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 a cement factory. 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 give you a question." She went on to say, "Look at these six glasses for laboratory tests. The first three are water and the last three are empty. Can you just move 1 cup and separate the cup filled with water from the empty cup? " 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 is "cleverness" tempered?

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. However, now there is a new prisoner in this cell, and now there are three people to share 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.

How to measure the radius of a ball with a ruler whose length is about 2/3 of its diameter? There are many ways to see who is smart.

Five one-dollar coins of the same size. Require two-phase contact, what should I say?

8 guess the card problem

Mr. S, Mr. P and Mr. Q all know that there are 16 playing cards in the desk drawer: hearts A, Q, 4, spades J, 8, 4, 2, 7, 3, K, Q, flowers 5, 4, 6 and diamonds A, 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! Everyone can see the other two numbers, but not his own.

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 hit someone and ran away in a city.

There are only two colors of cars in this city, blue 15% and green 85%.

Someone saw it at the scene when it happened.

He testified that it was a blue car.

However, according to the on-site analysis of experts, the possibility of correct conditions at that time was 80%.

So, what is the probability that the car that caused the accident 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, medium and small. 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: Every time a person with $65,438+0 buys a ticket, how many queuing methods can make the cinema get 50 cents change?

Note: 1 USD = 100 cents.

A person with 1 dollar owns 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 event get 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 in five colors.

The owner of each house has different nationalities.

Each of these five people drinks only one kind of drink, smokes only one brand of cigarettes and keeps only one kind of pet.

No one keeps the same pet, smokes the same brand of cigarettes and drinks the same drinks.

Tip:

1, the British live in a red house.

That Swede has a dog.

3. Danes drink tea

The green house is on the left of the white house.

5. The owner of the greenhouse drinks coffee

6. the smokers in pallmall have a bird.

7. The owner of the yellow house smokes Dunhill cigarettes.

People who live in the middle house drink milk.

9. Norwegians live in the first house.

10, people who smoke mixed cigarettes live next to cat owners.

1 1. Horse owners live next door to smokers on Dunhill Road.

12, Master Lan smokes and drinks beer.

13, Germans smoke prince cigarettes

14, Norwegians live next to the blue house.

15, the neighbor who smokes mixed cigarettes drinks mineral water.

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 Landlord attached the endgame

Louzhupai 2, k, q, j, 10, 9, 8, 8, 6, 6, 5, 5, 3, 3, 7, 7.

Foreman A holds Wang, Xiao Wang, 2, A, K, Q, J, 10, Q, J, 10, 9, 8, 5, 5, 4, 4.

Party b has 2, 2, a, a, a, k, k, q, j, 10, 9, 9, 8, 6, 6, 4, 4.

All three families know each other's cards. 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 the same time, and they must hold flashlights when crossing the bridge, so someone has to carry flashlights to and from both ends of the bridge. 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. What is the probability that the other person is also a girl?

(Assuming the probability of having 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 one of them.

Good chip, indicating the maximum number of comparisons you use.

Among them: when a good chip is compared with other chips, it can correctly give whether the other chip is good or bad.

When a bad chip is compared with other chips, it will be randomly classified as 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".

There is a song in Lushan called 3650 nights.

Now, how many days may there be in ten years?

29

1

1 1

2 1

1 2 1 1

1 1 1 2 2 1

What is the next line?

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.

39 monkey climbing rope

This strange mechanical problem is very 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 a word, at an unfortunate moment, he asked people's opinions on the following questions:

A rope passes through a frictionless pulley, one end of which is hung with a weight of 10 pound, and the other end of the rope is a monkey, which is 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 that the weight 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 the monkey, 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 coated with the same color paint. 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.

As the picture shows, three villages A, B and C and three towns A, B and C are located in the crater.

Due to historical reasons, only villages and towns with the same name have contacts. In order to facilitate transportation, they are going to build a railway. The problem is: how to build three railways in this crater to connect village A and town A, village B and town B, village C and town C, and these railways cannot cross each other. Digging a cave or building an overpass doesn't count. It must be a plane problem. Come up with the answer and think about what this question means.

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the meeting point

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In the three-light area inside the house, there are three switches outside the house, and one switch only controls one light, which is not visible outside the house. How do you know which switch controls which light only when you enter the house? How about four ~

442+7-2+7 are all made of matches. Move any one of them and ask for an answer of 30.

Note: Because the writing problem is explained as follows, 2 consists of three transverse folds and 7 consists of two transverse folds.

455 pirates snatched 100 gold coins from the cellar and planned to divide the spoils. These are pirates who talk about democracy (of course, their own unique democracy). Their habit is to distribute according to the following way: the most powerful pirate puts forward a distribution plan, and then all pirates (including the one who puts forward his own plan) vote. If 50% or more pirates agree to the plan, the plan will be passed and the spoils will be distributed accordingly. Otherwise, the pirates who put forward the plan will be thrown into the sea, and then the next most powerful pirate will repeat the above process.

All pirates are happy to see one of their accomplices thrown into the sea, but if they have a choice, they would rather get a sum of cash. Of course they don't want to be thrown into the sea. All pirates are rational and know that other pirates are rational. Besides, no two pirates are equally powerful-these pirates are arranged from top to bottom according to their grades, and everyone knows their own grades and others' grades. These gold nuggets can no longer be divided, and several pirates are not allowed to own gold nuggets, because no pirate believes that his accomplices will abide by the arrangement of enjoying gold nuggets. This is a group of pirates who only think of themselves.

What distribution scheme should the fiercest pirate put forward to get the most gold?

Which of them has the best chance of survival?

Five prisoners, according to 1-5, caught mung beans in sacks containing 100 mung beans. It is stipulated that everyone should catch at least one, and those who catch at most and at least should be put to death. And they can't communicate with each other, but when they catch, they can find out the remaining number of beans. Ask them who has the best chance of survival. Tip:

1, are very smart people.

Their principle is to save people first, and then kill more people.

3, 100 don't have to finish it all.

4. If there is any duplication, it will be regarded as the largest or smallest and executed together.