A short story about mathematics

1, children of gauss series, do you know the story of gauss, a mathematical genius, when he was a child? When Gauss was in the second grade of primary school, once the teacher wanted to have a rest after teaching addition, so he asked the students to do some calculations. The topic is:1234 ... 96 97 98 99100 =? I thought the students would be quiet for a while, but I was about to find an excuse to go out, but Gauss stopped me! It turns out that Gauss has worked it out. Little friend, do you know how he did it? Gauss told everyone how he worked it out: add 1 to 100 and 100 to1; I want to add in two lines, that is,12341kloc-0/065438. Since then, the learning process of Gauss Elementary School has already surpassed other students, which laid the foundation for his future mathematics and made him a mathematical genius.

2, chickens and rabbits in the same cage Have you ever heard of the problem of "chickens and rabbits in the same cage"? This question is one of the famous and interesting questions in ancient China. About 1500 years ago, this interesting question was recorded in Sun Tzu's calculation. The book describes it like this: "There are chickens and rabbits in the same cage today, with 35 heads on the top and 94 feet on the bottom. The geometry of chicken and rabbit? These four sentences mean: there are several chickens and rabbits in a cage, counting from the top, there are 35 heads; It's 94 feet from the bottom. How many chickens and rabbits are there in each cage? Can you answer this question? Do you want to know how to answer this question in Sunzi Suanjing? The answer is this: If you cut off the feet of every chicken and rabbit in half, then every chicken will become a "one-horned chicken" and every rabbit will become a "two-legged rabbit". In this way, the total number of feet of (1) chickens and rabbits changed from 94 to 47. (2) If there is a rabbit in the cage, the total number of feet is more than the total number of heads 1. So the difference between the total number of feet 47 and the total number of heads 35 is the number of rabbits, that is, 47-35= 12 (only). Obviously, the number of chickens is 35- 12=23. This idea is novel and strange, and its "foot-cutting method" has also amazed mathematicians at home and abroad. This way of thinking is called reduction. Reduction method means that when solving a problem, we do not directly analyze the problem first, but deform and transform the conditions or problems in the problem until it is finally classified as a solved problem.

3. Excellent math story: The door opened and a young man came in. Mr Liu Jianming asked him to sit down. The young man introduced himself and said, "I'm a tour guide from the mainland. My name is yujiang county. I'm taking a tour group to Hong Kong this time. I heard that your hotel has a comfortable environment and good service. We want to stay in your hotel. " Mr Liu Jianming immediately said enthusiastically, "Welcome, welcome, welcome. I wonder how many people are there in your group? " "People, not bad, are a big group." Liu Jianming was overjoyed: It's great to have a big group and another big enterprise. As a tour guide, Yu Jiang saw Mr. Liu Jianming's mind. He remembered and said slowly, "Sir, if you can count the number of people in our group, we will stay in your hotel." "Please go ahead." Mr Liu Jianming said confidently. "If I divide my group into four groups on average, there will be one more person, and then divide each group into four groups on average, there will be one more person, and then divide the four groups into four groups on average, there will be one more person, including me, of course. How many people are there at least? " "How much is a * *?" Mr Liu Jianming immediately thought of this. He must take this business. "Without specific figures, how should we start?" He was a shrewd businessman and soon learned the answer: "At least 85 people?" Mr. Yu Jiang said happily, "Exactly, it's eighty-five. Please tell me how you worked it out? " "The least number of cases, is the last quartile, each is a person. It is concluded that there are 1×4 1=5 (person) before the third score, 5×4 1=2 1 (person) before the second score, and 2 1 (person) before the first score. " How many men and women do you have? ""There are 55 men and 30 women. " "We only have rooms for 1 1, rooms for 7 people and 5 people. How do you want to live? " "Of course, Sir, you have arranged, but men and women must be separated, and there can be no empty beds. "There will be a problem. Liu Jianming had never met such a guest, so he had to spend some time again. After thinking hard, he finally came up with the best plan: 1 1 two people, seven people in four rooms, five people in one room; One female room 1 1 person, seven people in two rooms, five people in one room, and one room * * *1/. After seeing his arrangement, Mr. Yu Jiang was very satisfied and immediately went through the accommodation formalities. Made a big deal. Although it is a bit complicated, Mr. Liu Jianming is still very happy in his heart. Zhu Bajie, a wise fighter, said that Tang Priest and his disciples came to guo jia cun to learn Buddhist scriptures in the West and were warmly welcomed by the villagers. Everyone regards them as heroes of exorcism, not only taking photos with them, but also dragging them home. Facing the hospitality of the villagers, the teachers and apprentices felt very sorry, and helped them harvest crops, plow fields and rake fields whenever they had the chance. Pig Bajie just started to work hard for a few days, and after a few days he became lazy. He thinks it's too hard to work like this, and the master is more comfortable. As long as you sit and preach and recite Buddha, you will have everything. In fact, the master is nothing. If it weren't for the Monkey King's critical eye and skill, I'm afraid I couldn't even go to the Western Heaven, let alone learn from the Buddhist scriptures. If I have such an apprentice, I can do something, and then, haha, I can enjoy my retirement. So Bajie began to talk. Within a few days, he recruited nine apprentices, and he named them: Xiao Yi Huan, Xiao Er Huan ... Xiao Jiu Huan. It stands to reason that Bajie should concentrate on practicing and teaching his disciples now. However, he still did not change his bad habits, and often took his disciples out to eat and drink, which made the people complain. People are thinking about the good things they have done for everyone, and no one is embarrassed to complain to Wukong. In this way, Bajie people are even more fearless, eating five or six hundred steamed buns at a time, and the people are almost boiling. There is a girl named Ganoderma lucidum in the neighboring village. She is clever and kind, and often uses her wisdom to fight the wicked skillfully. Hearing this, she decided to punish Bajie. When she came to guo jia cun to open a restaurant, Bajie heard the news. Lingzhi girl pretended to be surprised and said, "Master Wuneng, it's a great honor for you to come to my restaurant. Come to my place for dinner in the future and don't go anywhere else. " She paused and said, "Here is a round table, specially prepared for you. You ten people sit in a different order every time. When you complete all the orders, I will provide you with meals for free. But before that, every time you eat a meal, you should do a good deed for a villager in the village. what do you think? "Hearing this tempting suggestion, Bajie was so excited that he repeatedly said yes. So they always eat according to the agreed conditions and write down the seats. A few years later, new orders are still emerging, and Bajie is puzzled and has to ask Wukong for advice. Wukong couldn't help laughing when he heard this. "You idiot, you can't calculate such a simple account, and you still want to take advantage of it. You will never get this free meal. " "Don't we eat for twenty or thirty years still don't understand? Wukong said, "Then I will calculate this account for you." . Let's start with a simple number. Suppose there are three people eating. We gave them the serial numbers of 1, 2, 3, and there were six sequences, namely 123, 132, 2 13, 23 1 3 12, 3265433. If four people eat a piece of metal, the first person will sit still, and the seats of the other three people will change six times. When four people sit still as the first person in turn, the overall arrangement order is 6×4=24. According to the same method, it can be inferred that if five people go to eat, there will be 24×5= 120 arrangements ... 10 people will have 3628800 different arrangements. Because you have to eat three meals a day, you can calculate the number of days to eat with 3628800÷3: 1209600 days, which is nearly 3320 years. Think about it, can you eat this free leek? "After the calculation of Wukong, Bajie suddenly understood the intention of Ganoderma lucidum girl and felt ashamed. From then on, Bajie often took his migrant brother to help the villagers. They regained people's love.

