Xu Da and Zhu Yuanzhang played a game of chess, and on the premise of defeating Zhu Yuanzhang, Xu Da used chess pieces to put the word "long live" on the chessboard.

The group of people from the Chinese Mathematical Society asked questions to challenge the bottom line of the candidates.

MMP has to understand the rules of Go to do a math problem, so I ask you if you are angry, this kind of problem is also possible for Chinese students to solve, and crooked nuts will cry after reading it.

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

If there is a player who doesn't know anything about Go, then it's sad, and you are embarrassed to participate in the math national finals if you don't have any special skills?

Shen Qi can play Go, Chess, Flying Chess, and Beast Chess, putting aside his chess skills, he is clear about the rules.

And Shen Qi knows that many of the other national finalists know all kinds of chess rules and play very well, such as the group of players in the Northern Hubei Provincial Mathematics Competition Team, who can play blind chess with their eyes closed.

"Looking at the essence through the phenomenon, the essence of this problem has nothing to do with Zhu Yuanzhang and Xu Da, it is just a mathematical problem, except for the last sentence to ask about probability and this chess game, the previous allusions are all disguises. ”

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 there are people under the flyover who have long relied on it for a living.

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

Regardless of how the word "long live" came up, it is nothing more than a probabilistic event, a trick of those who understand mathematics. If Zhu Yuanzhang knew mathematics, he would immediately cure Xu Da's sin and reward Mochou Lake with wool.

The theory of the distribution of gambling money jointly drafted by Fermat and Pascal and the related theories derived from it is the theoretical basis for the major casinos around the world to make a long profit or lose money, and the probability of calculating the word "long live" is similar to the theoretical principle of calculating the two kings and four twos with one straight left.

Shen Qi wrote: Let the black son be p, let the white son be q, if p is the probability of a single event, then q is the probability that the event will not appear.

Then, the probability that the event will occur at least m times in n trials is equal to the sum of the terms in the nth power expansion of (p+q) from the n term of p to the m terms including p multiplied by the (n-m) terms of q.

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According to this theory, Shen Qi quickly calculated the probability of the occurrence of the word "long live", which was only 0.2 per 10,000, 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 a gambling king, but the difficult thing is to walk out of the casino alive with sound limbs.

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

From a mathematical point of view, playing 50,000 games of chess can only occur once "long live", a game of chess is as short as dozens of minutes, as long as several hours, and it is more than three or five games of chess a day.

Zhu Yuanzhang and Xu Da don't do anything else every day, they play chess, and it takes 27 years to see a "long live" posed by black and white.

Zhu Yuanzhang is the founding emperor, he doesn't have to deal with state affairs?

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

So it's a legend and can't be taken seriously.

"This first question, it hurts at first glance, but it doesn't hurt after doing it, and there is even a little shaking pleasure, this question is actually quite interesting. Oh, I haven't been to Mochou Lake, so I really want to see it. Shen Qi ate a Snickers frame and celebrated his success in solving the first question of the national decision.

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

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

It may seem like an axiom that single-fold elliptic geometry corresponds to subgroups of projective transformations, but don't be fooled by its appearances, or you'll go astray.

The most rational number contestant only needs to smash the yellow dragon and find the imaginary ellipse absolute shape on the plane, and the second question is the Dao send sub-question.

Shen Qi used an economical and practical way to find imaginary ellipses, and the Klein continuous transformations written in college textbooks were too complicated, and he was completely asking for trouble for himself.

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

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

In the plane coordinate system, there are many ways to obtain an absolute shape through a curve, and Poincaré's degradation re-law is simply an artifact for the competition system, and Shen Qi uses this kind of degenerate re-law, which is simple and rude to the point. It's so easy to use, it's like it's made for math competitions.

2 hours passed, Shen Qi solved two problems, he drank a sip of Dongpeng special drink to beat chicken blood, accompanied by bear biscuits, Snickers and wife biscuits to replenish his strength.

Don't think that math is a purely mental work, and it is also very physically demanding, just sit there and do not move, keep writing and writing, and ask if you are tired after writing for two hours in a row.

The 60 national finalists are distributed in 7 classrooms, and Shen Qi has a total of 10 players in this classroom, from 10 different provinces and cities.

There are as many as 11 invigilators, and the remaining one is a guerrilla fight.

After all, it is the national finals, and the gold medal in the national competition is extremely heavy, and after the big waves, only six people can win the gold medal in the end.

The invigilator in charge of keeping an eye on Shen Qi walked behind Shen Qi and snorted softly: "Have you eaten enough?"

"When you're full, eat a spicy strip to be auspicious, and it's booming. Shen Qi had spicy strips in his left hand and compasses in his right hand, drawing a concentric circle while eating.

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

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 just a protracted war, and if you don't eat, you'll be hungry." ”

"Eat less, eat too much and get sleepy. The invigilator kindly reminded him, and looked at Shen Qi's exam papers, the Nanyue Provincial Mathematics Competition Team, Shen Qi, yes, this little boy, he finished two questions in just two hours, and he is also a good eater of spicy strips, he is likely to be a dark horse!

The invigilator who kept an eye on Shen Qi was a staff member of the Chinese Mathematical Society, a full-time mathematics researcher himself, and he paced to the door of the classroom and asked a young man: "The No. 56 player in the national final, Shen Qi, how many points did he score in the national pre-examination?"

The young man had an iPad in his hand, and he swiped out the message and glanced at it: "Shen Qi, the national preliminaries, 21 points, full scores." It is not easy for the players of the Nanyue team who are involved in danger to advance to the national finals to get full scores, and Shen Qi is the only one in their team who has a full score in the national pre-finals. ”

"Well, it's a talent, and the purpose of our mathematical society is to reduce talents without sticking to one pattern. The older invigilator nodded and said to the young man, "Xiaowen, go and help me buy a pack of spicy strips, the same style as the one Shen Qi brought." It's past 11 o'clock, hungry. ”

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(Hey, hey, hey, classmates voted for recommendations (*?▽?*))