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Han Xin said: "Your Majesty, you can only command 100,000 people. Liu Bang said
How much can you command? ”
Han Xin said: "The more I (command the soldiers), the better." Liu Bang smiled
Command the soldiers) the more, the better, so why am I accused of serving me? Han Xin said: "Your Majesty, you are not (good) at commanding soldiers, but you are good at commanding generals, which is why Han Xin and I are controlled by the emperor and serve you."
Moreover, Your Majesty's ability to command generals is innate, not something that people can achieve with their efforts.
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Liu Bang asked him: "How much do you think I can lead troops?" ”
Han Xin: "Up to 100,000." ”
Liu Bang asked puzzledly: "What about you?" ”
Han Xin said proudly: "The more the merrier, the more the merrier!"
Liu Bang said half-jokingly and half-seriously: "Then I can't beat you?" ”
Han Xin said: "No, the lord is a talent who controls the generals' mountain and disadvantages, not the soldiers, and the soldiers are specially trained soldiers. ”[1]
Chinese name. Han Xin points troops.
Foreign name. han xin--the more ,the better...
Characters involved. Liu Bang, Han Xin.
Legend**. Huai'an, Jiangsu.
Related idioms. Han Xin ordered troops, the more the merrier.
Idiom stories. Huai'an folklore has a story - "Han Xin points soldiers", followed by the idiom "Han Xin points soldiers, the more the merrier".
Han Xin led 1,500 soldiers to fight, killed four or five hundred people, stood in a row of 3 people, and 2 more people; Standing in a row of 5 people, there are 4 more people; Standing in a row of 7 people, there are 6 more people. Han Shin quickly named the number: 1049.
Arithmetic problems. In the "Sun Tzu's Calculation and Dou Chong Sutra" more than 1,000 years ago, there was such an arithmetic problem: "Today there are things that do not know their number, the remaining two of the three or three numbers, the remaining three of the five or five numbers, and the remaining two of the seven or seven numbers.
In today's words: divide a number by 3 and leave 2, divide by 5 and leave 3, divide by 7 and find this number. Such a problem is also called "Han Xin's point soldiers".
It forms a class of problems, i.e., solution congruence in elementary number theory.
There is a number, divide by 3 and leave 2, divide by 4 and leave 1, ask how much is this number divided by 12?
Solution: Divide by 3 and balance 2 are: 2, 5, 8, 11, 14, 17, 20, 23 ......
The remainder of them divided by 12 is: 2, 5, 8, 11, 2, 5, 8, 11, ......
Divide by 4 and get 1 to get 1 as follows: 1, 5, 9, 13, 17, 21, 25, 29, ......
The remainder of them divided by 12 is: 1,5,9,1,5,9......
The remainder of a number divided by 12 is unique. In the remainder of the above two rows, only 5 is common, so the remainder of this comma family divided by 12 is 5. If we change the problem a bit, instead of finding the remainder divided by 12, we find this number.
Obviously, there are many numbers that meet the conditions, it is a 5+12 integer, and the integer can be taken as 0, 1, 2 ,......Endless.
In fact, after first finding 5, we notice that 12 is the least common multiple of 3 and 4, and plus the integer multiple of 12, it is a number that satisfies the condition. In this way, the two conditions of "divide by 3 and remainder 2, divide by 4 and remainder 1" are combined into one condition of "divide by 12 and remainder 5".
There are three conditions for the question raised in Sun Tzu's Sutra, and we can first merge the two conditions into one. Then merge it with the third condition to find the answer.
Divide a number by 3 and balance 2, divide by 5 and balance 3, divide by 7 and balance 2 to find the minimum number that meets the requirements.
Solution: List the numbers divided by 3 and the remainder 2: 2, 5, 8, 11, 14, 17, 20, 23, 26, ......
Re-list divided by 5 to remainder 3
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Liu Bang was named the king of Han by Xiang Yu (in fact, he was squeezed out of Hanzhong), and dozens of generals fled from Chang'an to Zeqi Yin to Nanzheng. Han Xin estimated that Xiao He and others had recommended themselves in front of Liu Bang many times, but King Han didn't use it, and also fled, if it is gold, it will always shine, and if it is talent, it will not be buried. As a generation of generals, Han Xin was finally worshiped as a general after Xiao He's strong recommendation, which was one of the important conditions for Liu Bang to win the world and establish the Han Dynasty.
After Liu Bang entered Shu, Han Xin left Chu and returned to Han, and he was still unknown as a petty official who managed the warehouse. Later, Han Xin sat on the law and beheaded, and the thirteen people in the same case had been beheaded, and it was Han Xin's turn, Han Xin raised his eyes and looked up, saw Teng Gong Xiahou Ying, and said: "Doesn't the King of Han plan to win the world?"
Why did Sun Hall kill the strong man?Xiahou Ying felt that this person's words were extraordinary, and seeing his mighty appearance, he let him go, talked to him, and admired him very much, so he spoke to Liu Bang. Liu Bang only gave Han Xin an official position in charge of food and salary, and did not find anything unusual about him.
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