Xu Da and Zhu Yuanzhang played a chess game. On the premise of defeating Zhu Yuanzhang, Xu Da used chess pieces to put the word "Long Live" on the chess board. What is the probability of this incident occurring? And explain the reason.

The Chinese Mathematics Association’s group of people challenged the candidates’ bottom line when setting questions.

MMP has to understand the rules of Go when doing math problems, so I ask if you are angry. This kind of question is possible for Chinese students to solve, and the bad guys will cry after reading it.

This is the national final, the most difficult high school mathematics competition in China.

If a player knows nothing about Go, then it would be miserable. If you don’t have any special skills, would you be embarrassed to participate in the national math qualifiers?

Shen Qi can play Go, chess, flying chess, fighting beasts, putting aside chess skills, he is clear about the rules.

Moreover, Shen Qi knew that many other national finalists knew various chess rules and played well, such as the players in the Hubei Provincial Digital Competition Team, who could play blind chess with their eyes closed.

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

Shen Qi quickly thought of Ferma and Pascal's theory on the distribution of gambling funds. In a sense, playing chess is also a kind of gambling, and there have been people under the overpass for a long time relying on it for a living.

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

No matter how the word "Long Live" is made, it is just a probability event and a trick for those who know mathematics. If Zhu Yuanzhang understood mathematics, he would immediately cure Xu Da's crime and reward Mochou Lake with yarn.

The theory of gambling funds distribution jointly drafted by Ferma and Pascal and the subsequently derived related theories are the theoretical basis for major casinos around the world to make long-term profits. The probability of calculating the word "long live" is similar to the theoretical principle of calculating two kings, four twos, and one hand left.

Shen Qi wrote: Suppose the blackspot is p and the whitespot is q. If p is the probability of a single event occurring, then q is the probability that the event does not occur.

Then, the probability that the event occurs at least m times in n-time experiments is equal to the sum of the terms from the n-mean term of p to the m-mean term including p multiplied by the (n-m) term of q in the n-mean term of (p+q).

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Based on this theory, Shen Qi quickly calculated the probability of the word "Long Live" appearing, which was only 0.2 per ten thousand, and discussed the reasons in detail.

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

Shen Qi inferred that it was true that Zhu Yuanzhang and Xu Da played chess, but Xu Da used the word "Long Live" to win Mochou Lake, which is very likely just a legend.

From a mathematical perspective, playing 50,000 chess games can only happen once. One chess game can be as short as dozens of minutes and as long as several hours. It is more than enough to play three or five chess games a day.

Zhu Yuanzhang and Xu Da did nothing else every day, and just played chess. It took 27 years to see the "Long Live" presented by the black and white pieces once.

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

Of course, it is also possible that the "Long Live" event will appear randomly for the first time in 50,000 times.

So this is a legend, and you can't take it seriously.

"This first question is very painful at first glance. After finishing it, the balls don't hurt anymore, and there is even a little trembling pleasure. This question is actually quite interesting. Oh, I haven't even been to Mochou Lake, so I really want to go and see it." Shen Qi ate a Snickers and celebrated his successful solution to the first question of the national solution.

Without stopping, Shen Qi entered the answer to the second question, which is a plane analytical geometry problem.

For Shen Qi, who is at level 5 of mathematics, it is not difficult to analyze the affine transformation of two-dimensional homogeneous coordinates with determinants. It is nothing more than seeking a set of invariants for rotation, translation and reflection.

It seems a natural axiom to correspond to the subgroup of projective transformations, but don't be confused by its appearance, otherwise you will go astray and go in the opposite direction.

The most rational number contestant just needs to go straight to the yellow dragon and find the absolute shape of the virtual ellipse on the plane. The second question is the free points question.

Shen Qi used an economical and practical way to find the virtual ellipse. The Klein continuous transformation written in university textbooks was too complicated, and it was just causing trouble for himself.

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

From provincial competitions to national competitions, Shen Qi has used Poincaré's theory to solve problems more than once. Poincaré is an omnipotent in mathematics and a master in physics, astronomy, philosophy and other fields.

In a plane coordinate system, there are many ways to obtain absolute shapes through a curve. Poincaré's degradation and overlapping law is simply a magical tool for the competition system. Shen Qi used this degradation and overlapping law, which was simple and crude at the nail on the head. It is very useful, just like a tailor-made for mathematical competitions.

Two hours passed, and Shen Qi solved two questions. He took a sip of Dongpeng's special drink and used chicken blood, accompanied by bear biscuits, Snickers and wife cakes to replenish his energy.

Don’t think that mathematics is a pure mental job and is also very physically exhausted. Just sit there and keep writing, and ask if you are tired after writing for two hours.

The 60 national finalists were distributed in 7 classrooms. Shen Qi and his team had 10 contestants in this classroom, each from ten different provinces and cities.

There were as many as 11 invigilators, and one of them was left to guard against guerrilla warfare.

After all, it is the national finals, and the gold medal in the national competition is extremely important. After the waves wash away the sand, only six people can win the gold medal. These six lucky people will surely become popular among major prestigious schools.

The invigilator who was in charge of guarding Shen Qi walked behind Shen Qi and hummed softly: "Are you full of classmates?"

"When you are full, eat spicy bars to make auspicious and prosperous." Shen Qi used spicy bars in his left hand and compass in his right hand. He made a picture while eating, and drew a concentric circle.

"Student, why do you bring so many snacks into the venue?" The invigilator frowned and asked in a low voice.

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

"Eat less, eating too much will make you sleepy." The invigilator kindly reminded him and looked at Shen Qi's test paper. The Guangdong Provincial Digital Competition Team, Shen Qi, OK, this little boy finished two questions in just two hours, and was having sex with spicy strips. He was very likely to be a dark horse!

The invigilator who was guarding Shen Qi was a staff member of the Chinese Mathematics Society and was a full-time mathematical researcher. He walked to the door of the classroom and asked a younger young man: "Player No. 56 of the National Final, Shen Qi, how many points did the preparatory exam in other countries have been scored?"

The young man had an IPAD in his hand. He took a look at the information: "Shen Qi, the national preparatory score is 21 points, full score. It is not easy for the player of the Guangdong team who is in danger to advance to the national finals to get full scores. Shen Qi is the only national preparatory score in their team."

"Well, it's a talent. The purpose of our Mathematics Society is to subdue talents in a non-conspicuous manner." The older invigilator nodded and said to the young man: "Xiaowen, go and buy a bag of spicy strips for me, which is the same as the one that Shen Qi brought. It's past 11 o'clock, and I'm hungry."

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(Hehehe, students, vote for some recommendation votes (*?▽?*))
Chapter completed!