I, winter vacation homework, urgently need to do more math thinking questions in Grade Two and Grade Two (Grade Three is OK, not too difficult). The better, the more difficult it is.

1. Excuse me, how many minutes does it take when the box is half full?

There is a magic box with eggs in it. As soon as the magic is performed, the number of eggs doubles every minute 10 minutes later, the box is full of eggs. How many minutes, is the box half full?

How many pairs of socks should I take out at least?

There are ten black socks and ten white socks in the drawer. If you open a drawer in the dark, reach for socks; How many socks do I have to take out to make sure I get a pair?

3. When can it climb out of the dry well?

A monkey was trapped in a dry well 30 feet deep. If it can climb three feet up and one foot down every day, when can it climb out of the dry well at this speed?

4. How many minutes at most?

Suppose three cats can kill three mice in three minutes. How many minutes does it take for a hundred cats to kill a hundred mice?

5. Who is the oldest among them? Who is the youngest?

Zaza is bigger than Feifei, but smaller than Juan. Feifei is older than Jojo and Matthew. Matthew is younger than Carlos and Jojo. Juan is older than Feifei and Matthew, but younger than Carlos.

Who is the oldest of them? Who is the youngest?

6. Please use+,-,×, ⊙, () and other operation symbols.

1. Please connect five 3-component formulas with operators such as+,-,×, and () so that their numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 respectively.

2. Please add an operation symbol between four 5s, so that the operation results are equal to 0, 1, 2, 3, 4, 5, 6 and 7 respectively.

3. The following formula only writes numbers, but forgets to write operation symbols. Please select+,-,×, ⊙, () and [] to fill in the formula, and the equation will be established.

1 2 3= 1

1 2 3 4= 1

1 2 3 4 5= 1

1 2 3 4 5 6= 1

1 2 3 4 5 6 7= 1

1 2 3 4 5 6 7 8= 1

1 2 3 4 5 6 7 8 9= 1

7. How many kilometers did the dog run?

A and B start from the east and west at the same time, facing each other, with a distance of 10 km. A walks 3 kilometers per hour and B walks 2 kilometers per hour. How many hours did they meet? If A takes a dog and starts from A at the same time, the dog runs to B at a speed of 5 kilometers per hour, and then runs back to A after meeting B; Run back to B when you meet A, and the dog won't stop until they meet. How many kilometers did the dog run?

8. What are the two digits represented by "North China" in the following formula?

Hua was born in 19 10. What are the two numbers of "North China" in the following formula?

19 10

+North China

9. Runway

There is such a racetrack. On the racetrack, Ma A can run 2 laps a minute, Ma B can run 3 laps and Ma C can run 4 laps. Three horses started from the starting line at the same time. How many minutes later, the three horses met at the starting line again?

10. Load apples

There are 1000 apples and 10 boxes, so that any integer number of apples can be combined in the whole box (when you need any). How to package them?

1 1. Age

One day, a man walked into a small restaurant, ordered a light meal and chatted with his boss while eating. The boss said he had three children, so the guest asked him, "How old are your children?" Boss: "Let you guess! The age of the three of them is equal to 72. The guest thought for a moment and said, "It doesn't seem enough! Boss: "All right! I tell you again, if you go out and look at our house number, you can see the sum of their three ages. "The guest went out to have a look 14. When he came back, he shook his head and replied, "It's still not enough! The boss smiled and said, "My youngest child likes to eat that kind of giant egg bread. What are the ages of these three children?

12. Poker

On the way back to Arabia, Alabin passed by the Sunday holiday market and saw a crowded place, so he stopped to see what was interesting. It turned out that a busker girl and her father were performing, interspersed with some poker guessing games from time to time. The first person who guesses can get a magic lamp! This time, the lovely girl gave a question. Guess the correct order of the three playing cards according to the following tips: 1. There is a square on the left of spades; 2. Old K has an 8 on the right; 3. There is a10 to the left of the red heart; There is a red heart on the left of spades. Can you help Arabin get the magic lamp he needs most? By the way, the question given by the hygienist is very simple. Maybe you can answer it in a few seconds!

