This mathematical problem was first put forward and described in the mathematical book Sun Tzu's Calculations in the Northern and Southern Dynasties. The title of this "things are unknown" is like this: "Today, there are some things whose numbers are unknown. If three or three." If you count it five by five, there are three left in the end; If you count it seven by seven, there are two left in the end. Q: How many of these things are there? " It's not what you understand. In fact, 7 is divisible by 5 and 7, but divided by 3. 1,21 is divisible by 3 and 7, but 5 is divisible by 1,15 is divisible by 3 and 5, but divided by 7. 1. In the title, this number is divided by 3, so multiply 7 by 2, divide 5 by 3, then multiply 21 by 3, divide 7 by 2, and then multiply 15 by 2. Add .7 * 2+21 * 3+15 * 2 = 233. Depending on the situation, subtract the multiple of the least common multiple of 3, 5 and 7. This problem is subtracted twice from 15 to get 23. This systematic algorithm was obtained after the research of Qin Jiushao, a mathematician in the Southern Song Dynasty. This is the famous China remainder theorem. 2. Be quick on the questions and answers of the first grade Chinese ancient prose test paper
7-1. Confucius said in "Ten Analects of Confucius": "It's not bad to learn from the times, isn't it? Is it not delightful to have friends coming from distant quarters? Isn't it a gentleman to be ignorant and not satisfied? " (2) Zeng Zi said: "I save myself three times a day: are you unfaithful for others?" Make friends without believing them? Can't you learn it? " ③ Confucius said, "Reviewing the past and learning the new, you can be a teacher."
④ Confucius said, "Learning without thinking is useless, and thinking without learning is dangerous." ⑤ Confucius said, "Why, teach your daughter to know! One’s true knowledge lies in recognizing what one knows and what one does not know.
"⑥ Confucius said," When you see the sage Si Qi, you should reflect on yourself if you don't. " ⑦ Confucius said, "In a threesome, there must be a teacher; Choose the good and follow it, and change it if it is not good. "
⑧ Zeng Zi said, "Scholars have to be unyielding and have a long way to go. Isn't it important to think that benevolence is your own responsibility? After death.
Isn't it far? " ⑨ Confucius said, "When you are cold, you will know that pine and cypress will wither." Attending Zi Gong asked, "Who can walk for life with a word?" Confucius said, "It's forgiving! Don't do to others what you don't want. "
Confucius, whose name is Qiu, whose name is Zhong Ni, was born in Huyi, Lu (now Qufu, Shandong) in the Spring and Autumn Period. He was a great thinker and educator in the history of our country and the founder of the Confucian school, and was honored as "the greatest achievement". His thoughts and theories have made immortal contributions to China culture and even world civilization, and UNESCO has listed him as one of the top ten celebrities in the world.
The Analects of Confucius is a book that records the words and deeds of Confucius and some of his disciples, with 2 articles, which is one of the classic works of Confucianism. The style is mainly recorded style, dialogue style and narrative style.
Education is the main content, including philosophy, history, politics, economy, art and religion. From this, we can see the political life of the society at that time, and see the personality cultivation, academic attitude and way of life of Confucius and his disciples.
A generic word (saying-pleasing a girl-knowing-wisdom) means that people don't know and don't care (yùn) learning without thinking is useless (w∥ ng) thinking without learning is dangerous (dài) It's also said that (yuè yi) is related to three provinces (xǐng) and my body biography (chuán) is unfamiliar. Is it not delightful to have friends coming from distant quarters? People don't know and don't care (yùn), isn't it a gentleman? " [Explanation] "Shi" is an adverb here, which is equivalent to "Shi" and can be interpreted as "according to a certain time" or "timely". The original meaning of "learning" is "birds fly" and it is extended to "practice" and "exercise".
The lessons taught by Confucius, such as etiquette, music, archery, and imperial defense, all need practice to master; But other lessons, such as lectures, can only be "review" or "review" "Friends" old note: "Friends from the same door."
It is similar to "classmates" and "classmates" now. "Friends" refer to like-minded people.
"people don't know" and "don't know" what? I didn't say it, but the meaning was clear, that is, "myself". "Gentleman" has many meanings in The Analects of Confucius: sometimes it refers to a moral person; Sometimes refers to a person in a high position.
in this sentence, the former meaning can be taken. Because this word is also commonly used now, everyone knows its meaning, and we have no translation; It must be translated, or it can be translated as "noble man".
Confucius said, "Isn't it a pleasure to learn (knowledge) and then practice (review) it at a certain time?" Isn't it happy to have like-minded people coming from afar? People don't know me, but I don't resent it. Isn't it also a gentleman? " The first sentence is about learning methods. The second sentence is about the fun of learning.
