"Please note, please note, please note, there is still half an hour before the end of the exam!"

"Please be careful to check whether the test paper has been written with its name, test number, and hometown. Please check it carefully, otherwise you will not be on the list!"

In the examination room, the inspectors couldn't help but shout, reminding the candidates to grasp the time and remember to write their names on the test paper. At this time, the day was northwest, and it was already sixteen:30 pm, and the Ming Cunning Department exam was coming to an end.◢Suzu Dream◢Xiao*.lā

In a corner of the examination room, Wang Xiaotong, who was invigilating the examination room, was watching the "Exam Outline (Question Solution)". The relevant content is the subject of the clarification subject, and the example question is the classic "Chicken and Rabbit Cage"

There are chickens and rabbits in the same cage, with thirty-five heads on top and ninety-four feet on bottom. What are the chickens and rabbits on top?

This question comes from "Sun Tzu's Arithmetic Sutra". It can be said that everyone who has learned arithmetic will learn this question.

A chicken has one head and two legs, and a rabbit has one head and four legs. This is a known number. The unknown number required to be solved is the number of chickens and rabbits.

"Exam Outline (Question Solution)" gives different equations to the solution of "chicken and rabbit in the same cage", which makes Wang Xiaotong quite moved by the content of using the "equivalence method".

The equation method is an algorithm in Xiyang arithmetic. It is used to solve problems. It is divided into two steps: "making equations" and "solving equations". It also requires "suppose the unknown number is so-and-so". This "some" has mathematical symbols, which are "Ex(x)", "Wei(y)", "sun(z)", etc.

At the same time, in Xiyang arithmetic, there are a series of numerical symbols and calculation symbols.

The process of using equations to solve the problem of "chicken and rabbit in the same cage" is very simple, and there are two solutions.

First, list the "one-element equation"

If the rabbit has x, then the chicken has (35-x), and the equation 4x+2(35-x)=94.

Solve the equation and get x=12, that is, there are twelve rabbits and twenty-three chickens.

Another solution is to list "systems of binary equations"

Suppose that rabbits have x and chickens have y, so we get equation one x+y=35; equation two 2x+4y=94.

Solve the system of equations and get x=12 and y=23.

The solution given in the "Sunzi Sutra" is to solve it using calculations. Although it is not very troublesome, it is somewhat inferior to the "eq method".

The question type of "Chicken and Rabbit in the same cage" can be further evolved, the problem becomes more complicated, and more known and unknown numbers are involved. At this time, using calculation formulas will become more and more troublesome.

As for the "equivalence method" of Xiyang arithmetic, the answerer still only needs a pen, a piece of paper, and an abacus.

The equations listed in its equation method and the process of solving equations are much simpler and more computationally efficient than planning.

If you encounter such extremely complex calculation problems, the advantages of Xiyang arithmetic will become more and more prominent.

And when it comes to Tianyuan Technique

Wang Xiaotong was a little lost when he thought of Tianyuan Technique.

The calculation formula of Tianyuan Technique is called "Tianyuan Technique", which is very complicated to put. Using the equation method of Xiyang arithmetic to formulate equations is a few "one-element multi-order equation".

In this Yuzhou provincial examination, the additional questions for the Ming Case Studies are at the first level of the Imperial Examination. It requires the Tianyuan Art to calculate an application problem. There are two ways to solve the problem: one is to calculate and the other is to "make equations and solve equations".

For both solutions, as long as the steps are correct, you can get a score. If the result is calculated correctly, you can get a full score of ten.

Therefore, whether candidates taking the exam are studying planning or Xiyang arithmetic, as long as they are familiar with Tianyuan Art (one-to-one multi-order equation), they can solve this question.

This is a different path to the same destination.

The problem is that using calculations to create the Tianyuan style is time-consuming and easy to make mistakes in the middle. If you are not familiar with Tianyuan Technique and Tianyuan style, it is very difficult to solve the problem successfully within two hours.