13. Go to the villa

"They took the whole family to the villa," Bob said. It's nice there. It's quiet at night, and there is no car horn. ""But the police go to work as usual, "Ryan commented." Don't you have a policeman there? ""We don't need the police! Bob said with a smile, "but there is a problem in our driving that deserves your consideration." What's the situation: before 15 miles, we averaged 40 miles per hour. Then, after walking about nine times, we drove faster. We have been driving very fast for the remaining seventh of the distance. The average speed of the whole journey is exactly 56 miles per hour. " "What do you mean by' a few tenths'?" Ryan asked if the number here was an exact integer, "Bob replied," and the speed of the next two journeys was also an integer mile per hour. "Bob naturally won't race crazy with his family, although there may be no police on that road! Excuse me, what is Bob's average speed in the last seventh mile?

14. Cross the bridge

There are four people, a b c d, who have to 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, b 3, c 8, d 10.

Fast walkers have to wait for slow walkers. How to let everyone cross the bridge within 2 1

15. Competition game

One of the most common matching games is for two people to play together. First, put some matches on the table, and two people take turns to take them. You can first limit the number of matches taken at a time and stipulate that the last match is the winner. Rule 1: How can we win if the number of competitions we participate in at one time is limited to at least one and at most three? For example, there are n= 15 matches on the table. Party A and Party B take turns to take it, and Party A takes it first. How should Party A lead them to win? Rule 2: If the number of matches taken at one time is limited to 1 4, how can we win? Rule 3: How to limit the number of matches taken at one time to some discontinuous numbers, such as 1, 3, 7?

16. Weekly salary

"ah! Johannes, "Joe met a young man in the street on Sunday and shouted to him," Long time no see, I heard you started working! " "A few weeks," Johannes replied. "This is a piece-rate job, and I have done quite well. I earned more than 40 yuan in the first week, and every week after that, I earned 99 cents more than the previous week. " "What a coincidence!" Joe continued with a smile, "May you continue as always!" "I estimate that I can earn 60 dollars a week before long," the young man told Joe. "I have earned a full 407 yuan since I started working. This is really not bad! " How much did Johannes earn in the first week?

17. Two cylinders have the same area, which one has the larger volume?

As shown on the right, there is a rectangular iron sheet with a length of 50cm and a width of 30cm. The iron sheet can be rolled into a cylinder (1) with the short side as the bus, or it can be rolled into a cylinder (2) with the long side as the bus. If a bottom surface is added under them, which of the two cylinders is larger?

Answer: The answer to this question is not obvious. Because the bottom of the cylinder (1) is large but short, and the bottom of the cylinder (2) is small but high, both of them have their own advantages. So whose size is big has to be calculated to determine.

It is known that the height of a cylinder (1) is 30cm and the circumference of its bottom surface is 50cm, so the radius of its bottom surface is

The volume of is v (1) =πR2? 30=π

Given that the height of cylinder (II) is 50cm, the perimeter of bottom surface is 30cm, the radius of bottom surface is ∴, and the volume of cylinder (II) is V (II) =πr2? 50=π( )2×50= ∴V (1) > V (2) indicates that the volume of cylinder (1) is greater than the product of cylinder (2).

Higher Challenges From the above comparison results, we can draw a conclusion that if the side areas of two cylinders are equal, the volume of the short and thick cylinder must be greater than that of the tall and thin cylinder. If you want to accept a higher level challenge, please see the following proof:

Let the area of a rectangle be S, with one side being A and the other side being B (let a>b), then S=ab.

If a is the perimeter of the bottom surface, the height of the cylinder is b, and the volume of the cylinder v( 1)= 1

If b is the perimeter of the bottom surface, the height of the cylinder is a, and the volume of the cylinder is v (2) = > a >; b，∴v①> v②。

That is to say, in the case of equal side areas, the larger the bottom, the larger the volume of the cylinder.

18. Can solve "Goldbach conjecture"

According to the Morning News, the day before yesterday, an old man who claimed to have created the theory of fuzzy mathematics called our hotline and said that he had solved the famous Goldbach conjecture.

