The answers on page 56 to page 70 of the fifth grade math problem card of people's Education Press

The answers on page 56 to page 70 of the fifth grade math problem card of people's Education Press

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Interesting math problems and answers

【1】 Suppose there is a pond with infinite amount of water in it. There are two empty kettles with the volume of 5 L and 6 L respectively. The problem is how to get 3 L of water from the pond only with these two kettles
【2】 Zhou Wen's mother is a chemist in Yulin cement plant. One day, Zhou Wen came to the laboratory to do her homework. After finishing her homework, she wanted to go out to play. "Wait a minute, my mother has another question for you," she continued. "Look at these six glasses for laboratory use. The front three are full of water, and the back three are empty. You can only move one glass, Is the cup full of water separated from the empty one? "Zhou Wen, who loves to use her brain, is a famous" little smart "in the school. She just thought about it for a while and then did it. Please think about how" little smart "is made?
【3】 Three young men fall in love with a girl at the same time. In order to decide who can marry the girl, they decide to fight with a pistol. Xiao Li's shooting rate is 30%, and Xiao Huang is better than him, with a shooting rate of 50%. The best shooter is Xiao Lin, who never makes mistakes, with a shooting rate of 100%, They decided to shoot in this order: Xiao Li first, Xiao Huang second, and Xiao Lin last. Then they went through this cycle until there was only one person left. So which of the three people had the greatest chance of survival? What strategies should they adopt?
【4】 There are two prisoners in a cell. Every day, the prison will provide a pot of soup for the two prisoners to share. At first, the two people often quarrel because they always think that each other's soup is more than their own. Later, they find a perfect way: one person shares the soup, and the other person chooses it first. So the dispute is settled Yes, now a new prisoner has been added to this cell. Now it is three people who share the soup. We must find a new way to maintain the peace between them. What should we do?
Press: psychological problems, not logical problems
【5】 N round coins of the same size are put on a rectangular table. Some of these coins may not be completely in the table, or some may overlap with each other. When another coin is put and its center is in the table, the new coin must overlap with some original hard coins. Please prove that the whole table can be completely covered with 4N coins
【6】 A ball, a ruler whose length is about 2 / 3 of the diameter of the ball. How do you measure the radius of the ball? There are many ways to see whose is more clever
【7】 Five one yuan RMB coins of the same size are required to contact each other. How should they be placed?
【8】 The problem of guessing cards
Mr. s, Mr. P, Mr. Q. they know that there are 16 playing cards in the drawer of the table: hearts a, Q, 4 spades J, 8, 4, 2, 7, 3 grass flowers K, Q, 5, 4, 6 diamonds a, 5. Professor John picks out one of the 16 cards and tells Mr. p the number of the cards and Mr. Q the color of the cards, Professor John asked Mr. P and Mr. Q: can you tell what card this card is from the known points or patterns? So Mr. s heard the following dialogue: Mr. P: I don't know this card
Mr. Q: I know you don't know this card
Mr. P: now I know the card
Mr. Q: I know, too
After listening to the above dialogue, Mr. s thought about it and correctly put out the card
Excuse me: what is this card?
【9】 A professor of logic, there are three students, and three students are very smart!
One day, the professor gave them a question. The professor pasted a note on the door of each person's brain and told them that each person's note had a positive integer, and the sum of some two numbers was equal to the third! (each person can see the other two numbers, but can't see his own)
The professor asked the first student: can you guess your own number? Answer: No, ask the second, no, the third, no, ask the first, no, the second, no, the third: I guess, it's 144! The professor was very satisfied with the smile. Can you guess the number of the other two?
【10】 A car hit and ran away in a city
There are only two colors of cars in the city, blue 15%, green 85%
A man saw it at the scene
He identified the blue car
However, according to the analysis of experts at the scene, the possibility of seeing the right conditions at that time was 80%
So, what is the probability that the car causing the accident is a blue car?
【11】 There is a man who has 240 kg of water. He wants to transport it to the arid area to make money. He can carry 60 kg of water at most each time, and he has to consume 1 kg of water for every kilometer. Suppose that the price of water is 0 at the place of departure, and then it is proportional to the distance of transportation (that is, 10 yuan / kg at 10 kilometers and 20 yuan / kg at 20 kilometers). And suppose that he must return safely. Excuse me, How much money can he make at most?
【12】 At present, there are 100 horses and 100 stones. There are three kinds of horses: large horse, medium horse and small horse. One big horse can carry three stones at a time, medium horse can carry two stones, and small horse can carry two stones. How many horses do you need, medium horse and small horse
【13】 1 = 5 2 = 15 3 = 215 4 = 2145 then 5 =?
【14】 Among them, N had only 50 cents, and the other N had one dollar (paper). The stupid cinema didn't have a penny when it began to sell tickets
Q: how many ways to line up so that every time a person has a dollar to buy a ticket, the cinema has 50 cents to change
Note:
One dollar = 100 cents
People who own one dollar have paper money and can't break it into two 50 cents
