2. Legend of the King's Reward Indian King Shehan intends to reward the inventor of chess-Minister Sass? 6? 1 class? 6? 1 Dar. The wise minister knelt before the king and dared to say, "Your Majesty, please give me a grain of wheat in the first box, two grains in the second box and four grains in the third box. At this speed, each compartment is twice as big as the previous one. Your Majesty, give all the 64 grains of wheat like this on the chessboard to the servant? " The king said, "Your request is not high, and you will get it." . With that, he ordered a bag of wheat to be taken to the throne, and the work of counting wheat grains began. ..... Before the 20th cell, the bags were empty, and bags of wheat were transported to the king. However, the number of wheat grains increased rapidly one after another, and it soon became clear that even if all the food in India was taken out, the king could not fulfill his promise to the inventor of chess. Calculate, how many grains of wheat should the king give to the chess inventor?
3. the prince's math problem legend once upon a time, there was a prince. One day, he called his sisters together and gave them a math problem. The title is: I have two jewelry boxes, gold and silver, which contain several pieces of jewelry. If I give 25% of the jewels in the gold box to the first person who solves this problem correctly, I will give 20% of the jewels in the silver box to the second person who solves this problem correctly. Then I took five pieces from the gold box and gave them to the third person who got the title, and then took four pieces from the silver box and gave them to the fourth person who got the title. Finally, I lost 10 pieces of jewelry left in the gold box, and the ratio of the remaining pieces in the silver box to the divided pieces was 2: 1. Can anyone figure out how many jewels were in my gold box and silver box?
4. In ancient times, it is said that Princess Lubusha of the Czech Republic wrote an interesting question: "How many plums are there in a basket? Give half to the first person, the remaining half to the second person, and the last half and three to the third person. Then there are no plums in the basket. How many plums are there in the basket? "
Goldbach guessed that Goldbach was a German mathematician more than 200 years ago. He found that every even number greater than or equal to 6 can be written as the sum of two prime numbers ("1+ 1" for short). Such as: 10 = 3+7, 16 = 5+ 1 1 and so on. He tested many even numbers, which showed that this conclusion was correct. But he can't prove that this conclusion is correct in theory. 1748, he wrote to Euler, a famous mathematician at that time, asking him to give directions. Euler wrote back that he thought this conclusion was correct, but he couldn't prove it. Because it is not proved theoretically that it is only a conjecture, the problem raised by Goldbach is called Goldbach conjecture. Many mathematicians in the world have made great efforts to prove this conjecture. From "1+4" to "1+3" to 1966, China mathematician Chen Jingrun proved "1+2". That is to say, any large enough even number can be expressed as the sum of two numbers, one of which is a prime number and the other is either a prime number or a product of two prime numbers. Can you write the following even numbers as the sum of two prime numbers? ( 1) 100=(2)50=(3)20=
6. Bewick's Seven Years At the beginning of the seventies and twentieth centuries, the British mathematician Bewick put forward a special division problem. Please fill in this special branch.
7. Diao Fandu's epitaph is a mathematician in the third century AD. His epitaph reads: "Diao Fandu was buried here. The epitaph tells you that one-sixth of his life was a happy childhood and one-twelfth was a happy youth. He was married, but he never had children, so he spent another seventh of his life. Five years later, he will have a son; It's a pity that my son only lived half his father's life and died four years earlier than his father. How long did Diao Fan live?
8. Legend has it that when the ancient Romans died, they wrote a will to their pregnant wife: if they gave birth to a son, they would give him 2/3 of the inheritance, and the mother would take1/3; If the baby is a daughter, give 1/3 of the inheritance to the daughter and 2/3 to the mother. As a result, my wife gave birth to a boy and a girl. How to distribute it to meet the requirements of the will?
9. There are two kinds of flowers, A and B, in Hascal's Arithmetic Park. A swarm of bees flew in and dropped 1/5 on the A flower and 1/3 on the B flower. If a bee falls on two flowers three times before it falls on the flower, then there is only one bee flying up and down to enjoy the flower. How many bees are gathered here?
10.Matani Tsky's arithmetic problem An employer agreed to give workers 12 yuan and a jacket every year. The worker wanted to leave after working for seven months and only gave him 5 yuan money and a short coat. How much is this shirt worth?
1 1. Tolstoy's arithmetic problem Tolstoy, a great Russian writer, once wrote a question: A group of mowers want to cut the grass of two grasslands. The big one is twice as big as the small one. In the morning, everyone mows the grass in the big yard. Half the people stay on the big grass in the afternoon and finish cutting at night. The other half went to mow the grass, and there was one piece left in the evening, which was cut by the lawn mower one day later. How many lawn mowers are there in this group? Everyone mows the grass at the same speed.
12. Canovschi's arithmetic problem (1) A dog chases a horse. Dogs jump six times, and horses can only jump five times. The distance between a dog jumping four times and a horse jumping seven times is the same. After the horse ran 5.5 kilometers, the dog began to chase. How long did the horse run before the dog caught up with it?
