1 Suppose there is a pond with infinite water. At present, there are two empty kettles with a capacity of 5 liters and 6 liters respectively. The problem is how to get 3 liters of water from the pond with only these two kettles.
Zhou Wen's mother is a chemist in Yulin Cement Plant. One day, Zhou Wen came to the laboratory to do his homework. I want to go out to play when I'm done. "Wait, mom will test you on another question," she continued. "Look at these six glasses for laboratory testing. The first three are all water, and the last three are just empty. Can you just move 1 glass and separate the glass filled with water from the empty one? " Zhou Wen loves to think, and is a famous "cleverness" in the school. She just thought about it for a while and then did it. Please think about it, how does "cleverness" work?
Three boys fell in love with a girl at the same time. In order to decide which of them can marry the girl, they decided to duel with pistols. Xiao Li's hit rate is 30%, and Xiao Huang is better than him, with a hit rate of 50%. The best shooter is Kobayashi, who never makes mistakes, and the hit rate is 100%. Because of this obvious fact, in order to be fair, they decided in this order: Xiao Li shot first, Huang Xiao second and Xiao Lin last. And so on until there is only one person left. So which of these three people has the best chance to survive? What strategies should be adopted?
There are two prisoners in the cell. Every day, the prison will provide this cell with a can of soup for two prisoners to share. At first, these two people often have arguments, because one of them always thinks that the other has more soup than his own. Later, they found a way to kill two birds with one stone: one person divided the soup and let the other person choose first. In this way, the dispute was settled. But now there is a new prisoner in this cell, and now there are three people sharing the soup. New ways must be found to keep the peace between them. What should I do? Press: Psychological problems, not logical problems.
Put n round coins of the same size on a rectangular table. Some of these coins may not be completely on the table, and some may overlap each other; When another coin is placed on the table with its center, the newly placed coin will definitely overlap with some of the original coins. Please prove that the whole desktop can be completely covered by 4n coins.
A ball and a ruler about 2/3 of the diameter of the ball. How do you measure the radius of the ball? There are many ways to see who is smarter.
Five one-dollar coins of the same size. Require two-phase contact, what should I say?
8 Mr. S, Mr. P and Mr. Q all know that there are 16 playing cards in the desk drawer: spades A, Q, 4, flowers J, 8, 4, 2, 7, 3, diamonds K, Q, 5, 4, 6, A and 5. Professor John chooses a card from 16 card, tells Mr. P the number of points in this card, and tells Mr. Q the color of this card. At this time, Professor John asked Mr. P and Mr. Q: Can you infer what this card is from the known points or colors? So, Mr. S heard the following conversation: Mr. P: I don't know this card. Mr q: I know you don't know this card. Sir: Now I know this card. Mr. Q: I know that, too. After listening to the above conversation, Mr. S thought about it and correctly deduced what this card was. Excuse me: What kind of card is this?
A professor who teaches logic has three students, all of whom are very clever! One day, the professor gave them a question. The professor put a note on everyone's forehead and told them that everyone had written a positive integer on the note, and the sum of some two numbers was equal to the third! The professor asked the first student: Can you guess your own number? Answer: No, ask the second, the third, the first, the second, the third: I guessed right, it was 144! The professor smiled with satisfaction. Can you guess the numbers of the other two?
10 A car accident occurred in a city. There are only two colors of cars in this city, blue 15% and green 85%. When the accident happened, someone saw him at the scene and testified that it was a blue car. However, according to on-site experts' analysis, the probability of correct conditions at that time was 80%. So, what is the probability that the car involved is a blue car?
1 1 A man has 240 kilograms of water, and he wants to transport it to the arid area to make money. He can carry up to 60 kilograms at a time, and he needs to consume 1 kilogram of water per kilometer (even if it is water consumption). Assuming that the price of water is zero at the place of departure, it is directly proportional to the transportation distance (that is, 10 km/0 yuan/kg, 20 km/kg/20 yuan ...), and assuming that he must return safely, how much money can he earn at most?
12 Now * * there are 100 horses and 100 stones. There are three kinds of horses, big ones; Medium and small horses. A big horse can carry three stones at a time, a medium-sized horse can carry two stones, and a pony can carry two stones. How many horses do you need? The key to the problem is that it must be exactly 100 horses.
131= 52 =153 = 2154 = 2145 so 5=?