The old man named Sui, 66 years old, comes from Xinjiang and lives in a small hotel beside the traffic road. After welcoming reporters into the secret shop, the old man did not rush to introduce his own argumentation method, but first took out a lot of invitations sent to him by various "Who's Who", saying that his research had been recognized by many institutions across the country. Under the guidance of the reporter many times, the old man reluctantly moved the topic to the theme.

"Although I only have a secondary school education, I was admitted to the university later. In the years of the' Cultural Revolution', I was not idle when others tormented me. I taught myself the "Unified Volume of Addition and Subtraction Algorithms" during the Yongle period of the Ming Dynasty, and I have been fascinated by mathematics since then. " "Chen Jingrun's article about Goldbach's conjecture was published in the annual report 1978. In my opinion, his research can only reach the level of 1+2, and the method is wrong. I started the theory of fuzzy mathematics that year, and quickly completed the argument of'1+1'with new theories, and conquered Goldbach's conjecture. "

After introducing the history of Cloud Covering, the old man finally found the "manuscript". To the reporter's surprise, just a piece of white paper with 16 covers all the theoretical essence of the elderly, and there is almost no abstruse advanced mathematics in it, which even journalists from liberal arts can read. To sum up, the old man's way to solve the problem is to change the original description of Goldbach's conjecture into his own description, and then use his own "fuzzy mathematics theory" to verify the changed description to the result that conforms to Goldbach's conjecture.

"Is your description absolutely consistent with Goldbach's conjecture?" The reporter is somewhat puzzled.

The interview failed to continue, because in the old man's bed, the reporter accidentally saw the rejection letter from Mathematics Magazine to the old man. What it says above is: In your articles Fuzzy Mathematics Theory, Goldbach Conjecture and 1+ 1 Theorem, none of the conjectures have actually been proved. ...

19. The squares on the chessboard

Title:

Eight rows and eight columns of black and white squares form a chessboard.

Can be combined into squares of different sizes.

The sizes of these squares range from 8×8 to 1× 1.

Q: How many squares of different sizes can be found on the chessboard?

Answer:

* * * There are 1 8×8 squares; 4 7×7 squares; 9 6×6 squares; 16 5×5 square; 25 4×4 squares; 36 3×3 squares; 49 2×2 squares; 64 squares 1× 1, a total of 204 squares.

20. What do bees do with math?

Bees … know from some geometric predictions that hexagons are bigger than squares and triangles, and the same material can store more honey.

Pappas of Alexandria

Bees have never studied geometry, but the honeycomb structure they build conforms to the mathematical principle of minimax.

For squares, equilateral triangles and equilateral hexagons, if the areas are all equal, then the perimeter of equilateral hexagons is the smallest. This means that bees choose to build hexagonal columnar nests, which can enclose as much space as possible with less beeswax and less work, thus storing more honey than building square or regular triangular prism nests.

Now let's prove that the perimeter of a regular hexagon is the smallest among a regular triangle, a square and a regular hexagon with a certain area.

It is proved that given an area of S, the side lengths of a regular triangle, a square and a regular hexagon with an area of S are a3, a4 and a6, respectively. rule

Perimeter of a regular triangle

Square perimeter C4 = 4；; Regular hexagonal circumference

2 1. Mathematical Games in Poker

First, arrange the order skillfully.

Put 1-k * * 13 cards, which seems out of order (in fact, they are arranged in a certain order). Put 1 cards behind13 cards, take out the second card, and finally put1cards in your hand.

Please try it!

The order of playing cards is: 7, 1, q, 2, 8, 3, j, 4, 9, 5, k, 6, 10.

Do you know how this is discharged?

This is the result of "reverse thinking". According to the initial operation flow, just reverse the cards arranged in the order of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q and K.

You have heard the story of Sima Guang smashing a jar! When a child falls into a water tank, most people consider letting the child leave the water, while Sima Guang smashed the tank to let the water leave the child. This is reverse thinking, and so is the clever order of playing cards. You can't live without reverse thinking in your study life. I wish you to think like this consciously as soon as possible and become smarter.

