Example 1 Observe and analyze the arrangement of the following columns, and then fill in the blanks.

⑴ 5,9, 13, 17, , 。

⑵ 10, 12, 16,22, , 。

⑶ 1,4,9, 16, , 。

⑷ 4,5,7, 1 1, 19, , 。

⑸ 2,4,8, 16, , 。

The idea is to analyze the arrangement law of a sequence. Generally, the same four operations are performed on the adjacent numbers in this series in turn, and the law is found by comparing the calculation results.

(1) Subtract the adjacent previous number from the latter one in turn, and the difference is all 4. So the last two spaces are 2 1, 25 in turn.

(2) Subtract the adjacent previous number from the latter number in turn, and their differences are 2, 4 and 6 in turn. So the last two differences should be filled in 8, 10 in turn, and the last two spaces should be filled in 30, 40.

(3) Because 1= 1× 1, 4=2×2, 9=3×3, 16=4×4, the last two numbers should be 5×5 and 6×6 respectively. So the last two spaces should be filled with 25 and 36 in turn.

(4) Because 5=4+ 1, 7=5+2, 1 1=7+4, 1 9 =1+8, observe/kloc-0. So the two spaces should be filled in 16+ 19 = 35 and 32+35 = 67 respectively.

5] Because 2=2, 4=2×2, 8=2×2×2, 16=2×2×2×2, the last two numbers should be multiplied by five twos and six twos respectively. Therefore, fill in 2×2×2×2×2=32 and 2× 2× 2× 2 = 64 respectively.

The analysis of the arrangement law of mathematical thinking sequence is usually to perform some operation on this sequence, and then write down the operation results in turn to form a new sequence. Then, observe the arrangement law of the new series, so as to get the arrangement law of the original series.

Example 2 Find out the arrangement rules of the following series and fill in the appropriate numbers on the horizontal lines.

⑴ 5, 15,45, 135, , 。

⑵ 60,63,68,75, , 。

⑶ 180, 155, 13 1, 108, , 。

⑷ 0， 1， 1，2，3，5，.

⑸ 6, 1, 8, 3, 10, 5, 12, 7, , 。

The crowning touch of the train of thought (1) Because15 = 5× 3,45 =15× 3, 135=45×3, the arrangement rule of this series is: the last number is always three times that of the previous one. So the number to be filled in is 405 12 15.

(2) If the difference between two adjacent numbers is calculated, there are 63-60 = 3, 68-63 = 5 and 75-68 = 7. It can be seen that the difference between two adjacent numbers is 3, 5, 7, 9, 1 1. So the number after 75 will be 75+9 = 84,84+11= 95.

(3) Because the arrangement of this series is from big to small, the difference between two adjacent numbers is 25, 24, 23, 22, 2 1 in turn. So the number after 108 should be108-22 = 86,86-21= 65.

(4) Calculate the sum of two adjacent numbers. 0+1=1,1+1= 2,1+2 = 3, 2+3 = 5. Obviously, the arrangement rule of this series is that the last number is the sum of the first two numbers. So the two numbers after 5 should be 8, 13 respectively.

It is difficult to see the inherent law of this problem only from two adjacent figures. After careful observation, I realized that the original series should be considered in two series. The first series is 6,8, 10, 12, 14, and the difference between every two adjacent numbers is also 2. The second series is 1, 3, 5, 7, 9, and the difference between every two adjacent numbers is also 2. Since the first series and the second series are arranged at intervals, 7 should be followed by14,9.

Example 3 Find out the rules and fill in the appropriate figures on the horizontal lines.

⑴ 17, 1, 15, 1, 13, 1, , , 9, 1。

⑵ 45， 1，43，3，4l，5，，，37，9 .

⑶ 10,20,2 1,42,43, , , 174, 175。

⑷ 4,9, 19,34,54, , , 144。

After observing this series, it is found that 1 appears every other number, and the other numbers decrease by 2 in turn. So the two spaces should be filled in 1 1 and 1 in turn.

⑵ Observing this series, we can find that the first number minus 2 is the third number, the third number minus 2 is the fifth number, …… the second number plus 2 is the fourth number, and the fourth number plus 2 is the sixth number … Therefore, the spaces are filled in 39 and 7 in turn.

(3) The second number is twice the first number, the third number is more than the second number 1, the fourth number is twice the third number, and the fifth number is more than the fourth number 1. According to this law, the sixth number should be twice that of the fifth number, and the seventh number should be more than the sixth number 1. So, fill in the blanks with 86 and 87 in turn.

(4) The second number is 5 more than the first number, the third number is 10 more than the second number, and the fourth number is 15 more than the third number ... The law can be expressed as follows:

4,9, 19,34,54,(79),( 109), 144

+5 + 10 + 15 +20 +25 +30 +35

Therefore, fill in the blanks with 79, 109 in turn.

Example 4 first observe the following formula, find out the law, and then fill in the numbers.

(1) because 19 = L× 9+( 1+9), 29 = 2× 9+(2+9), 39 = 3× 9+(3+9),

So 89 =;

Because199 =19× 9+(19+9),

So 1999 =

(2) Because 1+2× 9 = 19, 1+22× 9 = 199,

So1+222× 9 =;

Because 2+232× 9 = 2090, 3+343× 9 = 3090,

so 4+454×9 =； 8+898×9= ;

And because11+121× 9 =1100; 12+232×9=2 100,

So 13+343× 9 =, 15+565× 9 =,

18+898×9= 。

The crowning touch of the train of thought is to give the law first, and then fill in the numbers according to this law.