14 2n people lined up to enter the cinema, and the fare was 50 cents. Of these 2n people, n people only have 50 cents, and the other n people have 1 USD (paper tickets). When the stupid cinema started selling tickets, there was no 1 cent. Q: How many queuing methods can make the cinema get 50 cents change whenever a person with $65,438+0 buys a ticket? Note: A person with $ 1 = 1 has paper money and cannot break it into two 50 cents.
15 A person bought a chicken for 8 yuan and sold it for 9 yuan. Then he thought it was not worthwhile, 10 yuan bought it back and sold it to another person for 1 1 yuan. Ask him how much money he earned.
16 There is a sports competition * * * with m events, in which athletes A, B and C take part. The first place, the second place and the third place in each project were scored x, y and z respectively, where x, y and z are positive integers, and X >；; Y>z. In the end, A got 22 points, B and C both got 9 points, and B won the first place in the 100 meters. Find the value of m and ask who is the second place in the high jump?
17 premise: 1 There are five houses and five colors. The owners of each house have different nationalities. Each of these five people only drinks one kind of drink, smokes one brand of cigarettes and keeps a pet. No one keeps the same pet and smokes the same brand of cigarettes. Tips for drinking the same drink: 1 British people live in red houses, 2 Swedes have dogs, 3 Danes drink tea, 4 green houses are on the left of white houses, 5 owners of green houses drink coffee, 6 people who smoke PALL MALL have a bird, 7 owners of yellow houses smoke Dunhill cigarettes, 8 people who live in the middle house drink milk, and 9 Norwegians live in the first house./kloc People live next to cat owners 1 1 Horse owners live next to smokers in Dunhill Road 12 Blue owners smokers drink beer 13 Germans smoke prince cigarettes 14 Norwegians live next to blue houses 15 People who smoke mixed cigarettes drink mineral water next door. The question is: Who raises fish?
185 People come from different places, live in different houses, keep different animals, smoke different brands of cigarettes, drink different drinks and like different foods. Determine who owns a cat according to the following clues. 1. The red house is on the right of the blue house and the left of the white house (not necessarily adjacent). The owner of the yellow house is from Hong Kong, and his house is not on the far left. People who like pizza live next door to people who like mineral water. Beijingers love Maotai and live next door to Shanghainese. Hilton smokers live next door to the owner's right. 6. People who like beer also like chicken. 7. People in green houses have dogs. 8. People who love noodles live next door to snake farmers. 9. There is a neighbor from Tianjin who likes beef, and another from Chengdu. 10. Fish farmers live in the rightmost house. 1 1. Marlboro smokers live between Hilton smokers and "555" smokers. 12. People in the red house like drinking tea. 13. People who love wine live next door to people who love tofu. 14. People who smoke Hongtashan cigarettes don't live next door to people who smoke Jianpai cigarettes, nor are they adjacent to Shanghainese. 15. Shanghainese live in the second house on the left. 16. People who love mineral water live in the middle house. 17. People who like noodles also like to drink. 18. People who smoke "555" live on the right side than those who smoke Hilton cigarettes.
19 The landlord attached the cards 2, k, q, j, 10, 9, 8, 8, 6, 5, 5, 3, 3, 7, 7, 2, A and Xiao Wang in the landlord's hand. The requirement is that the three companies don't play the wrong cards, and the landlord will win or lose. Q: Who will win?
There is a diamond at the door of every elevator from the first floor to the tenth floor. Diamonds vary in size. When you take the elevator from the first floor to the tenth floor, the elevator doors on each floor will open once, and you can only bring diamonds once. How can I get the biggest one?
2 1U2 choir will arrive at the concert site in 17 minutes. On the way, it is necessary to cross a bridge. Four people start from the same end of the bridge. You have to help them reach the other end. It was dark and they only had one flashlight. At most two people cross the bridge at a time, and they must hold flashlights when crossing the bridge, so someone has to walk back and forth at both ends of the bridge with flashlights. You can't send out the flashlight if you throw it away. Four people walk at different speeds. If two people go together, the slower one shall prevail. It takes 1 minute for Bono to cross the bridge, 2 minutes for Archie, 5 minutes for Adam and 10 minute for Larry to cross the bridge. How do they cross the bridge in 17 minutes?
A family has two children, one of whom is a girl. Ask the probability that the other person is also a girl (assuming that the probability of giving birth to boys and girls is the same).
Why is the cover of the sewer round?
There is a 7-gram and 2-gram weight and a balance. How to use these items to divide140g salt into 50g and 90g respectively for three times?
25 Chip Test: There are 2k chips, and there are more known good chips than bad chips. Please design an algorithm to find a good chip and explain the upper limit of the number of comparisons you use. Among them, when a good chip is compared with other chips, it can correctly give whether another chip is good or bad. When a bad chip is compared with other chips, it will randomly give good or bad.
