A person went out to play 10 Jin of wine at night and met a friend on his way home. It happens that this friend is going to play wine, too. But there is no extra wine in the restaurant, and it's getting late at this time, and other restaurants are closed, so my friend looks worried. So the man decided to give him half of his wine, but his friend only had a barrel of 7 Jin and 3 Jin, and neither of them had a scale. How can he divide the wine equally?

30. How much did you lose?

One day, a customer came to a store in Xiao Zhao and chose goods from 20 yuan. The customer took out 50 yuan. Xiao Zhao couldn't change it without change, so he went to Han Xiao's shop next door to change 50 yuan into change, and then came back to give the customer 30 yuan change. After a while, Han Xiao came to Xiao Zhao and said that it was fake money just now. Xiao Zhao immediately replaced Xiao Li with real money.

Q: How much did Xiao Zhao lose in this process?

3 1. The horse drinks water.

Lao Wang wants to raise horses, and he has such a pool of water:

If you have 30 horses, you can drink all the water in 8 days;

If you have 25 horses, you will drink all the water in 12 days.

Lao Wang wants to raise 23 horses. How many days will it take to find water for them?

32. Competition results.

Xiao Qiang participated in the knowledge and ability competition for primary school students. After the game, Lele asked Xiao Qiang where he won. Xiao Qiang deliberately sold a pass and said, "The product of my score, ranking and my age is 1958. You guess. " Lele thought for a long time, and then told Xiao Qiang's score, ranking and age.

Do you know how old Xiao Qiang is? What about his game rankings and scores?

33. Buy and sell clothes.

Xiao Lihua 90 yuan bought a dress. She had a brainwave and sold the dress for 65,438+020 yuan. She thought it was a good deal, so she bought another dress 100. She thought 150 yuan sold it, but she lost money and 90 yuan sold it. Q: Do you think Xiao Li lost or won? How much did you lose or gain?

34. The hen counts.

The hen took her children out to find food. In order to prevent the chicken from getting lost, she always counts, counting from back to front to 8 and from going to back to 9. Mother hen finally figured out that she had 17 children, but mother hen clearly knew that she didn't have that many children. So how many children does this confused hen have? Why did the hen count wrong?

35. Cross the bridge.

On Sunday, the Lolo family went out to play. Because they were so happy, they forgot the time. They came to a small river in panic. There is a bridge over the river, and only two people are allowed to cross it at a time. If they cross the bridge one by one, Lolo needs 15 seconds, sister needs 20 seconds, father needs 8 seconds, mother needs 10 seconds and grandma needs 23 seconds. If you cross the bridge together, you can only walk at a slow pace. It takes two minutes to walk after crossing the bridge. The lolos are anxious to catch the last bus across the street. They only have 3 minutes to ask Xiao Ming's family if they can catch the bus. How should they cross the bridge? How long did it take to cross the bridge?

36. sell apples.

A businessman drove a carriage 50 kilometers to the county seat to sell 50 boxes of apples, each with 30 apples. This carriage can pull 10 boxes of apples at a time. But the businessman likes to take his son with him when he goes to town. On the way to town, his son ate an apple every kilometer because he was thirsty. So how many apples can a businessman sell when he walks to Xiancheng?

37. The frog jumped into the well.

There is a well with a depth of 4 meters and a smooth wall. There is a frog at the bottom of the well that always jumps out of the well, but this frog can jump up to 3 meters at a time. Do you think this frog can jump out of the well several times? Why?

38. Divide the peaches.

The kindergarten teacher gave peaches to three groups of children. If only the first group of children are given peaches, each child will get seven peaches. If you only give it to the second group, each child can get 8; If you only give it to the third group, each child will get 9.

Now the teacher will divide these apples into three groups of children equally. Can you tell her how many apples to give to each child?

39. Transportation of rice.

There is 100 stone rice, which needs to be transported to Mihang by ox cart. Mihang happened to find 100 ox carts of different sizes. The big ox cart can transport three stones at a time, the middle ox cart can transport two, and the small ox cart needs two to transport one. Excuse me, if you want to transport all the rice and 100 cars, how to distribute the ox carts?

40. How many marbles are there?

Play marbles with Tian Tian on the grass every day and say, "Give me two of your marbles, so my marbles will be three times as big as yours." Tian Tian said to Tian Tian, "Give me two of your marbles, so that we can have as many marbles." Let's analyze, how many marbles are there with candy every day?