Second, clever card guessing.

[play]

1. Shuffle 54 cards;

2. Count 30 cards from 54 cards (face up) one by one, turn them over (face down) and put them on the table. When the performer counts 30 cards, remember the design and number of the ninth card.

3. From the 24 cards in hand, please ask the audience to choose any card. If it is one of 10, j, q, and k, it is counted as 10, and it is set aside as the first column facing upward; If the number of cards of a 1 is less than 10 (the king number is 0), put this card face up to one side, take 10-A 1 from your hand and put it under this card as the first column, and then ask the audience to take any card from their hands and form the second column according to the above method. Finally, please draw a card from your hand and form the third column according to the above method. If they don't have enough cards in their hands, they will make up from the 30 cards already placed on the table, but they must take them from top to bottom.

4. Add the points of the first card in each column a 1, a2 and a3 to get A = A1+A2+A3;

5. The performer starts with the number of cards left in his hand, then counts from the first card among the 30 cards placed on the table (if there are no cards left in his hand, then counts from the first card left on the table) to the A card, and accurately guesses the number and color of this card (that is, the color and number of the ninth card recorded when counting 30 cards).

[principle]

Total number of cards in three columns:

a = 3+( 10-a 1)+( 10-a2)+( 10-a3)

=33-(a 1+a2+a3)

Number of cards left in hand:

B=24-A。

∫B+9 = 24-A+9 = 33-[33-(A 1+a2+a3)]

=33-33+(a 1+a2+a3)

=a，

Judging from the number of cards left in the hand, the first card at this time happens to be the ninth card in the original 30 cards.

22. pigeon hole principle and computer fortune telling

Pigeon hole principle and computer fortune telling

"Computer fortune telling" looks mysterious. As long as you report the year, month, day and sex of your birth, a so-called character and destiny will appear on the screen when you press the button. It is said that this is your "destiny".

In fact, this is just a computer game at best. We can easily use the pigeon hole principle in mathematics to illustrate its absurdity.

Pigeon hole principle, also known as pigeon cage principle or Dirichlet principle, is a special method to prove the existence in mathematics. For the simplest example, if you put three apples in two drawers in any way, there must be two or more apples in one drawer. This is because if there is at most one apple in each drawer, there are at most two apples in two drawers. Using the same reasoning, we can get:

Principle 1 If more than n objects are put into n drawers, at least one drawer has more than two objects.

Principle 2 If there are more than mn objects in N drawers, at least one drawer has more than m+ 1 or m+l objects.

If calculated in 70 years, the number of combinations with different sexes according to the date of birth should be 70× 365× 2 = 5 1 100, and we regard it as the number of drawers. The current population of China is 1 1 100 million, and we regard this figure as the number of "things". Since the ninth power of 1. 1× 10 = 21526× 51100+21400, according to principle 2, there is 2/kloc.

In ancient China, people knew how to use the pigeon hole principle to expose the fallacy of birth. For example, in Qing Dynasty, Chen Qiyuan wrote in Notes on Leisure Zhai: "I don't believe in the theory of pushing the stars, thinking that one person is born at a time (note: one hour, two hours), and twelve people are born in one day, which is 4,320 people in terms of age. Counting a Jia (note: 60 years), there are only 259,200 people. Today, only one county is counted. During this period, when the princes were born, there must be people born at the same time. What is the difference between the rich and the poor? " Here, a year is calculated as 360 days, and a day is divided into 12 hours, and the number of drawers obtained is 60× 360× 12 = 259200.

The so-called "computer fortune-telling" is nothing more than storing the manually compiled fortune-telling sentences in their respective cabinets in advance like Chinese medicine cabinets. Who wants to tell fortune, that is, according to the different combinations of birth date, date and gender, according to different codes, mechanically take out the so-called fate sentence from the computer cabinet. It is blasphemy to put the aura of modern science on the dead who were superstitious in ancient times.