Countermeasures for Winning During the Warring States Period, Qi Weiwang and General Tian Ji raced, and Qi Weiwang and Tian Ji each had three good horses: getting on, winning and dismounting. The race is divided into three times, and thousands of dollars are bet on each horse race. Because the horsepower of the two horses is almost the same, and Qi Weiwang's horse is better than Tian Ji's, most people think that Tian Ji will lose. However, Tian Ji took the advice of his disciple Sun Bin (a famous strategist) and dismounted Qi Weiwang, Ma Zhong of Qi Weiwang and Qi Weiwang. As a result, Tian Ji beat Qi Weiwang 2-/kloc-0-and got a daughter. This is an example of China's ancient substitution game theory to solve problems. Here is a game played by two people: take turns to report numbers, and the number reported cannot exceed 8 (nor can it be 0). Add up the figures reported by two people, and whoever reports more figures will win if the total is 88. If you were allowed to count first, how many times should you count first to win? Analysis: Because everyone reports at least 1 and at most 8 at a time, someone reports and another person will find a number, so the sum of this number and a reported number is 9. According to the rules, whoever counts and makes the sum 88 wins, so it can be inferred that whoever counts and makes the sum 79(=88-9) wins. 88 = 9× 9 7, and so on. Whoever counts 16 wins. Furthermore, whoever reports 7 first will win. Therefore, the winning strategy of the first whistleblower is: report 7 first, and then if the other party reports K( 1≤K≤8), you report (9-K). In this way, you will win if you quote 10.

When does the snail climb up the well? A snail accidentally fell into a dry well. It lay at the bottom of the well and began to cry. A toad (Lai) crawled over and whispered to the snail, "Stop crying, little brother! It's no use crying. The shaft wall is too high. If you fall here, you can only live here. I have been here for many years, and I haven't seen the sun for a long time, let alone want to eat swan meat! " The snail looked at the old and ugly toad and thought, "What a beautiful world outside the well! I can never live in a dark and cold well like it! " The snail said to the toad, "Uncle toad, I can't live here. I have to climb up! "How deep is this well?" "Ha ha ha ..., are you kidding! The depth of this well is10m. How can you climb up with such a heavy shell at a young age? " "I am not afraid of suffering, not afraid of being tired. I can always climb out after a while every day! " The next day, the snail ate and drank enough and began to climb the wall. It kept climbing and finally climbed 5 meters at night. The snail was very happy and thought, "At this rate, I can climb up tomorrow night." Thinking about it, it fell asleep unconsciously. In the morning, the snail was awakened by a purr. At first glance, it turned out that Uncle Tu was still sleeping. It was surprised: "How come I am so close to the bottom of the well?" It turned out that this snail slipped 4 meters from the borehole wall after falling asleep. The snail sighed, gritted his teeth and began to climb again. At night, it climbed another 5 meters, but at night the snail slipped another 4 meters. Climb and climb, and finally the strong snail climbed up the well platform. Children, can you guess how many days it will take a snail to climb the drilling platform?