4 1. Will it get dark?

School is over at 6 o'clock, and it's still raining. In order to test Qingqing, Lily said to Qingqing, "Qingqing, it has been raining for three days. It seems that it will not stop. Do you think it will be dark after 40 hours? "

42. Turn on the light.

Mom and Xiaojun went shopping, and it was dark the next day after they came back. Mom asked Xiaojun to turn on the light. Xiaojun tried to play a trick on his mother and pulled the light seven times. Guess if Xiaojun is turned on? What if you pull it 20 times? What about 25 times?

43. Divide the bookshelves.

After graduation, five people in the dormitory need bookcases. A * * * has three identical bookshelves. Give these three bookshelves to three people, and then each of the three people assigned to the bookshelves will take out 1000 yuan and share it equally with the other two people. Everyone thinks this score is quite reasonable. After that, one of them didn't know how much a bookcase was. Can you tell him?

44. Buy drinks.

Xiao Li has 40 yuan. He wants to buy drinks with them. The boss told him that 2 yuan could buy one bottle of drinks, and four bottles could be exchanged for one. Then, how many bottles of drinks can Xiao Li buy

45. Cut the watermelon.

Cut a large watermelon evenly with a fruit knife. How many pieces of watermelon can you cut at most? A * * * chop 10 knife? How many pieces can you cut at least?

46.how old are they?

A family has four sons. Multiply the ages of these four sons to get 15. So, how old are the four sons in this family?

47. Which number is the smallest?

There are four numbers A, B, C and D, which have the following relations: the sum of A and B is greater than the sum of C and D, the sum of A and D is greater than the sum of B and C, and the sum of B and D is greater than the sum of A and C. Can you know which of these four numbers is the smallest from these conditions?

48. do the problem.

The teacher assigned two homework questions to 60 students in the class, of which 40 were right in the first question, 365,438+0 were right in the second question, and 4 were wrong in both questions. So, can you figure out the number of people who answered both questions correctly?

49. Solve the problem

My brother asked his sister to help him solve a math problem. Multiply a two-digit number by five to get a three-digit number, and the sum of the units of the three-digit number and the hundred-digit number is exactly equal to the number in the tenth place. After reading it, my sister was very anxious and felt that she could not get a clue. Can you help her get the answer to this question?

50. The color of the headscarf.

A group of people went for an outing together. Some of them are wearing blue headscarves, others are wearing yellow headscarves. In the eyes of people wearing blue headscarves, there are as many blue headscarves as there are yellow headscarves, while in the eyes of people wearing yellow headscarves, there are twice as many blue headscarves as yellow headscarves. So how many people wear blue headscarves and how many people wear yellow headscarves?

5 1. Divide the jelly.

Xiaohong's mother bought a lot of jelly. There are 48 jellies. Xiaohong's mother said to Xiaohong, if you can divide these jellies into four parts, so that the first part adds 3, the second part subtracts 3, the third part multiplies 3 and the fourth part divides 3, the result is the same, then you can eat these jellies. Xiaohong thought for a long time and finally came up with this problem. Do you know how to divide the smart ones?

52. Buy books.

Xiaohong and Xiao Li go to Xinhua Bookstore to buy books. They both want to buy the book Comprehensive Exercise, but they don't have enough money. Xiaohong is short of 4.9 yuan and Xiaoli is short of 0. 1 yuan. They bought a book with their money, but the money is still not enough. So, what's the price of this book?

Intermediate question:

53. When do the three stitches coincide?

During the day (including day and night), can the three hands of the clock coincide? When will it coincide?

54. What is the probability?

At a trade fair, five people entered the trading hall and had to give their briefcases to the security guard for verification. After verification, the security guard returned them. Due to the negligence of the security guard, four people left and found that everyone didn't take a briefcase. Think about it, what is the probability of this happening? What if it's n people? (n & gt 1)

55. Sell silk scarves.

A jewelry store handled the goods before closing, and the price of a silk scarf in 20 yuan could not be sold, so the boss decided to reduce the price to 8 yuan. As a result, no one wanted it, so the boss had to reduce the price again, down to 3.2 yuan, and still couldn't sell it. Helpless, the boss had to reduce the price to 1.28 yuan. The boss thinks that if it can't be sold this time, it will be sold at the cost price. What is the cost price of this silk scarf?