13. Canovschi's arithmetic problem (2) The captain was asked how many people were under his command, and he replied, "Two-fifths went to stand guard, two-fifths were at work,14 was in the hospital, and 27 were on board." How many people are under his command?
14. What happened to mathematician D'Alembert? It is said that D'Alembert, a famous French mathematician in the18th century, threw two nickels. What will happen? There are only three situations: both may be positive; Maybe one is the front, one is the back, or both are the back. So the probability that both are positive is 1: 3. Think about it. What's the matter?
15. Egyptian pyramids The world-famous pyramids are the tombs of ancient Egyptian kings. This building is magnificent and tall, shaped like a "gold". Its bottom is square and the four sides of the tower are inclined isosceles triangles. More than 2600 years ago, a king in Egypt invited a scholar named Pharisee to measure the height of the pyramids. The Pharisees chose a sunny day and organized an investigation team to come to the pyramid. Sunlight casts a long shadow on every survey team and pyramid. When the Pharisee measured that his shadow was equal to his height, he immediately asked his assistant to measure the shadow length (CB) of the pyramid. He quickly calculated the height of the pyramid according to the length of the tower bottom and the length of the tower shadow. Can you calculate?
16. In the18th century, there were seven bridges in Konigsberg. At that time, many people wanted to cross seven bridges at a time, and each bridge could only cross once. This is the world-famous problem of the Seven Bridges in Konigsberg. Can you walk all seven bridges at once without repeating them?
17. Han Xin told the story that Han Xin, a general of the Han Dynasty, counted the number of soldiers in a special way. His method is: let the soldiers line up in three rows (three people in each row), then five rows (five people in each row) and finally seven rows (seven people in each row). As long as he knows the approximate number of soldiers in this group, he can calculate the exact number of soldiers in this group according to the number of soldiers in the last line of these three parades. If Han Xin saw three processions at that time, and the number of soldiers in the last line was 2, 2 and 4 respectively, knowing that the number of soldiers in this team was about 300 to 400, can you quickly calculate the number of soldiers in this team?
18.*** How many peaches Professor Li Zhengdao, a famous American physicist, visited the University of Science and Technology of China while giving lectures in China, and met some students in the juvenile class? During the dinner, I asked the students in the junior class a question: "There are five monkeys sharing a string of peaches, but they can't share them equally." So everyone agreed to go to bed first and talk about it tomorrow. At night, a monkey sneaked up and threw a peach down the mountain, which was just divided into five parts. It hid its part and went to sleep again. The second monkey got up and threw a peach, which happened to be divided into five parts and put away his own. The third, fourth and fifth monkeys are all like this. If you throw one, you can divide it into five parts and put your own away. How many peaches are there? Note: children may not be able to solve this problem. If I add a condition, there are 1020 peaches left in the end. Let's see who can work it out
19. Nine Chapters of Arithmetic is one of the oldest mathematical works in China. This book is divided into nine chapters and has 246 themes. One of them is like this: a person uses a car to transport rice from place A to place B. The car carrying rice walks 25 kilometers a day, the empty car without rice walks 35 kilometers a day, and goes back and forth three times on the 5 th. How many kilometers are there between these two places?
20. Problems in Zhang Shu Zhang Shu is an ancient book in China. There is a topic in the book: Every cock is worth 5 yuan, every hen is worth 3 yuan, and every chick is worth 1 yuan. Now 100 yuan is used to buy 100 chickens. /kloc-How many chickens are there in 0/00 chickens?
2 1. The problem in Arithmetic Unity is one of China's ancient mathematical works. There is a topic in the book: A took a fat sheep and asked the shepherd, "There are about 100 sheep you drove." The shepherd replied, "If you double this flock of sheep, add half of the original flock of sheep, and add 1/4 of the original flock of sheep, even the fat sheep you are leading will only make up a hundred." Please count how many sheep this shepherd has driven.
22. Washing dishes (China ancient title) A woman was washing dishes by the river. Passers-by asked her why she washed so many dishes. She replied: There are many guests at home. They share a rice bowl for every two people, a soup bowl for every three people and a vegetable bowl for every four people, and * * * uses 65 bowls. Can you infer how many guests have been to her house from the situation of her household bowls?
23. Monks eat steamed buns (an old topic in China). Big monks eat four, and young monks eat 1. Monk monk 100, * * * ate 100 steamed bread. How many monks are there? How many steamed buns do you eat?
24. Hundred Eggs (an ancient foreign topic) Two farmers brought 65,438+000 eggs to the market for sale. They sell the same money. The first man said to the second man, "If I have as many eggs as you, I can sell 15 klitsche". The second man said, "If I have your eggs, I can only sell them for 6 2/3 kilometers." Ask them how many eggs each has.