The third sentence is about people's attitude, which belongs to the scope of personal cultivation. ◆ Zeng Zi said: "I am in three provinces in Japan (xǐng). My body: Is it disloyal to others? Make friends without believing them? Can't you learn it? " [Explanation] In The Analects of Confucius, Confucius' disciples generally call it Zi Lu for Zhong You, Zi Gong for Duanmu Ci, and Zi for Zeng Shen, because this book was written by the disciples of Confucius' second or third biography, and was once taught by Zeng Shen.
"Three Provinces", reflecting many times. In classical Chinese, the words "three" and "nine" all have the meaning of "many", not exact numbers.
the following three things are coincidental. Zhu Xi believes that learning is the most important thing, and "transmission" means learning from teachers, while "learning" is familiar with oneself, while "loyalty" and "faith" are the basis of "transmission and learning".
Ceng Zi said, "I reflect on myself many times every day: Do I do my best to work for others? Is it honest to associate with friends? Have you reviewed the studies taught by the teacher? " It can be seen from this that ancient scholars attached great importance to moral cultivation. ◆ Review the past and learn the new, and you can be a teacher.
[explanation] Confucius said, "After reviewing old knowledge, you can have new experiences and discoveries, and you can become a teacher." This one is also about learning methods, emphasizing the necessity of independent thinking, because only "reviewing the past" without independent thinking will definitely not achieve the purpose of "knowing the new".
In the past, there was an understanding that "reviewing old knowledge" (reviewing old knowledge) and "learning new knowledge" (acquiring new knowledge) were two complementary aspects. For example, Zi Xia said that "the day knows what it has, and the month never forgets what it can do" (see The Analects of Confucius, Zi Zhang). This is because the following word "being a teacher" was ignored. Confucius recorded this sentence in the Book of Rites: "Learning by memorizing questions is not enough to be a teacher."
This shows that Confucius thinks that he can only recite some knowledge and cannot be a teacher of others. We must master the knowledge and find something in reviewing the old knowledge before we can "be a teacher". It can be seen that "reviewing the past" and "knowing the new" are not two things in parallel. The key is to "know the new", which requires independent thinking.
◆ Confucius said, "Learning without thinking is useless, and thinking without learning is dangerous." [Explanation] Confucius said: "If you only read without thinking, you will be confused and gain nothing; Just dreaming without reading is in danger. "
This one also talks about learning methods, and expounds the dialectical relationship between learning and thinking, and thinks that they cannot be neglected. ◆ Confucius said: "You, teach your daughter to know! Knowing it is knowing it, not knowing it is not knowing it, but knowing it. "
[explanation] Confucius said, "Let me teach you the attitude towards knowing and not knowing: knowing means knowing, and not knowing means not knowing-this is wisdom." The last word "knowledge" should be broken and read, and "wisdom" should be passed.
what Confucius meant by this remark was that we should be careful in our words and deeds, and don't exaggerate our knowledge and skills. To use modern expression means to have a modest learning attitude.
◆ Confucius said, "When you see a sage Si Qi, you should reflect on yourself if you don't." ◆ Confucius said: "There must be a threesome. 3. There are 1 interesting math problems with answers in the first volume of Grade 5.
1. There are 1 chickens and rabbits, and the number of legs of chickens is 28 less than that of rabbits. How many chickens and rabbits are there? 6. pigeonhole principle, parity problem 1. A cloth bag contains gloves of the same size but different colors, including black, red, blue and yellow. How many gloves must be pulled out to ensure that there are three pairs of gloves of the same color? 2. There are a number of building blocks with four colors. Everyone can take 1-2 pieces at will, and at least a few people can take them to ensure that there are 5 balls in a box, of which 1 are red, 1 are green, 1 are yellow, 1 are blue, and the rest are white and black balls. In order to ensure that the balls taken out contain at least 7 balls of the same color, Q: How many balls must be taken out of the bag at least? 1. Party A, Party B and Party C plant trees in two plots A and B, with 9 trees to be planted in plot A and 125 trees to be planted in plot B. It is known that Party A, Party B and Party C can plant 24, 3 and 32 trees each day, with Party A planting trees in plot B, and Party B planting trees in plot A first, and then transferring to plot B. Both plots start and end at the same time, and Party B starts and ends at the same time. 2. There are three grasslands with an area of 5, 15 and 24 mu respectively. The grass on the grassland is as thick and grows as fast. The first grassland can feed 1 cows for 3 days, and the second grassland can feed 28 cows for 45 days. How many cows can feed 8 days in the third grassland? 3. A project, contracted by Party A and Party B, can be completed in 2.4 days, and it needs to pay 1,8 yuan; It can be completed in 3+3/4 days by contracting by teams B and C, and it needs to pay 15 yuan; It will be completed in 2+6/7 days by two teams, and it will cost 16 yuan. On the premise of ensuring the completion within one week, which team should be selected for the least cost? 4. There is a rectangular iron block in a cylindrical container. Now turn on the tap and pour water into the container. In 3 minutes, the water just doesn't pass the top of the cuboid. In 18 minutes, the container has been filled with water. It is known that the height of the container is 5 cm and the height of the cuboid is 2 cm. Find the ratio of the bottom area of the cuboid to the bottom area of the container. 