2, Han Xin's soldiers only "three, three, five, three, seven, seven, two", this relatively small number, if it becomes a relatively large number, it needs the theory of congruence to calculate.
Question 2: What is the implication of Han Xin ordering more troops? Describe what? The idiom Han Xin points soldiers comes from Huai 'an folklore. Often the more the better! The more meanings the better!
Liu Bang asked him, "How many troops do you think I can lead?"
Han Xin: "Up to 100,000."
Liu Bang asked, "What about you?"
Han Xin proudly said, "The more the better, the more the better!
Liu Bang said half jokingly and half seriously, "Then I can't beat you?"
Han Xin said: "No, the master is the person who controls the generals, not soldiers, but soldiers who train soldiers."
Chinese name: Han Xin ordered soldiers.
People involved: Liu Bang, Han Xin.
Legend Source: Huai 'an, Jiangsu
Related Idiom: Han Xin points soldiers, the more the better.
Question 3: What does Han Xin mean by ordering soldiers-the more the better? Han Xin ordered the soldiers.
Emperor Gaozu Liu Bang once asked General Han Xin, "How many soldiers do you think I can take?" Han Xin gave Liu Bang an oblique look and said, "You can take 100,000 soldiers at most!" Emperor gaozu was unhappy, thinking, how dare you look down on me! "What about you?" Han Xin proudly said: "Of course I am the more the better!" Liu added three points of unhappiness to his heart and reluctantly said, "I admire the general for being so talented." Now, I have a little question for the general. With the great talent of the general, it will be easy to answer. "Han Xin said casually," Yes, yes. " Liu bang smiled cunningly and ordered a small group of soldiers to stand in a row across the wall. Liu bang ordered: "every three people stand in a row." After the team stood, the monitor came in and reported, "There are only two people in the last row." "Liu Bang also ordered:" Every five people stand in a row. " The monitor reported, "There are only three people in the last row." Liu bang also ordered: "every seven people stand in a row." The monitor reported, "There are only two people in the last row." Liu Bang turned to Han Xin and asked, "General, how many soldiers are there in this team?" Han Xin blurted out, "Twenty-three people." Liu bang was surprised and quickly increased to ten o'clock. He thought, "This man is so capable. I have to find a fault and kill him to avoid future trouble. " On the other hand, he pretended to smile and praised a few words, and then asked, "How do you calculate?" Han Xin said, "When I was young, Huang Shigong taught my grandson how to calculate. This grandson is a disciple of Guiguzi. Calculate the algorithm that contains this problem. The formula is:
The three of them lost 70 times,
Five plum blossoms are in full bloom,
Seven sons reunited in the first half of the first month,
Divide by 105. "
Liu Bang's problems can be expressed in modern language as follows:
"A positive integer, divided by 3, divided by 5, divided by 7, is 2. If this number does not exceed 100, look for this number. "
Sun Tzu's calculation gives the solution to this kind of problem: "If three numbers or three numbers have two left, it is140; Set the remaining three to sixty-three; The number of July 7th is still two, 30 sets; If the total is 233, subtract 2 10. Where there is one left in the number of three or three, then set 70; There is one left in the number of five or five, which is twenty-one; If there is one left in the number of 77, it is more than 15 160, MINUS 150. " Explaining this solution in modern language is:
First, find out the number 70 that can be divisible by 5 and 7 and 3, the number 2 1 that can be divisible by 3 and 7 and 5, and the number 1 that can be divisible by 3 and 5 and 7.
If the required number is divided by 3 and the remainder is 2, then 70× 2 = 140, 140 is a number that can be divisible by 5 and 7 as well as by 3, and the remainder is 2.
If the required number is divided by 5 and the remainder is 3, then the number 2 1× 3 = 63, 63 is a number that can be divisible by 3 and 7, and can be divided by 5, and the remainder is 3.
If the required number is divided by 7 and the remainder is 2, then the number 15×2=30, and 30 is a number that can be divisible by 3 and 5, and then divided by 7, and the remainder is 2.