When using Xiyang arithmetic to make equations and solve equations, as long as the candidate is familiar with the one-yuan multi-order equation (Tianyuan Technique), two hours will be enough to verify and review.

This involves calculation efficiency. It is obvious that during the Ming-calculation subject examination, candidates can save a lot of valuable time by using Xiyang arithmetic to solve problems. If they use calculations, candidates must be extremely skilled.

For exams, answering questions at a limited time, under this premise, calculating those complex calculation questions, application questions, and planning are very unfavorable because the calculation formula takes a long time and is difficult to verify during the calculation process.

It can be said that in order to achieve good results in the future imperial examinations, the proportion of candidates who study Xiyang arithmetic will become higher and higher.

Wang Xiaotong felt that it was a bit unfair.

Daily calculations do not require such complex calculation formulas, so calculations are enough to meet the calculation needs. Even for a new civil engineering project, whether it is an estimated earthwork or project volume, there is no reason to limit it to be completed in just a few dozen minutes, so calculations are still competent.

But now, in the fiercely competitive imperial examination, if candidates want to achieve good results in the Mingjuan exam, they will tend to choose Xiyang arithmetic, using those strange numerical symbols and calculating symbols to make equations and solve equations, rather than using calculations to solve problems.

If this continues, what should I do?

Whenever he thought of this, Wang Xiaotong felt a little sad. He studied since he was a child and especially liked arithmetic, and he had a special relationship with planning.

He likes to use calculations to form calculation formulas and likes to look at complex calculation formulas. He thinks that these complex calculation formulas are beautiful patterns, like gossip diagrams, making people think a lot.

And Xiyang arithmetic uses strange symbols to represent numbers, add, subtract, multiply and divide, and uses a plucking abacus as a calculation tool, which always makes people feel something is wrong.

Although Wang Xiaotong also mastered Xiyang arithmetic, he was closer to planning. However, the development momentum of Xiyang arithmetic was strong, and even if he was unwilling to accept it, he could only face reality.

Efficient calculation methods can save calculators a lot of energy and time to deduce more complex formulas. Wang Xiaotong and others have realized this.

The emergence of various types of steam engines, steamships, and new workshops has led to the increasing complexity of various computing requirements and the increasing exaggeration of the calculation volume. The huge demand has rapidly promoted the development of arithmetic.

Therefore, over the past decade, various new algorithms and formulas have emerged one after another.

Wang Xiaotong felt that whether it is planning or Xiyang arithmetic, they are all calculation methods, and the purpose is to solve problems. It can be said that the same destination is the same. It doesn’t matter which one is better or worse.

The Tianyuan Technique, born in Huangzhou Prefecture, appeared at the same time, two versions of it, namely the Tianyuan formula of calculation and the "one-element multi-order equation" of Xiyang arithmetic. Wang Xiaotong had to admit that in terms of computing efficiency, the "one-element multi-order equation" is better.

So, how many candidates are familiar with Tianyuan Art in this provincial examination? How many candidates can solve the problem?

Wang Xiaotong thought it was very difficult. Tianyuan Art had only appeared for more than a year. For publicly published publications, only the journals (special issues) of the Xuexi Society published relevant content in detail. Even if someone saw it, just by reading it, at most it could be understood.

If you want to apply it in practice, for example, if you solve an application problem, as long as the problem is more complicated, it will be very difficult to solve the problem.

It is basically impossible for candidates to get full marks, and the additional questions are set in this way, which is not a bonus question.

Only those students who are studying arithmetic will pay attention to Tianyuan Art, and the additional questions of this exam are also to convey a message to the candidates in advance.

In the Imperial Examination, the Tianyuan Art Test is very likely to appear. If you pass the provincial examination, you will have several months left. If you don’t know how to do it, you will find exercises and practice them quickly.

The clock hand pointed to 16:50. Wang Xiaotong put down his book, got up and put his official uniforms in order, lined up with other invigilators, and came to each examination room.

At about seventeen o'clock, a harsh gong sounded in the examination room, and then countless shouts rang out, "Time is up, stop writing immediately and hand in the paper!"
Chapter completed!