How talented is Han Xin in mathematics, and what problems he left in his life are still classic?

It is said that Han Xin once met two old men who bought oil in the street and quarreled. It turned out that they were selling oil in partnership and were ready to leave because of disagreement, but only 10 kg of oil, 7 kg of canned food and 3 kg of oil gourd were left in the oil basket. Two people are not allowed to quarrel because of uneven oil distribution. There are many people watching, but no one can help them divide the oil. After listening to this, Han Xin thought a little, and said: The gourd belongs to the pot, the basket belongs to the basket, and the two of them share the oil and go home. Sure enough, they each got 5 Jin of oil and went home happily. Originally, Han Xin's method was: first pour the oil in the oil basket into the oil bottle gourd, and then pour the oil in the oil bottle gourd into the fuel tank. Do this for three times, and there is 1 kg of oil left in the oil basket, 7 kg of oil in the oil tank and 2 kg of oil in the oil bottle gourd. The oil in the oil tank is poured into the oil basket. Now pour the oil from the gourd into the tank. At this time, there are 2 Jin of oil in the tank. Then fill the oil basket with oil gourd. At this time, the oil gourd is 3 kg of oil, 5 kg of oil is poured into the oil tank, and 5 kg of oil is left in the oil basket. On one occasion, Han Xin led a 1500 army to fight fiercely with Li Feng, the general of Xiang Yu, and about 4,500 people were injured. On the way back, 500 pursuers suddenly came. The number of casualties is unknown because of the fighting just happened. In order to quickly know how many soldiers are left, Han Xin asked the soldiers to line up three times, the first time with three people, two more, the second time with five people, four more and the third time with seven people, six more. Han Xin quickly figured out the number of soldiers, so Han Xin shouted: We are twice as many as the enemy, and we will surely defeat them. The soldiers defeated the pursuing enemy with high enthusiasm.

Born in Han Xin, a commoner, without the ability to make a living in business. When he was young, he often lived on alms from others. People are disgusted with him. A young man insulted him: you are tall and like to wear swords, but you are a coward. If you are not afraid of death, stab me with the sword, if you are afraid of death, go through my crotch. ? As a result, Han Xin was prone on the ground and climbed from his crotch. People all over the street laughed at him and thought he was weak and incompetent. Since I met Liu Bang, life has been like hanging out. First, Liu Bangding's Sanqin was presented to determine the basis for competing with Xiang Yu for the world. Then Han Xin led all the way to destroy Wei, eastward to destroy Anlo Zhao, and was named King of Qi. It is said that there is no boat crossing the river in Han Xin, but clay pots are used to cross the river. Han Xin is good at forming and training new recruits. His troops were often borrowed by Liu Bang in various names when Mazhuang was stronger than Ma Zhuang, and he was able to recruit new soldiers quickly and train them into excellent soldiers. Finally, Xiang Yu and overlord Gaixia ambushed on all sides and eventually became famous. Then he was quickly suspected of killing. A sly rabbit dies, a hunting dog cooks, and birds are exhausted.

Han Xin has always been highly respected in history, with many praises from emperors, generals and civil servants. Especially the sentence: The more soldiers Han Xin uses, the better, which fascinates many people. There are many legends and stories about him. It is said that chess was invented by him. As for the story of distributing oil and preparing for war, it also proves that Han Xin's mental arithmetic ability is unparalleled.