It is said that there are twelve eggs, one of which is bad (the weight is different from other eggs). Now it is required to weigh three times with a balance to know which egg is bad!
27 100 people answered five questions, 8 1 people answered the first question correctly, 9 1 people answered the second question correctly, 85 people answered the third question correctly, 79 people answered the fourth question correctly, 74 people answered the fifth question correctly, and those who answered three or more questions correctly were regarded as passed. So, among the 100 people, at least
Eason Chan has a song called "Ten Years" and Lu Shan has a song called "3650 Nights". Now, how many days may there be in ten years?
2911121111/kloc-0.
It takes an hour to burn an uneven rope. How to judge half an hour with it? It takes 1 hour to burn an uneven rope from beginning to end. Now several ropes are made of the same material. How to time an hour and fifteen minutes by burning rope? (Microsoft's pen test)
31* * There are three kinds of medicines, weighing 1g, 2g and 3g respectively, which are put in several bottles. Now it can be determined that there is only one medicine in each bottle, and there are enough tablets in each bottle. Can you know what medicine is in each bottle at once? What if there are four drugs? What about the fifth category? What about n-class (n-countable)? What if there are * * * M bottles containing n kinds of drugs (m, n is a positive integer, and the quality of drugs is different but the quality of various drugs is known)? Can you know what each bottle of medicine is? Note: Of course, there is a price. We don't need to weigh the medicine.
Suppose there are three sealed boxes on the desk. One box contains two silver coins (1 silver coin = 10p), one box contains two nickel coins (1 nickel coin = 5p), and the other box contains 1 silver coin and 1 nickel. These boxes are labeled 10p, 15p, 20p, but each label is wrong. You can take out 1 coin from a box and put it in front of the box. When you see this coin, can you tell what is in each box?
There is a big watermelon, cut evenly with a fruit knife, a total of 9 knives. How many pieces can you cut at most, and how many pieces can you cut at least? It's mainly the process, not the result.
A huge circular pool surrounded by a rat hole. The cat chased the mouse to the pool, and the mouse fell into the pool before it could get into the hole. The cat continued to try to catch the mouse along the pool. It is known that V cat =4V mouse. Ask the mouse if there is any way to get rid of the cat's chase.
There are three buckets, two big ones can hold 8 Jin of water and one small one can hold 3 Jin of water. There is 16 Jin of water now. The two big barrels are 8 kg barrels, and the small one is empty. How can this 16 kg of water be given to four people, each with 4 kg? Without any other tools, four people brought their own containers, and the separated water could not be returned.
Once upon a time, there was an old watchmaker who installed a big clock for a church. He was old and dizzy, and he put the long and short needles wrong. But the speed of the short needle is 12 times that of the long needle. It was 6 o'clock in the morning when it was assembled. He pointed the short needle at "6" and the long needle at "12". The old watchmaker packed it and went home. People look at this clock at 7 o'clock and 8 o'clock. It was strange, so they immediately went to the old watchmaker. When the old watchmaker arrived, it was already past 7 pm. He took out a pair of pocket watches, and the clock was accurate. He suspected that people were playing tricks on him, so he got angry and went back. The clock was still running at 8 o'clock and 9 o'clock, and people went to the watchmaker again. The old watchmaker came to use a pair of watches at 8 o'clock the next morning, which was still accurate. Please think about it. When the old watchmaker first set his watch, what time was 7 o'clock? What time did you set your watch to 8: 00 for the second time?
Today, there are 2 horses, 3 cows and 4 sheep, and their total price is less than 10000 pence (ancient monetary unit). If two horses add 1 cow, or three cows add 1 sheep, or four sheep add 1 horse, then their respective total price is exactly 10000 pence. Q: What is the unit price of horses, cows and sheep?
One day, a customer came to Harlan's shop and chose the goods from 25 yuan. The customer withdrew 100 yuan. Harlan couldn't change it without change, so he went to the store next to Bai Fei to change 65,438+000 yuan into change, and came back to give customers 75 yuan's change. After a while, Bai Fei came to Harlan and said it was fake money. Harlan immediately changed Bofei into real money and asked Harlan how much he lost.