【15】 A man bought a chicken for 8 yuan and sold it for 9 yuan. Then he thought it was not worthwhile. He bought it back for 10 yuan and sold it to another man for 11 yuan. How much did he earn?
【16】 There is a sports competition with m events, athletes a, B and C take part in. In each event, the first, second and third place respectively have X, y and Z points, where x, y and Z are positive integers and x > y > Z. finally, a gets 22 points, B and C both get 9 points, and B gets the first place in the 100 meter race
【17】 Premise:
There are five houses of five colors
Every house owner has a different nationality
These five people only drink one kind of drink, smoke one brand of cigarette and keep one kind of pet
No one has the same pet, smokes the same brand of cigarettes and drinks the same drink
Tips:
The British live in the red house
The Swede keeps a dog
Danes drink tea
The green house is on the left of the White House
Green house owners drink coffee
The man who smokes Pall Mall keeps a bird
The owner of the Yellow House smokes Dunhill
People who live in the middle room drink milk
Norwegians live in the first house
People who smoke mixed cigarettes live next to cat owners
11 horse owners live next to Dunhill smokers
People who smoke blue master drink beer
13 Germans smoke Prince
Norwegians live next to the blue house
People who smoke mixed cigarettes drink mineral water next door
The question is: who raises fish?
【18】 Five people come from different places, live in different houses, raise different animals, smoke different brands of cigarettes, drink different drinks, and like different foods
1. The red house is on the right side of the blue house and on the left side of the White House
The owner of the yellow house is from Hong Kong, and his house is not on the far left
People who like to eat pizza live next door to people who like to drink mineral water
People from Beijing like to drink Maotai and live next door to people from Shanghai
5. The people who smoke Hilton cigarettes live next to the horse keeper on the right
People who like to drink beer also like to eat chicken
People in green house have dogs
The noodle lover lives next door to the snake keeper
9. One of the neighbors from Tianjin loves beef, and the other is from Chengdu
The fishman lives in the house on the far right
11. Marlboro smokers live between Hilton smokers and 555 smokers
People in the red house like to drink tea
13. Wine lovers live next to tofu lovers on the right
14. People smoking Hongtashan cigarettes neither live next door to those smoking Jian cigarettes, nor are they adjacent to those from Shanghai
People from Shanghai live in the second house on the left
16. People who like to drink mineral water live in the middle house
People who like noodles also like wine
18. People who smoke "555" cigarettes live on the right side of the house than people who smoke Hilton cigarettes
【19】 Fight against the landlord
Landlords hold cards 2, K, Q, J, 10, 9, 8, 8, 6, 6, 5, 5, 3, 3, 3, 7, 7, 7 and 7
Changgong A's hand cards are Wang, Xiao Wang, 2, a, K, Q, J, 10, Q, J, 10, 9, 8, 5, 5, 4 and 4
Changgong B holds cards 2, 2, a, a, a, K, K, Q, J, 10, 9, 9, 8, 6, 6, 4 and 4
The requirement is that the landlord must either lose or win if the three players do not play the wrong card
Which side will win?
【20】 There is a diamond at the door of every elevator from the first floor to the tenth floor. The size of the diamond varies. When you take the elevator from the first floor to the tenth floor, the door of every elevator will open once, and you can only get the diamond once. How can you get the biggest one?
[21] U2 chorus has to get to the concert venue in 17 minutes. On the way, they have to cross a bridge. Four people start from the same end of the bridge, and you have to help them get to the other end. It's very dark, and they only have one flashlight. At most two people can cross the bridge at one time, and they have to carry a flashlight when they cross the bridge, so someone has to bring the flashlight, It takes Bono 1 minute to cross the bridge, edge 2 minutes, Adam 5 minutes and Larry 10 minutes. How do they cross the bridge in 17 minutes?
[22] a family with two children, one of whom is a girl, asked the probability that the other is also a girl
(assuming the probability of having a boy or a girl is the same)
Why is the cover of the sewer round?
[24] there is a weight of 7g and 2G, and a balance. How to divide 140g of salt into 50g and 90g parts three times with these items?
[25] chip test: there are 2K chips. There are more good chips than bad ones. Please design an algorithm to find one of them
Good chip, state the maximum number of comparisons you use
Among them: when a good chip is compared with other chips, it can correctly tell whether another chip is good or bad
When a bad chip is compared with other chips, it will give good or bad randomly
[26] there are twelve eggs, one of which is bad (the weight is different from other eggs). Now we need to weigh them three times with a balance to find out which egg is bad!
[27] among the 100 people who answered five questions, 81 answered the first question correctly, 91 answered the second question correctly, 85 answered the third question correctly, 79 answered the fourth question correctly, 74 answered the fifth question correctly, and those who answered three or more questions correctly were considered to have passed. Then, among the 100 people, at least () were qualified
[28] Eason Chan has a song called ten years
Lu Shan has a song called 3650 nights
Now, how many days in a decade?
【29】
one
1 1
2 1
1 2 1 1
1 1 1 2 2 1
What's the next line?
[30] it takes one hour to burn an uneven rope. How to use it to judge half an hour?
It takes an hour to burn an uneven rope from the beginning to the end