56. Buy apples.

There are five people to buy apples. The number of apples they bought was A, B, C, D and E respectively. Given that A is three times that of B, four times that of C, five times that of D and six times that of E, what is the minimum value of A+B+C+D+E?

57. getaway car.

A car accident happened in a city, and the driver ran away after hitting someone. It is understood that there are only two colors of cars in this city, 25% are black and 75% are gray. When the accident happened, a person witnessed the process of the accident. He testified that it was a gray car, but according to expert analysis, the possibility of seeing the right situation at that time was 90%. So, what is the probability that the escaped car is a black car?

58. Calculate the volume.

There was once a story that a student who graduated from the Department of Mathematics of a famous university was arrogant because he was the best in the whole school. An old man didn't like it very much, so he gave him a question to ask for a paper. The old man just took a light bulb and asked him to calculate its volume. Arrogant students took a ruler to calculate for a long time, remembered a lot of data, and didn't work it out, just listed a complicated formula. The old man just filled the light bulb with water and then measured the volume of water with a measuring cylinder. Calculating the volume of a light bulb is very simple.

Now, if you only have a ruler and a beer bottle in your hand, the bottom 2/3 of this beer bottle is a right cylinder, and only the top 1/3 is not a right cone. Taking the above example as a reference, how to find its volume?

59. What is the unit price of pigs, cows and sheep?

There are 2 pigs, 3 cows and 4 sheep, and the total price is less than 1000 yuan. If two pigs and 1 cow are put together, or three cows and 1 sheep are put together, or four sheep and 1 horse are put together, then their respective total price is exactly 1000 yuan. So what is the unit price of pigs, cattle and sheep?

60. Pay.

Someone rented a car and set out from City A to City B. On the way, they met two acquaintances in a small town, so the three of them went together. The three men stayed in city B for a day to go back to city A, but his friend A decided to get off at the town where they met. Friend B decided to go back to City A with him, and they went Dutch on AA system. It costs 40 yuan to go back and forth from city A to city B, and the town where they met is just the midpoint of AB. How should three people pay?

6 1. Planting corn.

Once upon a time, there was a landlord who hired two people to grow corn for him. One of them is good at farming, but not good at growing corn. The other, on the contrary, is good at growing corn and not good at farming. The landlord asked them to plant 20 acres of corn, and each of them was allowed to pack half of it. So worker A started farming in the north and worker B started farming in the south. It takes 40 minutes for A to plow an acre of land and 80 minutes for B, but the speed of B corn is three times faster than A ... After planting corn, the landlord gives them twenty taels of silver according to the workload. Q: How fair is it to let them share the twenty taels of silver equally?

Change.

A Hong Kong man traveled to Thailand and took a fancy to a camera in a shop. This kind of camera holster and camera costs HK$ 3,000 in Hong Kong, but the shopkeeper deliberately charges US$ 4 10, and not Thai baht, only US dollars, not to mention HK$. Now the price of the camera is 400 yuan more than that of the holster, and the rest is the money of the holster. The Hong Kong man has now paid $65,438+000. Can he buy this holster back?

63. Wolf and sheep.

There are a pack of wolves and a pack of sheep. It takes a wolf ten minutes to catch up with a sheep. If a wolf chases a sheep, there is no sheep to chase. If two wolves chase a sheep, a sheep can escape. Q, how many sheep will there be in ten minutes?

64. Guess the numbers.

Three classmates of Xiaoming come to play with Xiaoming. Xiao Ming said, "Let's play a game." The other three agreed. Xiao Ming put a piece of paper on the foreheads of the three of them, with a positive integer written on it, and the sum of the two numbers is equal to the third. But all three of them can see other people's numbers but not their own. Then, Xiao Ming asked the first classmate: Do you know what is written on your note? The classmate shook his head and asked the second one. He also shook his head. He shook his head when he asked the third one, so Xiao Ming asked the first one again. The first and second students still don't know. When he asked the third one, he said: 144! Xiao Ming was surprised. So, what are the other two numbers?

65. snails crawl.

