What is Hanshin Point Soldier? What is Han Xin s explanation of the soldiers?

Han Xin points troopsThe idiom ** Huai'an folklore. Always paired with the more the merrier. The more implications, the better.

Liu. Ask him, "How much do you think I can lead with troops?" ”

Han Xin: "The most important thing is more than 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, my lord.

It is the generals who control the generals, not the soldiers, and the soldiers are specially trained soldiers. ”

Xiao He chased Han Xin under the moon.

Han Xin talked with Xiao He many times, and Xiao He also appreciated him very much. Liu Bang was Xiang Yu.

He was named the King of Han. In fact, it was squeezed out to Hanzhong), from Chang'an to Nanzheng.

Dozens of generals fled. Han Xin estimated that Xiao He and others had recommended themselves in front of Liu Bang many times, but King Han didn't need to use them, and they also fled. When Xiao He heard that Han Xin had escaped, he went to chase after Han Xin before he had time to report to Liu Bang.

Someone in the army reported to the king of Han, "Why is the prime minister dead?" (Historical Records: Biography of the Marquis of Huaiyin.)

Liu Bang was furious, as if he had lost his left and right hands. After a day or two, Xiao He came to see him, Liu Bang was angry and happy, and scolded Xiao He for why he ran away, Xiao He said that he didn't dare to run away, he just went to chase Han Xin who was fleeing. Liu Bang scolded again, "The generals and the dead are counted in tens, and the public has nothing to pursue; Follow-up, fraud also. ”

Xiao He said: "The generals are easy to hear. As for those who believe, there is no one in the country.

The king will want to grow up in the king's Hanzhong, and he will have nothing to believe; He who wants to fight for the world, not those who believe in nothing and have nothing to do. Gu Wang Ce'an's decision was purely sleepy. Liu Bang said that he also wanted to develop to the east, and he was by no means willing to live in Hanzhong, and he was determined to take the world.

The problem with Han Xin's troops is that Han Xin, a general of the Han Dynasty, is good at using troops, and every time Han is not a bad letter, he only asks his subordinate soldiers to report the number from 1 to 7, and then report the remainder of each time to know the common multiple and the shortfall of the exercise. This problem and its solution are quite famous in the history of mathematics in the world, and Chinese and foreign mathematicians call it Sun Tzu's theorem or the Chinese residual theorem.

The solution to the problem of Han Xin's soldiers is based on:

1. If the dividend increases or decreases several times of the divisor, the divisor does not change, and the remainder does not change.

2. If the dividend is enlarged by several times and the divisor remains unchanged, the remainder will be expanded by the same multiple.

3. If the dividend is reduced by several times and the divisor remains unchanged, the remainder will be reduced by the same multiple.

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 to a different one, 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 adding the integer multiple of 12 is a number that satisfies the condition. In this way, the two conditions of "divide by 3 and leave 2, divide by 4 and leave 1" are combined into one condition of "divide by 12 and leave 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