23. The problem of chickens and rabbits

Another kind of ancient problem which belongs to binary linear equations and has a simple solution is "Chicken and Rabbit Problem", which originated from Sun Tzu's Art of War Calculation, a mathematical work in ancient China (the date of birth and death is unknown, and the author of Sun Tzu was born in the 4th century AD, not Sun Wu, the author of Sun Tzu's Art of War). The 31st topic in Sun Tzu's Calculations is: "There are pheasants and rabbits in the same cage, with 35 heads on the top and 94 feet on the bottom. What are the geometric shapes of pheasants and rabbits? The understanding method is given in the book, and the final answer is: pheasant 23, rabbit 12. The pheasant here is commonly known as pheasant. This kind of topic is usually called "chicken and rabbit problem" in China. After it was spread to Japan, the typical topic became "turtles and cranes in the same cage", so they generally called this kind of topic "turtle-crane problem"

The problem of chickens and rabbits is widely spread among our people. In rural or pastoral areas, when people are resting in the fields, they sometimes hear some old people ask teenagers such questions: "A chicken doesn't matter, one hundred legs walk on the ground. How many chickens are there? How many rabbits? " The normal solution to this problem is to set a chicken as a chicken and a rabbit as a rabbit and list a set of linear equations.

The answer can be obtained by solving this binary linear equation group, so it should be said that it is not difficult to solve such a problem. However, because it is a question raised in the field, it is generally not necessary to use paper and pencil to calculate equations and equations (by the way, the "Brother Buying a Turtle" mentioned earlier also belongs to the question raised in the field). Usually, the answer is obtained through oral calculation and mental calculation (called "mouth-to-mouth calculation" by the people), and sometimes a simple and ingenious algorithm is used: "Chickens in the same cage are free." There is a reasoning process of verbal arithmetic plus mental arithmetic: if a rabbit lifts its front legs, then each chicken and rabbit has only two legs standing on the ground, and 39 chickens and rabbits should have 78 legs standing on the ground at this time, which is 22 less than the front 100 legs. These legs were lifted by rabbits. Since each rabbit lifts its legs, now * * * lifts 22 legs, so we know that there must be 1 1 rabbits, and 1 1 of 39 chickens and rabbits are only rabbits, that is to say, there must be 28 chickens among them.

There are other simple solutions. For example, if a chicken has four legs, 39 chickens and rabbits will have 65,438+056 legs, 56 more than 65,438+000 legs, because each chicken has two more legs. If you count two more legs, each chicken has 56 extra legs. You can see that there are 28 chickens, 39 chickens and rabbits, 28 chickens and 1 1 rabbit. Because it is mental arithmetic, it is more convenient to calculate with smaller numbers and there are fewer opportunities for mistakes. Therefore, although the two algorithms are similar, the latter solution is slightly more complicated than the former.

As an exercise, we can use the above method to calculate this interesting question with a history of more than 1500 years in Sunzi Suanjing. Please check the answer by yourself after the calculation.

In the first Huajin Cup Junior High School Mathematics Invitational Tournament, an examiner changed the chicken-free test question into an interesting topic, which was written below for reference.

Example 2.7 The female squirrel can pick 20 pine nuts every day in sunny days and only 12 in rainy days. She has picked 1 12 pine nuts continuously, with an average of 14 per day. How many days has it rained these days?

Used to solve 1 mother squirrel * * *

1 12÷ 14=8 (days)

If it is sunny for 8 consecutive days, you can pick pine nuts.

20×8= 160 (piece),

Picking pine nuts in rainy days is less than in sunny days.

20- 12=8 (pieces),

* * * less mining now.

160-112 = 48 (pieces)

So it is rainy.

48÷8=6 (days)

Solution 2 It took Mother Squirrel 8 days to pick pine nuts. If it rains for 8 days, you can only pick pine nuts.

12×8=96 (pieces),

Pick more pine nuts on sunny days than on rainy days.

20- 12=8 (pieces),

Now * * * is colorful.

1 12-96= 16 (pieces)

So it's sunny

16÷8=2 (days)

It's raining.