It is said that one hundred snails were trapped on a stick 1m long at the same time because of the flood. Snails can climb 1cm in one minute. If they meet two snails, they will turn around and continue to climb. So, how long does it take to put all the snails into the water?

66. Businessmen buy horses.

A businessman bought a horse from a herdsman for 1000 yuan. In a couple of days, he thought he had suffered, and asked the herdsmen to return to 300 yuan. The herdsman said, "Yes, as long as you buy 12 nails on horseshoes according to my requirements, the first one is 2 yuan, and the second one is 4 yuan. According to the fact that each nail is twice as big as the previous one, I'll give you the horse. How about it? " The businessman thought he took advantage and agreed. What's the final guess? Why?

67. Bus seats.

There is a bus that always runs on a fixed route. Besides the starting station and the terminal station, there are eight stops in the middle. If the bus has passengers at the starting station, it is not the terminal. One of the passengers who get on the bus at each station happens to get off from this station to every subsequent station. If you are a bus conductor, how many seats do you have to arrange at least to ensure that every passenger has a seat?

68. Sell watermelons.

Xiao Zhang and Xiao Wang often sell watermelon together. One day, Xiao Zhang had something at home, so he entrusted Xiao Wang with the watermelon to be sold. Before selling, Xiao Zhang had as many watermelons as Xiao Wang, but Xiao Zhang's watermelons were smaller, so he sold three watermelons at the price of 10, while Xiao Wang's watermelons were larger, so he sold two watermelons at the price of 10. Now Xiao Wang mixes all the watermelons and sells them at the price of 5 20 yuan for the sake of fairness. When the watermelons were sold out, Xiao Zhang and Xiao Wang began to divide the money. At this time, they found that the money was 20 yuan less than what they sold alone. What's going on here? How many watermelons did Xiao Zhang and Xiao Wang have then?

69. The alarm clock in the small supermarket.

Xiao Zhang bought some things in a small supermarket. When he left, he found that the clock in the supermarket pointed to 1 1: 50. When I got home, the clock at home was 12: 05, but Xiao Zhang found that he still had some important things to buy, so he returned to the small supermarket at the same speed. When I arrived at the supermarket, I found that the clocks in the supermarket pointed to 12 and 10. The clock at home is very accurate, so is the clock in the small supermarket fast or slow?

70. How many people were lost?

Nine people lost their way in the desert, and all their food was only enough for these people for five days. The next day, these nine people met a group of lost people. This group of people have no food. Everyone calculated that the two teams can only eat food for three days. So, how many people did the second team lose?

7 1. Two people race.

A boy and a girl are running together. When the boy reached the finish line of100m, the girl ran to the place of 90m ... Now if the boy's starting line is set back to 10m, will both men and women start at the same time?

72. Free meals.

There are five people in a family. On weekends, the family always goes to a high-end restaurant for dinner. After eating several times, the family suggested that the boss give them a discount and give them a free meal. The clever boss thought for a moment and said, "Your family is also a frequent visitor here, as long as each of you changes seats every time until the arrangement order of the five of you is not repeated." After that day, don't say I'll give you a free meal, just 10. How's it going? "So, how long will the family eat in this restaurant before the boss can deliver 10 meals for free?

73. The speed of ringing the bell.

In a temple, monks ring bells every day. The first monk 10 seconds rings 10, the second monk rings 20 times in 20 seconds, and the third monk rings 5 times in 5 seconds. The time spent by each of these monks is calculated as follows: from the first knocking to the last knocking. Do these monks ring bells at the same speed? If it's different, knock 50 times at a time, which one of them knocks first.

74. How early is the train?

One day, Xiao Zhang took a train to deliver goods to Xiao Wang. It was supposed that Xiao Wang would pick him up. But when the train arrived at the station ahead of time, Xiao Zhang began to walk to Xiao Wang alone. After walking for half an hour, I met Xiao Wang head-on. Xiao Wang took something and turned around and went back without stopping. When Xiao Wang arrived at his residence, he found that the delivery time was earlier than usual 10 minute. So, how long did the train arrive earlier than usual?

How many walnuts are there?

There is a pile of walnuts. If there are five numbers of five, there are four left. If there are four numbers of four, there are three left; If there are three numbers of three, there are only two left; If there are two numbers of two, it leaves 1. So, how many walnuts are there in this pile at least?