5. Two bosses, Party A and Party B, bought a fashion at the same price, and Party B bought 1/2 more sets than Party A. Then, Party A and Party B sell them at a profit rate of 8% and 5% respectively. After both of them are sold out, Party A still gets more profits than Party B, which is just enough for him to buy another 1 sets of this fashion. How many sets of this fashion did Party A originally buy? 6. There are two water pipes, A and B, which inject water into two pools with the same size at the same time. At the same time, the ratio of water injection volume of A and B is 7:5. After 2+1/3 hours, the sum of water injected into A and B is just one pool. At this time, the water injection speed of A pipe is increased by 25%, and the water injection speed of B pipe is unchanged. Then, when A pipe is filled, 7. Xiao Ming walked from home to school in the morning. When he finished half the distance, his father found that Xiao Ming's math book was left at home, and then he rode to deliver it to Xiao Ming. When he caught up, Xiao Ming still had 3/1 of the distance to walk, so he got on his father's car and was sent to school by his father. So Xiao Ming arrived at school five minutes earlier than walking alone. How long does it take for Xiao Ming to walk from home to school? 8. Both cars A and B start from place A and go to place C via place B, and the distance between them is equal to the distance between places B and C. The speed of car B is 8% of that of car A. It is known that car B started 11 minutes earlier than car A, but stayed in place B for 7 minutes, but car A kept driving to place C. Finally, car B arrived at place C four minutes later than car A. How many minutes after car B left? Car A surpasses car B. 9. Two cleaning cars A and B perform the task of cleaning the road between the east and west cities. It takes 1 hours for car A to clean alone, and 15 hours for car B to clean alone. Both cars leave from the east and west cities at the same time. When they meet, car A cleans 12 kilometers more than car B. How many kilometers are there between the east and west cities? 1. Today, there are 4 containers weighing 3 tons, 5 containers weighing 2.5 tons, 14 containers weighing 1.5 tons and 7 containers weighing 1 ton. So how many cars with a load of 4.5 tons are needed to transport all the containers at once? . 4. Find an interesting strange math problem ~
1. Five students who copied it lined up to take pictures and asked: (1)*** How many arrangements are there? (2) If someone doesn't sit at both ends, how many arrangements does * * * have? (3) If two seats are adjacent, how many arrangements are there? In the analysis (2), you can limit someone's sitting method by arranging this person first, and then arranging others. It can be done in two steps, using the principle of multiplication, or you can not consider this restriction first. Calculate the total number of arrangements, and then remove the exceptions (subtract the number of arrangements where someone is sitting at both ends). (3) You can treat those two people as one person first. Then consider the arrangement of those two people (that is, multiply by 2). Solution (1) 5x4x3x2x1 = 12 (2) 3x (4x3x2x1) = 3x24 = 72 or 5x4x3x2x1-2x (4x3x2x1) = 72 (3) (2x1) x (4x3x2x1) = 48. A drives a flock of sheep to chase the grass, and B drags a fat sheep, and then jokes about A and a hundred. Jia Yun said that there is no difference. If you have to gather together in such a group, you can add a small semi-group of semigroups (a small semi-group is a quarter group) to gather together. Who can guess the mystery? The answer is that there are 36 sheep in armour. I went to Ives, the holy land. There were seven women in Lu Yu, each with seven bags in his hand, and seven cats in one bag, followed by seven children in one cat. Cats and cats, cloth bags and women went to Ives, the holy land with geometry. Very simple, the answer is that there is something in 28 today, I don't know its number, three or three numbers leave two, five or five numbers leave three, and seven or seven numbers leave two. What is the geometry of things? This topic comes from Sun Tzu's Calculations, which is a famous "Sun Tzu's Problem", also known as "Ghost Valley Calculations" and "Pipe Cutting". The answer to this topic is 23. There is a red lotus standing half a foot above the mirror. It stands alone and is suddenly blown to one side of the water by the wind. A fisherman saw it with his own eyes, and it is now two feet away from its original location. Please. Answer. Guess for yourself first! This is the famous "Lotus Problem", which was written by the ancient Indian mathematician Beska in the form of poetry. It is very similar to the problem of "the pond" in China's "Nine Chapters of Arithmetic": "Today, there is a pond, and the pond (reed) is born in its center, and the water is one foot, which leads the pond to the shore, and it is suitable for the shore. Ask the water depth. 2. I remember that I saw it in an interesting math book in middle school. It is said to be a mathematical black hole. I don't know if there is a mathematical method to prove it now. That is: four digits are not the same, and its four digits are arranged from big to small, MINUS the arrangement from small to big. The result is repeated. You will get the result 6174 and then use letters instead of numbers to knock down his four digits, 1a+1b+1c+d-(1d+1c+1b+a) = 999a+9b-9c-999d = 999 (a-d)+9 (b-c).