8-2=6 (days)

Here are two simple solutions to the above-mentioned "chicken inspection-free problem" For the primary school students who take part in the competition, it is impossible to take the column equation as the test requirement, so they will not use the column equation to solve the equation and write the standard answer.

The above problems are all about the simple solutions of binary simultaneous equations in some special cases. As we said before, solving equations with series equations is the basic skill of mathematics and must be firmly mastered. Simple solutions must be based on solid basic skills.

Linear simultaneous equations are called "linear equations" in mathematics, and the index number can be two, three, four or more, but each equation can only be one linear equation. In China, Nine Chapters Arithmetic, which was written two thousand years ago, and Nine Chapters Arithmetic Note written by Liu Hui, an outstanding mathematician in the Three Kingdoms period in 263 AD, systematically expounded the understanding methods of this kind of equation. This is the method of transforming augmented matrix into ladder matrix by elementary transformation of matrix in linear algebra today. One thousand years later, at the beginning of19th century, the outstanding German mathematician Gauss also discovered this method. Since then, it has been called "Gauss Elimination Method" in books all over the world (including China). In fact, "gauss elimination" is an ancient law of China (interested readers can refer to "A Brief History of Linear Algebra" in Mathematics Bulletin No.8 of 1985 and "gauss elimination is an ancient law of China" in Textbook Newsletter No.1 of 1992).

40 interesting math problems

1. How many eggs did you buy?

When I bought eggs, I paid the grocer 12 cents, "said a chef," but because they were too small, I asked him to add two eggs for me for free. In this way, the price per dozen (12 eggs) is lower than the original asking price 1 cent. "How many eggs did the chef buy?

2. What's the hit rate?

Two shooters, one hit 80% and the other hit 90%. If they shoot the same target, what's the hit rate?

3. can ants reach point a?

On a one-meter-long rubber band, an ant climbs from B to a(a and B are the two ends of the rubber band). If the ant crawls forward at a speed of 1 cm/s and climbs to a point C in the middle of the rubber band, and the rubber band stretches at a speed of 2 cm/s, assuming that the rubber band can stretch indefinitely, can the ant reach the point A?

4. Which store is efficient?

There are two stores, one insists on "small profits but quick turnover", the interest rate is 6%, the capital turnover is 2.5 times a month, and the other has an interest rate of 20%, and the capital turnover is 0.5 times a month. Which store is efficient?

5. Who will arrive at the railway station first?

A thinks his watch is five minutes fast, but in fact it is ten minutes slow; B's watch is five minutes slow, but B thinks it is ten minutes slow. Both Party A and Party B want to catch the four o'clock train. Who will arrive at the station first?

6. Interesting blind date times

Since ancient times, the number of blind dates has aroused the strong interest of many mathematicians and amateurs. In mathematics, there are some numbers called love. It is really the so-called "you have me, and I have you." For example, 220 and 284, add up all the divisors of 220 (except 220 itself) and the sum is equal to another number 284; that is

1+2+4+5+ 10+ 1 1+20+22+44+55+ 1 10=284

Similarly, adding all the divisors of 284 (excluding 284 itself) equals 220, that is,

1+2+4+7 1+ 142=220

This is not' you have me, I have you'! "

A long time ago, the outstanding Arab mathematician Pepeto? Ben. Cora established a famous "blind date number formula":

Let: a = 3× 2x- 1

b=3×2x- 1- 1

c=9×22x- 1- 1

Where x is a natural number greater than 1, and if a, b and c are all prime numbers, then 2x×ab and 2x×c are a pair of blind date numbers.

For example, if x = 2, we can calculate that A = 1 1, B = 5, and C = 7 1 are all prime numbers, so

2x×ab=22× 1 1×5=220

2x×c=22×7 1=284

According to this formula, people can write a series of blind date numbers without difficulty.