Advanced questions:

76. Start work.

There is a young man who has been working on the construction site for 24 consecutive days, and his salary is 190 yuan (daily salary is 10 yuan, and he is sent to 5 yuan for half a day on Saturday, but he is not paid on Sunday). He can't remember when 1 started work in late October, but he knows that 1 this month is Sunday, which is the end of his work.

77. three musketeers.

There is a story in ancient England: three musketeers took a fancy to a girl at the same time, and this girl was difficult to choose, so he proposed that they should compete with each other in marksmanship. She will marry whoever wins. The accuracy of the first musketeer is 40%, the accuracy of the second musketeer is 70%, and the accuracy of the first three musketeers is 100%. Since everyone knows each other's strength, it's fair: the first musketeer shot the other two musketeers first, then the second, and finally three musketeers. And so on until there is only one person left. So which of these three people has the best chance of winning? What strategy should they adopt?

78. Tickets are sold in cinemas.

Someone queued up to enter the cinema, and the fare was 50 cents. After checking, the number of people entering the cinema is a multiple of 2. Among these people, half of them only have 50 cents, and the other half have a paper ticket of 1 yuan. When the cinema started selling tickets, there was no 1 cent. How many kinds of queuing ways can cinemas get 50 cents change every time they buy a ticket for 1 yuan? (Everyone who owns 1 yuan is a paper money, and cannot be broken into two 50-cent notes. )

79. Weigh.

There are four pigs, all of which weigh a whole kilogram. If these four pigs are weighed in pairs, they will be weighed five times, namely 99, 1 13, 125, 130, 144, and two pigs are not weighed together. So, how much does the heavier pig weigh?

80. How far is it?

Fang Jing is a child who loves reading. On her bookshelf, there are books on various subjects, and in one of the squares, they are all history books. In this square, Fang Jing is placed from left to right in historical order, because it has been placed for too long, which has caused moths. One of them, The History of China is divided into four volumes; The total thickness of each book is 5 cm, and the thickness of the front cover and back cover is 0.5 cm.

If a moth bites from the first page of the first book to the last page of the fourth book, can you calculate the biting distance of this moth?

8 1. Ice and water.

When we were very young, we understood the truth that "heat expands and cold contracts"; But there is a very special substance that does not follow this truth, that is, water, sometimes it is "cold expansion and heat contraction." After many experiments, it is concluded that when water becomes ice, its volume will increase111. Taking this as a reference, do you know how much the volume of ice will decrease if it melts into water?

82. Watchmakers install watches.

There is a very careless old watchmaker. Once, he installed clocks and watches for a church. As a result, he accidentally reversed the short hand and the long hand of the clock, and the speed of the short hand was 12 times that of the long hand. As it was 6 o'clock in the morning, the watchmaker pointed the short pointer to "6" and the long pointer to "12". After the installation, the watchmaker went home. As a result, careful citizens found that the clock was still 7 o'clock, and soon it was 8 o'clock. People informed the watchmaker to have a look. The watchmaker was very busy, so he said to see it in the afternoon. When the watchmaker arrived, it was already past 7 pm. The watchmaker visited the church, had a good time and went home. But the clock still went to 8: 00 or 9: 00, and the man went to the watchmaker again At 8 o'clock the next morning, the watchmaker came to use a pair of watches, which was still correct. Please think about it. When he set his watch, it was 7 o'clock and 8 o'clock.

83. buy onions

One person buys onions, 1 yuan a catty. The man discussed with the onion seller that he would buy all the onion leaves if they were weighed separately, and the onion white was weighed separately. The onion seller thought that he would not lose money anyway, so he agreed, only to find that he lost a lot of money. Do you know why onion sellers lose money? I let Liner think for a moment, and finally figured it out under my reminder. If I buy it in stages, then 1 yuan can buy 2 Jin of onions, but what is the reason?

84. Guess the age.

Two good friends met on the road. So they talk to each other. A said to B, "I remember you had three daughters. How old are they now? " B said, "Their product is 36, and their age happens to be today's date, which is 13." "Hey, man, you haven't told me your daughter's age." "Oh, really? My little daughter has red hair. " B said. "Then I know how old your three daughters are." A replied. Do you know the ages of B's three daughters?

