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 guess the card problem

Mr. S, Mr. P and Mr. Q know that there are 16 playing cards in the desk drawer: hearts A and Q, 4 spades J, 8, 4, 2, 7, 3 flowers K, Q, 5, 4 and 6 diamonds 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! 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 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 a cinema get 50 cents change whenever it has $65,438+0 to buy a ticket?

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 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 owner of each house has 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, smokes the same brand of cigarettes and drinks the same drinks.

Tip:

The Englishman lives in a red house.

The Swede has a dog.

Danes drink tea.

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

The owner of the green house drinks coffee.

Smokers in PALL MALL have a bird.

The owner of the yellow house smokes Dunhill cigarettes.

People who live in the middle house drink milk.

Norwegians live in the first house.

10 People who smoke mixed cigarettes live next to cat owners.

1 1 The owner lives next door to the smokers in Dunhill Road.

12 Master Lan smokes and drinks beer.

13 Germans smoke prince cigarettes

Norwegians live next to the blue house.

15 people who smoke mixed cigarettes drink mineral water in their neighbors.

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 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 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 another 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?

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