Euler, a famous mathematician, also studied the subject of blind date number. 1750, he threw 60 pairs of blind date to the public in one breath, which made people stunned. However, in this way, people no longer study the number of blind dates. People think like this: since such great mathematicians have studied it and created 60 records of blind date, it seems that this subject has definitely reached the "peak". More than one hundred years later, the topic of "blind date" seems to have been forgotten by the world. However, at 1866, hot chestnuts broke out from the cold pot. Bargeny, an Italian youth aged 65,438+06, was surprised to find that 65,438+065,438+084 and 65,438+0265,438+00 were only slightly larger than 220 and 284. It turns out that Euler counted the number of blind dates as long as dozens of "astronomical figures", but he just missed the second pair that was close at hand. Such a thing is also rare in the whole history of mathematical development. When experts are also negligent, it is really "the feet are short and the inches are long."

7. Ask the third person what color hat he is wearing.

Three people, stand in a vertical line. There are five hats, three blue ones, two red ones, one for each person, and no one is allowed to look at his own color. Then I asked the first man what color hat he was wearing, and he said he didn't know. Then I asked the second person what color hat to wear, and asked the third person what color hat to wear. He said I know. Ask the third person what color hat he is wearing.

8. Do you know how to recognize A?

A and B are both blind. One day, A bought four pairs of socks in the mall, two pairs of black socks and two pairs of white socks, two of which were for B. A came to B's house, took out his socks, and then quickly took out two pairs from it, saying with certainty, "One pair of these socks is black and the other is white." B was confused at that time. Do you know how A can tell?

9. Is it morning or afternoon? Which is my sister?

A pair of fairy sisters lived in the forest. Elder sister told the truth in the morning and lied in the afternoon. Sister and sister are just the opposite. A hunter got lost in the forest, met them and made friends. The hunter asked, "Who is the elder sister?" The tall man said, "It's me." The short man also said, "It's me." The hunter asked again, "What time is it now?" The tall man said, "It's almost dawn." The short man said, "A day has passed." Please judge whether it is morning or afternoon, which is sister?

10. Ask the seller how many sheep there are.

Traffickers have passed 99 levels. You can pass the customs by paying taxes to half of the sheep every time you pass the customs, and you can pass the customs if you give one to half. But after 99, the doorman refused to return the sheep. At this time, there is only one sheep left. How many sheep are there in the sheep seller?

1 1. How many games does it take to choose the champion?

There are 100 teams participating. How many fights will it take to choose the champion?

12. A and B race 100 meter sprint.

A and B sprint 100 meters. Results A reached the finish line 10 meter ahead of schedule. B and c compete 100 meter sprint. As a result, B won by 10 meter. Now A and C are playing the same game, what will happen?

13. What should be the next number?

In the following order, the next number should be? 2、5、 14、4 1

14. How many chickens are there?

There is a chicken farm. If you sell 75 chickens, the chicken feed can last for 20 days. If you buy 100 chickens, the chicken feed can only last 15 days. How many chickens are there now?

15. What is the asking price of each master?

Painters and painters: 1 100 $ painters and plumbers: 1700 $ plumbers and electricians:1/0/00 $ electricians and carpenters: 3,300 $ carpenters and plasterers: 5,300 $ plasterers and painters: 3,300. What is the asking price of each master?

16. How old is that boy?

"How old is this boy?" Asked the conductor. Someone was deeply interested in his family affairs, which really flattered the country people. He proudly replied, "My son is five times as old as my daughter, my wife is five times as old as my son, and my wife is twice as old as my wife. If we add up all our ages, it happens to be my grandmother's age. Today she is about to celebrate the birthday of 8 1. " How old is that boy?

17. When did the old man lose his horse? How many horses?

Once upon a time, an old man lost a horse and asked a scholar to write a notice for finding a horse. The scholar asked him, "When did you lose your horse?" The old man replied, "either last year or this year." The scholar asked again, "How many horses have you lost?" The old man replied, "Either one or two." The scholar wrote a notice for finding a horse and found it soon. When did the old man lose his horse? How many horses?

18. How many eggs did the chef buy?

"When I bought eggs, I paid the grocer 12 cents," said a chef, "but because they were too small, I asked him to add two eggs for me for free. In this way, the price per dozen (12 eggs) is lower than the original asking price 1 cent. " How many eggs did the cook buy?

19. There is one.