In addition, 140+63+30 = 233, because both 63 and 30 can be divisible by 3, so the remainder of 233 and 140 divided by 3 is the same, and they are both residues 2. Similarly, the remainder of 233 and 63 divided by 5 is the same, both of which are 2. So 233 is a number that meets the requirements of the topic.
The least common multiple of 3, 5, and 7 is 105, so the remainder divided by 3, 5, and 7 will not change after the integer multiple of 233 plus or minus 105, so the obtained number can meet the requirements of the topic. Because the demand is only the number of a small group of soldiers, that is to say, the number of soldiers does not exceed 100, so 233 MINUS twice of 105 to get 23 is the demand.
This algorithm has many names in China, such as "Han Xin points soldiers", "Ghost Valley calculation", "partition calculation", "pipe cutting" and "psychic calculation". The title and solution are contained in Sun Tzu's Art of War, an important mathematical work in ancient China. It is generally believed that this is the work of the Three Kingdoms or the Jin Dynasty, which is nearly 500 years later than Liu Bang's life. The arithmetic formula poem is contained in Cheng Dawei's "Arithmetic Unity" in the Ming Dynasty, and the formula implied by the numbers in the poem has long been explained. Qin, a mathematician in the Song Dynasty, popularized this problem and called it "the great solution". After this solution spread to the west, it was called "Sun Tzu's theorem" or "Chinese remainder theorem". On the other hand, Han Xin was finally killed by Liu Bang's wife Lv Hou in Weiyang Palace.
Please try to solve the following problems with the method just now:
A number between 200 and 400. Divided by 3 into 2, divided by 7 into 3 and divided by 8 into 5. Find the number.
(Solution:112× 2+120× 3+105× 5+168k. If k =-5, the number is 269. )
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Question 4: What aspects of Han Xin's personality does Han Xin show? Han Xin shows that his personality is only suitable for doing things, not for being a man, not for being an official. He is confident and arrogant, especially after defeating Xiang Yu, but he is actually a heartless doer. He thinks that Liu Bang can only take 65,438+10,000 soldiers, and Han Xin can win with as many soldiers as possible, so it is better to take more.
But he forgot that his immediate boss, Liu Bang, asked him that his intention was not to ask him how many soldiers he could take, but actually to test Han Xin. For a commander with outstanding military exploits, Liu Bang had to plan ahead, but Han Xin didn't understand the implication of Liu Bang and had to tell the truth. But in Liu Bang's eyes, you dare to brag in front of me that you can fight, which means that you don't take me seriously, and sooner or later you will turn against me.
Question 5: Han Xin's soldiers. Han Xin's point soldier is also known as China's remainder theorem. According to legend, Emperor Gaozu Liu Bang asked General Han Xin how many soldiers he had. Han Xin answered and said, there are 3 soldiers in one platoon 1 or above, 5 soldiers in two platoons or above, 7 soldiers in four platoons or above, and 13 soldiers in six platoons or above. Liu bang was at a loss and didn't know its number. Let's consider the following questions first: Suppose the number of soldiers is less than 10,000, and there are only three people left for every five, 13, 17, so how many soldiers are there? First find the least common multiple of 5,9, 13 and 17 (note: because 5,9, 13 and 17 are pairwise coprime integers, the least common multiple is the product of these numbers), and then add 3 to get 9948 (person). There is a similar question in China's ancient mathematical work Sun Tzu's Art of War: "There are things today, I don't know their numbers, three or three numbers, two, five or five numbers, three or seven numbers, two, ask about the geometry of things? Answer: The technique of "Twenty-three" says: "Two out of three, one hundred and forty, three out of five, one hundred and sixty-three, two out of seven, one hundred and thirty, the sum of which is two hundred and thirty-three, minus two hundred and ten, and you get it. Where the number of three is one, the number of seventy-five is one, the number of twenty-one is one, and the number of seventy-seven is one and fifteen, that's all. The calculation author and the date of completion of Sun Tzu's Art of War cannot be verified. However, according to textual research, the date of its completion will not be after the Jin Dynasty. According to this research, the solution of this problem was found earlier in China than in the west, so the generalization and solution of this problem is called China's remainder theorem. China's remainder theorem plays a very important role in modern abstract algebra.
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Question 6: What did Han Xin say? The more the better. .........