85. Find the surface area.

There is a cuboid iron block that can be sawed into three cubes. If sawed into a cube, the surface area will increase by 20 square centimeters. So, what is the original surface area of this cuboid iron block?

86. Packaging books.

Xiaohong wants to put seven schoolbags 40cm long, 30cm wide and 5cm thick together. Can you tell her how many square centimeters of wrapping paper she needs at least?

87.how many umbrellas are there?

There are three kinds of umbrellas *** 160. If the red umbrella 1/3, pholiota adiposa 1/4 and blue umbrella 1/5 are removed, there is still 120. If 1/5 of the red umbrella, 1/4 of pholiota adiposa and 1/3 of the blue umbrella are removed, 1 16 remains. Excuse me, how many umbrellas are there in these three kinds?

88. Seal.

There is a businessman who often asks horses to consign goods for him. Some of these horses are strong and some are weak. In order to distinguish them, the merchant decided to mark the horses in each area by stamping. When putting a seal on a horse, the horse will scream for three minutes because of pain. Suppose the horses' calls do not overlap. If 15 horse is on fire, how long can you at least listen to the horse barking?

89. Count the lanterns.

During the National Day, a hotel installed many lanterns in the lobby of the hotel to show off its luxury. One way is to install a big lantern and two small lanterns under a lamp, and the other way is to install a big lantern and four small lanterns under a lamp. There are 360 big lanterns and 360 small lanterns 1200. How many lights do you think there are in the lobby of this hotel?

90. Servant work.

A man works as a servant in a big family. The owner of a big house gave his servant a piece of wood 3 feet long and 1 foot wide, and asked him to make it into a wooden post. The servant put this piece of wood on the scale and weighed it, knowing that this piece of wood weighs 3 Jin, while the wooden post to be made weighs only 2 Jin. So the servant cut 1 cubic foot of wood from the square, but the master thought it was unreasonable for the servant to do so. How should a servant explain to the master?

9 1. Cleverly divide the heritage.

A man was terminally ill and died soon. This man had a legacy of 70,000 yuan before his death, and his wife was pregnant before his death. The man said in his will that if the wife gave birth to a son, the inheritance of the woman was half that of the son, and if it was a daughter, the inheritance was twice that of the daughter. As a result, the woman gave birth to twins, a son and a daughter. Now the lawyer is in a dilemma. At this moment, a high school student said a method to solve the problem easily. Do you know how this high school student is divided?

92. Black and red handkerchiefs.

A class of students held a party on New Year's Day. One of the game sessions requires the participation of all students in the audience. The monitor hung a handkerchief on everyone's back. Handkerchiefs are only black and red, and there is at least one black handkerchief. No one can see the color of the handkerchief on his back, only others. The monitor showed everyone the handkerchiefs on others' backs and then turned off the lights. If someone thinks their handkerchief is black, they will cough. The first time I turned off the lights, there was no response. After turning off the lights for the second time, there was still no response. After turning off the lights for the third time, I heard a continuous cough. How many people do you think have black handkerchiefs on their backs at this time?

93. Wages.

There are two people working on the construction site. Because one is an apprentice and the other is a mechanic, the salary is different. The wages of mechanics are $20 more than those of apprentices, but the difference between them is $265,438 +0. What do you think their salary is?

94. Snails climb the triangle.

Put the third snail on each corner of a regular triangle. Each snail begins to move in a straight line to the other snail, and the target angle is randomly selected. So what is the probability that snails won't collide with each other?

95. Buy toys

Six children went to the toy store to buy toys. They brought 14 yuan, 17 yuan, 18 yuan, 2 1 yuan, 25 yuan and 37 yuan respectively. When they arrived at the toy store, they all took a fancy to a game machine. Seeing the pricing, all six people found that the money was not enough, but three people had money together. So, what is the price of this game machine?

96. Who is the first in the tortoise-rabbit race?

The original version of the tortoise-rabbit race was because the rabbit loved to play, and the tortoise won. But according to the rabbit's speed, it can far exceed the tortoise. Now there is a total distance of 4.2km. Rabbits run 20km per hour and turtles run 3km per hour. Keep running. But the rabbit runs and plays. It runs 1 minute, and then plays 15 minutes. Run for another 2 minutes, and then play 15 minutes ... So, how many minutes are the people who arrive at the finish line first faster than those who arrive at the finish line later?