In ancient China, the people who could become generals were extraordinary. During the Three Kingdoms period, although Guan Yu was only a jujube seller, he had a wonderful knife technique, which was what he had trained from playing dates for many years. Although Zhang Fei was a butcher who killed pigs, because he often blew air to the pigs and molted, he practiced the strength and lung capacity of a very human enemy, so he could drink the Dangyang Bridge with a loud sound. Although Liu Bei is a person who sells straw shoes, he is also a martial arts master, because he has been weaving shoes for many years, so the kung fu of holding a double sword is not worse than anyone.
Therefore, the kung fu of many martial generals is closely related to his previous professional experience, Han Xin was a very famous military expert in the Western Han Dynasty, known as one of the "Three Masters of the Western Han Dynasty", not only was his ability to lead the war very strong, his mathematical talent was also unmatched at that time. And he also left two very difficult math problems, which have caused many students a headache for many years.
In the last years of the Qin Dynasty, the two kings of Liu Bang and Xiang Yu wanted to compete for imperial power, of which Han Xin was one of the generals under Liu Bang, at first Han Xin defected to Xiang Yu's hands, but was not reused, so he turned to Liu Bang. Once, Han Xin led 1,500 soldiers to fight against Li Feng, the king of Chu' subordinates, and after a fierce battle, the soldiers on both sides suffered heavy casualties, but Han Xin had a slight advantage. So Li Feng saw that the current situation was very unfavorable, so he immediately asked all the soldiers to withdraw and preserve their strength.
Han Xin saw that the other side had withdrawn his troops, and considering that his current strength did not account for much benefit, he also withdrew his troops. While passing by a hillside, a spy suddenly came and reported that the enemy army, which had just withdrawn, had sent troops to pursue. Han Xin heard that and looked back, and sure enough, he saw that the sand was all over the sky, and the sound of fighting came from far and near.
But now the soldiers under their command had already gone through a fight and a long journey and were already very weak, and now this situation made the soldiers very afraid. Han Xin thought for a moment, then rode his horse alone to the top of the mountain, saw that the enemy army was less than five hundred people, and had a bottom in his heart, and immediately let the soldiers rectify and fight.
In order to accurately calculate how many soldiers were left to fight, he had the soldiers in a row of three people, and finally two more people, five more people in a row, and finally seven people in a row, and six more people. So Han Xin knew that there were still one thousand and forty-nine soldiers left under his command. How exactly did Han Xin's algorithm come up with?
It was not easy for Han Xin to calculate the number of soldiers so accurately in a short period of time, and even students who had studied mathematics systematically now had difficulty calculating quickly without using paper and pencil drafts. In fact, the solution to this problem is not difficult, and the mystery lies in the residual theorem. And there is such a question in the "Sun Tzu Arithmetic Classic".
Han Xin's mathematical talent is not limited to this one thing. One day, Han Xin rode up to the street to pass the time, and saw two men on the side of the road arguing about something, so he was very curious to come forward and inquire, only to learn that they were oil sellers who cooperated together. However, because there are ten pounds of oil in the oil drum that need to be divided equally, there is no tool around to divide it equally, and there is no scale, only one gourd that can hold seven pounds of oil basket and three pounds. So the matter was not resolved, and the two men quarreled.
After Han Xin knew the reason for the matter, he laughed, rode on his horse, and left a sentence of "the gourd returns to the can and the basket, and the two people share the oil and go home" and left without looking back. Leaving the two people looking at each other stupidly, and then suddenly realized, according to Han Xin's method, they quickly divided the oil, and after several attempts to turn over, both of them got five pounds of oil, and finally went home happily.
The problem of oil distribution is much more difficult than the previous problem of counting soldiers, which belongs to a kind of improvisational transformational thinking, which requires people to think about the problem from another angle, and only needs to consider the capacity relationship between the two containers. Han Xin thought of a solution very quickly in a short period of time, which shows how superb his mathematical talent really is. In order to repay Liu Bang's reuse, Han Xin made a lot of contributions to Liu Bang's later world, but after he became famous, he did not get a good death. There have always been two theories about Han Xin's ending, one is that Liu Bang, as a commoner emperor, was afraid that his imperial power would not be secured, so he would kill the heroes to consolidate the imperial power.
Another theory is that Han Xin's ending was all caused by his own arrogance, and even wanted to rebel, and finally caused tragedy.