The strange mechanical problem of monkey climbing rope is simple at first glance, but it is said that it puzzles lewis carroll. It is not clear whether this strange question was put forward by a mathematical expert from Oxford University who is famous for Alice in Wonderland. In short, at an unlucky moment, he asked people's opinions on the following issues: a rope passed through a frictionless pulley, one end of the rope was hung with a 10 pound weight, and the other end of the rope had a monkey, which was just in balance with the weight. How does the weight move when the monkey starts to climb up? "It's strange," Carol wrote, "that many excellent mathematicians have given completely different answers. Price thinks farmyard will go up, and the speed will get faster and faster. Clifton (and Hackett) thought that the weight would rise at the same speed as monkeys, but sampson said that the weight would fall! " An outstanding mechanical engineer said that "this is not more effective than a fly crawling on a rope", while a scientist thought that "the rise or fall of weight will depend on the reciprocal of the speed at which monkeys eat apples", but the square root of the monkey's tail still needs to be found. Seriously, this topic is very interesting and deserves serious consideration. It can explain the close relationship between interesting problems and mechanical problems.
Two hollow balls, the same size and weight, but different materials. One is gold and the other is lead. The surface of the hollow ball is painted with the same color. Now it is necessary to point out which is gold and which is lead in a simple way without damaging the surface paint. 4 1 There are 23 coins on the table, 10 coins face up. Suppose someone blindfolds you and your hand can't touch the reverse side of the coin. Let you divide these coins into two piles in the best way, with the same number of coins facing up in each pile.
The problem of chickens and rabbits in the same cage is an ancient mathematical problem. At first, it was devoted to the quantitative relationship between head, feet and quantity when chickens and rabbits were mixed. People often use hypothetical methods to answer such questions. But if chickens and rabbits are given new life, we will get unexpected solutions. Example: There are 50 chickens and 140-foot rabbits today. How many chickens and rabbits are there? Analysis and solution: Method (1) Let each chicken stand on one foot and each rabbit stand on two hind feet, so the total number of feet on the ground is only half of the original, that is, 70 feet. The number of feet of a chicken is the same as the number of heads, while the number of feet of a rabbit is twice that of a rabbit. So, 70 MINUS the number of heads leaves 70-50 = 20 rabbits and 50-20 = 30 chickens. The golden rooster is independent and the rabbit stands up-what a clever idea! Method (2) Let each rabbit grow another head, and then split into two "half rabbits" with "one head and two feet". Half rabbits and chickens have two feet, so * * * has 140÷2=70 chickens and rabbits, and 70-50 = 20 rabbits, which is the number of rabbits. Divide the rabbit into "half rabbits"-brilliant idea! Method (3) If the two wings of each chicken are also regarded as feet, then each chicken has four feet, which is the same as that of rabbits. Then the chicken and rabbit have 50×4=200 feet, which is 200- 140 = 60 feet more. This is the number of chicken wings, so the chicken has 60÷2=30. Think of chicken wings as feet-good idea! Method (4) Make every chicken and rabbit have "special functions". The chicken flew and the rabbit stood up. At this time, all the feet standing on the ground are rabbits, and its number of feet is 140-50× 2 = 40, so the number of rabbits is only 40÷2=20, and then we know that there are 30 chickens. Chickens and rabbits have "special functions"-think more wonderfully! Students, do you have any thoughts after reading these four schemes? Elementary school math: chickens and rabbits are 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.
One night, three people went to a hotel and stayed in 300 yuan for one night. Three people just each paid 100 to make up 300 yuan for the boss. 3× 100=300 (yuan) Later, the boss said that there was an activity today, and the discount was given to 250 yuan. He took out 50 yuan's money and told the waiter to return it to the three of them. 300-250=50 (yuan) The waiter secretly hid 20 yuan and gave the rest of 30 yuan money to the three of them, each of whom gave it to 10 yuan. 50-20=30 (yuan) 30÷3 = 10 (yuan). Therefore, each of them only paid 100 yuan. 100- 10=90 (yuan) each person only spent 90 yuan money, and the 90 yuan of each of the three people was 3×90=270 (yuan) in 270 yuan, plus 20 yuan hidden by the waiter was 290 yuan, where did 270+20=290 (yuan) and 10 yuan go? 300-290= 10 (yuan)
