence is square plus one, and the first number is

, adding one to one side is one, the second number, adding one to two sides is five, and so on.

Naturally, the hundredth number, add one to the hundred squares, and the result is out.

Suddenly solved a difficult problem, Cao Cao felt very happy and his brows stretched.

Basic mathematical knowledge can be roughly divided into two categories: algebra and geometry.

Cao Cao mastered the knowledge of geometry questions and saw test questions such as Pythagorean, finding product, finding height, measuring length, measuring depth, etc., each one was more difficult than the last.

And this is still only the basic part.

Really difficult questions cannot be answered by any of the top bachelors of this era.

For example, ask Pythagorean.

Pythagorean is simple. Ordinary people can also say, "Gou three strands, four strings and five". But if you answer it like this, you can only answer one point for a ten-point question.

Only if there are really math masters can they answer the rigorous Pythagorean formula.

In addition, there is also a question about pi. There are three answers to this question.

Ordinary people usually answer, three days a week. If you answer like this, you only get one point.

Second, if someone answers that the diameter is one, three more than one or two, as long as his answer is not an integer, as long as he answers pi to more than three points, no matter how much more, no matter whether it is correct or not, then it means that this person has an understanding of pi.

The understanding is much deeper than that of the person who answered three. This second answer is worth five points.

The third type is to answer the exact pi. As long as you answer the last two digits of pi, as long as you answer 3.14, you will get twenty points.

For a small pi, if you want to improve by one digit, you have to wait a hundred years; if you want to improve by seven or eight digits, you have to wait until the Northern and Southern Dynasties, until Zu Chongzhi was born.

When Julu was recruiting scholars, he asked for the precision of pi in order to find a mathematical genius. However, among the hundreds of scholars in Julu, no one could answer the question of the precision of pi.

In a math paper, the final question is not one question, but many questions.

Cao Cao looked up at the test questions. The last part of the test questions was a ball, a circle, a ball inside a ball, another ball inside a circle, and they were put together in such a mess that Cao Cao felt dizzy.

Dizziness, heart sinking.

Soon after, the gong sounded and the exam was over.

Cao Cao lowered his head to read the scroll, but most of it was unwritten.

At the end of the day, we returned to the camp. The camp was quiet and the atmosphere was very low. There was no scene of lively discussions after the Confucian classics exam.

After finishing the math exam, the scholars were all in low spirits and quiet.

Cao Cao asked Yuan Shao how he answered. Yuan Shao scratched his hair in annoyance, "It's hard for a Japanese dog!" Yuan Shao cursed.

After taking a math test, more than 8,000 candidates were silent, and it was as difficult as a dog.

After passing the arithmetic examination, among the more than 8,000 candidates, no one despised the imperial examination, including Yuan Shao and Cao Cao.
Chapter completed!