I just want to be a quiet scholar

Chapter 32 I am the king of my arena

Xu Da and Zhu Yuanzhang played a game of chess. On the premise of defeating Zhu Yuanzhang, Xu Da used his pieces to place the word "long live" on the chessboard. What is the probability of this event?and explain why.

This group of people from the Chinese Mathematical Society challenges the candidates' bottom line.

MMP still needs to understand the rules of Go when doing a math problem, so if you are angry, it is possible for Chinese students to solve this kind of problem, and the crooked nuts will cry after reading it.

This is the National Final, the most difficult high school math field in China.

If there is a player who doesn't know anything about Go, it will be sad. If you don't have any special skills, would you be embarrassed to participate in the National Mathematics Competition?
Shen Qi can play Go, chess, flying chess, beast chess, and chess skills aside, the rules are clear to him.

Moreover, Shen Qi knew that many other national finalists knew the rules of various chess games and played them well. For example, the players from the Hubei Province Shuju Team, they could play blind chess with their eyes closed.

"Looking at the essence through the phenomenon, the essence of this question has nothing to do with Zhu Yuanzhang and Xu Da. It is just a mathematical question. Except for the last sentence asking about the probability and this chess score, the previous allusions are all pretense."

Shen Qi quickly thought of Fermat and Pascal's theory on the distribution of gambling money. In a sense, playing chess is also a kind of gambling, and people under the bridge have long relied on it for a living.

Since it is gambling, it is necessary to apply relevant professional knowledge of probability theory and number theory.

No matter how the word "long live" came up, it's just a probabilistic event, a trick for someone who understands mathematics.If Zhu Yuanzhang knew mathematics, he would immediately punish Xu Da and reward him with a woolen Mochou Lake.

The wage distribution theory jointly drafted by Fermat and Pascal and the related theories derived later are the theoretical basis for the long-term profits of major casinos around the world. The theoretical principles of second-hand and first-hand straightzi are similar.

Shen Qi wrote: Let the sunspot be p and the white one be q. If p is the probability of a single event, then q is the probability that the event does not occur.

Then, the probability that the event occurs at least m times in n trials is equal to the n-th expansion of (p+q) from the n-th term of p to the m-th term including p times the (nm) of q The sum of the items up to the next item.

……

Based on this theory, Shen Qi quickly calculated that the probability of the word "long live" appearing is only [-] in [-], and discussed the reasons in detail.

It's not difficult to calculate the probability. If you master the above mathematical principles, you can also become a gambling king. The difficulty is to walk out of the casino alive with healthy limbs.

Shen Qi deduced that it was true that Zhu Yuanzhang and Xu Da played chess, but Xu Da posed the word "long live" to win Mochou Lake, which is most likely just a legend.

Explained from a mathematical point of view, it takes 10 games of chess to appear once "Long Live".

Zhu Yuanzhang and Xu Da do nothing but play chess every day.

Zhu Yuanzhang was the founding emperor, so he didn't have to deal with state affairs?

Of course, it is also possible that the "Long Live" event will randomly appear for the first time in [-] times.

So this is a legend and cannot be taken seriously.

"This first question is very painful at first glance, but it doesn't hurt after finishing it, and there is even a little jittery pleasure. This question is actually quite interesting. Oh, I have never been to Mochou Lake, okay. I want to go have a look." Shen Qi ate a Snickers bar and celebrated his success in solving the first question of the national final.

Non-stop, Shen Qi entered the solution of the second question, which was a plane analytic geometry problem.

For Shen Qi, who is at the fifth level of mathematics, it is not difficult to analyze the affine transformation of two-dimensional homogeneous coordinates with the determinant. It is nothing more than finding a set of invariants for rotation, translation and reflection.

Singlet elliptic geometry corresponds to a subgroup of projective transformation, which seems to be a matter of course, but don't be fooled by its appearance, otherwise you will go astray.

The most rational number contestant just needs to hit Huanglong directly to find the absolute shape of the virtual ellipse on the plane, and the second question is the question of sending points.

Shen Qi used an economical and practical method to find the virtual ellipse. The Klein continuous transformation written in the university textbook is too complicated, and he is completely making trouble for himself.

Poincaré, who is known as the last "all-round scholar" in the world, is obviously more flexible. Shen Qi likes to use many of Poincaré's views and conclusions.

From the provincial competition to the national competition, Shen Qi used Poincaré's theory to solve problems more than once. Poincaré was an all-rounder in mathematics and a master in fields such as physics, astronomy, and philosophy.

In the plane coordinate system, there are many ways to obtain the absolute shape through a curve. Poincaré's degenerate and overlap method is simply an artifact for the competition system. Shen Qi uses this method of degenerate and overlap, which is straightforward and rude.It's very easy to use, like it's tailor-made for math competitions.

Two hours later, Shen Qi solved two problems. He drank a sip of Dongpeng Special Drink to beat chicken blood, accompanied by bear biscuits, Snickers, and wife cakes to replenish his strength.

Don't think that mathematics is purely mental work, and it is also very physically exhausting. Just sit there and keep writing, and ask if you are tired after two hours of writing.

The 60 national finalists were distributed in 7 classrooms. Shen Qi and his group had a total of 10 players in this classroom, from [-] different provinces and cities.

There are as many as 11 invigilators, and the remaining one is guerrilla guarding one-on-one.

After all, it is the national final, and a piece of gold in the national competition is very important. After the big waves wash the sand, only six people can win the gold medal. These six lucky ones will definitely become the sweet pastry of the major schools.

The invigilator in charge of guarding Shen Qi walked behind Shen Qi and snorted softly, "Are you full?"

"When you're full, eat the spicy strips again to make it auspicious and prosperous." Shen Qi left spicy strips in his left hand and a compass in his right. He drew a picture while eating, and drew a concentric circle.

"Classmate, why did you bring so many snacks into the hall?" the invigilator frowned and asked in a low voice.

Shen Qi was also surprised: "Hey, aren't you allowed to bring food? 4.5 hours, teacher, it's almost the same as the ancient imperial examination. It's a protracted battle. If you don't eat, you'll be hungry."

"Eat less, it's easy to get sleepy if you eat too much." The invigilator reminded kindly and looked at Shen Qi's test paper. , and also eat spicy strips leisurely, he is likely to be a dark horse!

The invigilator who marked Shen Qi was a staff member of the Chinese Mathematical Society, a full-time math researcher himself. He paced to the door of the classroom and asked a younger guy, "National Final No. 56, Shen Qi, has taken the pre-exam in another country. How many points?"

The young man had an iPad in his hand, and he took a look at the information: "Shen Qi, the National Preliminary Score is 21, a perfect score. It is not easy for a Nanyue team player who is in danger to advance to the National Finals to get a full score. ."

"Well, it's a talent. The purpose of our math club is to reduce talents without sticking to one pattern." The older invigilator nodded and said to the young man, "Xiao Wen, go and buy a bag of spicy sticks for me, brought with Shen Qi. The same kind. It's past 11 o'clock. I'm hungry."

……

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(Hey hey, classmates vote for recommendation (*▽*))

(End of this chapter)