44 "62-63 =1"is an incorrect equation. Can you move a number to make this equation hold? The tutor said that this is a very magical topic. A man can find his beloved girl when he succeeds, and a woman can find her own prince charming when she succeeds. Generally speaking, married people can't do it. Think for yourself, don't look at other people's answers. 1 interesting math problem let's take a look at this quiz question put forward by Einstein. Only 2% people in the world can do it, and explain why. 1: Five colors and five houses. 2. Every house has a different nationality. 3: Each of these five people smokes 1 kind of cigarettes and drinks 1 kind of drinks, raising 65438+. But the conditions are not repeated. 1. The British live in a red house. The Swede has a dog. 3. Danes drink tea. The green house is on the left of the white house. 5. The owner of the green house drinks tea. 6. The person who smokes Belle cigarettes keeps a bird. 7. The owner of the yellow house smokes Dunhill cigarettes. 8. The owner of the middle house drinks milk. 9. Norwegians live in the house of 1. 10. People living next door to smokers in Dunhill Road +0 1 owner 12 BLUEMASTER smokers drink beer 13 Germans smoke prince cigarettes 14 Norwegians live next door to the blue house 15 smokers who smoke mixed cigarettes drink mineral water: who raises fish? If you have difficulties, please think about 45 interesting math problems! A drugstore received ten bottles of some medicine. Each bottle 1000 capsules. Mr. White, the pharmacist, had just put the medicine bottle on the shelf when a telegram came one after another. Mr. White read the telegram to Miss Black, the drugstore manager. Mr. White: "It's urgent! All medicine bottles must be inspected before they are sold. Due to mistakes, several bottles of pills were overweight 10 mg each. Please return the wrong number of medicine bottles immediately. Mr. White is very angry. Mr. White: "Unfortunately, I have to take one from each bottle and weigh it. What nonsense. Mr. White was about to start work when Miss Black stopped him. Miss Black: "Wait a minute, there is no need to weigh it ten times, just once." How is that possible? Do the friends in the forum know how she did it?
One day, a young man came to a shoe store and bought a pair of shoes. The cost of this pair of shoes is 15 yuan, and the list price is 2 1 yuan. As a result, the young man took out 50 yuan to buy this pair of shoes. The owner of the shoes had no change, so he changed 50 yuan's change into 50 yuan nearby and gave it to Yang 29 yuan. But later, when the neighborhood found out that 50 yuan was counterfeit, the shopkeeper had no choice but to return it to the neighborhood 50 yuan. The question now is: How much did the shoe owner lose in this transaction? Everyone can only send it once! ! ! The answer you gave in 3 minutes is wrong, which means you are a failure, ............! ! !
47 If A B C D E F G H I J K L M N O P Q R S T U V W X Y Z are equal to12345 678 9111102103/respectively. 438+06171819 202122 23 24 25 26 So: work hard at H+A+R+D+W+O+R+K 8+1+6544. +0 = 98% knowledge k+n+o+w+l+e+d+g+e11+14+15+23+12+5+4. Uck (good luck) l+u+c+k12+21+3+1= 47% These things that we usually think are not the most important. What can make life complete? Is it money? ... no! M+O+N+E+Y =13+15+14+5+25 = 72% leader? ... no! l+E+A+D+E+R+S+H+I+P = 12+5+ 1+4+5+ 18+ 19+9+ 16 = 89%。 Every problem has its solution, as long as you look farther! Attitude A+T+T+I+T+U+D+E1+20+20+9+20+21+4+5 =100% Our attitude towards work and life can make our life reach 65438.
48 1. Crossing the bridge today, four people will walk from the left to the right of the bridge at night. Only two people can walk on this bridge at a time, and there is only one flashlight. You must cross the bridge with a flashlight. The fastest time for four people to cross the bridge is as follows: a 2 points; B 3 points; C 8 points; D 10。 Fast walkers have to wait for slow walkers. 2 1 How to cross the bridge? 2. Cleverly inserting the number 125 × 4 × 3 = 2000, this formula is obviously unequal, but if two numbers "7" are skillfully inserted into the formula, this equation can be established. Do you know where these two 7s should be inserted? 3. Warm four seasons, spring, summer × autumn and winter = spring, summer, autumn and winter × autumn and winter = spring, summer, autumn and winter respectively represent four different numbers. Can you point out what numbers they represent? 4. A broken car has to walk two miles down the mountain, one mile up and one mile down, and the average speed when going up the mountain is 15 miles/hour. How quickly can you reach an average speed of 30 miles per hour on the second mile? Is it 45 miles? You have to think about it! 5.*** How many eggs do you sell? Mrs. Wang went to the market to sell eggs. The first man bought half the eggs in the basket, and the second man bought the remaining half. At this time, there is an egg left in the basket. How many eggs did Mrs. Wang sell? 6. How many people took the exam? There are six multiple-choice questions on the test paper, and each question has three options. Results The marking teacher found that when choosing any three answers in all test papers, the choice of one question was different from each other. How many people will take the exam at most?