(1) We can see that among the four equations given, the number on the left side of the equation is 9, the first part on the right side of the equation is the number on the tenth place multiplied by 9, and the second part is the number on the tenth place plus 9. Therefore:

89-8×9+(8+9), 1999= 199×9+( 199+9)。

⑵ Observing the six equations given, it is found that the number of 9 times several 2 plus 1 equals the number of 9 and 1, in which the highest digit is1; 9 times a three-digit number, the hundred digits of the three-digit number are the same as the single digits, the ten digits are all 1 greater than the hundred digits, and one digit with the same hundred digits of the three-digit number is equal to a four-digit number. The ten digits of this four-digit number are all 9, the hundred digits and the single digits are all 0, and the thousand digits are the one to the left of the equal sign; Multiply 9 by the same three digits as above, plus a two-digit number. The ten digits of this two-digit number are all L, and the one digit is the same as the hundred digits of the three digits, so you get a four-digit number. Four digits and ten digits are O, the hundredth digit is 1, and the thousand digits are just one digit of the two digits to the left of the equal sign. therefore

1+222×9= 1999, 4+454×9=4090, 8+898×9=8090,

13+343×9=3 100, 15+565×9=5 100, 18+898×9=8 100。

Summary and tips

In the last chapter, we learned how to find rules from graphic arrangement. In this chapter, we will learn how to find rules from the arrangement of numbers.

How to find the rule from the arrangement of numbers? First, we should use our brains and carefully observe the characteristics of the numbers in the topic; The second is to flexibly use the relevant knowledge of integers, the calculation rules of addition, subtraction, multiplication and division and the relationship between them, find the rules from them, and fill in the numbers according to the rules, so that the questions can be answered.

Specifically, when looking for rules from the arrangement of numbers, we should strive to grasp the following points:

1. The general thinking step of analyzing the arrangement law of a column of numbers is: perform the same four operations on several adjacent numbers in the column in turn, and write down their operation results in turn to form a new column. Through the analysis of the arrangement law of this column number, we can understand the arrangement law of the original column number.

Sometimes it is necessary to divide a column number into two columns and find out their respective changing rules.

3. Analyzing the arrangement law of a column number often requires us to think flexibly and analyze specific problems, because the laws of different things are often different. Sometimes you need to use other knowledge comprehensively. When one method doesn't work, analyze it with another method.

4. The discovered rule should be applied to all the figures in this column, not just the first few figures or the last few figures, but not to other figures in this column. Pay special attention to this when solving problems.

Practice and thinking

1. 9,1l,15, 21,29, 2000.

⒉5, 14,4 1, 122, 。

⒊ 1,2,2,4,8,32, 。

⒋7, 14, 10, 12, 14,9, 19, 5, ,

⒌7,8, 10, , 22, 38

⒍ 1,3,9,27, ,243

⒎ 1, 3, 6, 10, , 2 1, 28, 36

⒏ 1,2,6,24, 120, ,5040。

Family ability test and improvement training

⒈5,7, 1 1, 19,35, , 13 1,259

2. There is a unique number in the following lines, please look it up.

⑴ 6， 12，3，27，2l， 10， 15，30

⑵ 2, 5, 10, 16, 22, 28, 32, 38, 24

⑶ 2,3,5,8, 12, 16, 17,23,30

⑷ 2, 4, 8, 12, 16, 32。

3. Observe the first three formulas, then find out the law, and write the product of the last two formulas directly according to the found law.

⑴ 123456789×9= 1 1 1 1 1 1 1 10 1

⑵ 123456789× 18=222 222 2202

⑶ 123456789×27=333 333 3303

⑷ 123456789×72=

⑸ 123456789×63= .

4. Observe the following three equations and find out the rules. Then write the fourth to eighth equations in turn.

1×9+2= 1 1, 12×9+3= 1 1 1, 123×9+4= 1 1 1 1

Reference answer

Practice and thinking

⒈39, 5 1 ⒉ 365 ⒊ 256 ⒋ 25, 0 ⒌ 14 ⒍ 8 1 ⒎ 15 ⒏ 720

Family ability test and improvement training

⒈ 67

⒉ 10, 5, 16, 12

⒊ 888 888 8808 777 777 7707

⒋ 1234×9+5= 1 1 1 1 1

12345×9+6= 1 1 1 1 1 1

123456×9+7= 1 1 1 1 1 1 1

1234567×9+8= 1 1 1 1 1 1 1 1

12345678×9+9= 1 1 1 1 1 1 1 1 1

================

Test questions and answers of the third grade Olympic mathematics competition

1. There are 10 red, yellow and blue balls with the same size and texture in the pocket. How many balls can you touch at least once to make sure that at least four balls are the same color?

Analysis and solution: If the four balls taken out at one time are all the same color, then the answer is "4", which is obviously wrong, because the colors of the four balls taken out may also be different. The answer of "4" is the most favorable situation, but in order to "ensure that at least four balls are the same color", the most unfavorable situation needs to be considered. If the most unfavorable situation meets the requirements of the topic, then other situations must meet the requirements of the topic.

What is the "worst case"? That is, we drew three red balls, three yellow balls and three blue balls. At this time, there are three three-color balls, and no four balls are of the same color. The nine balls found in this way are the "most unfavorable" situation. At this time, the other ball, whether red, yellow or blue, can guarantee that four balls have the same color, so the answer should be: 3+3+3+ 1= 10 (each).

As can be seen from the example, the most unfavorable principle is to consider the problem from the "extremely bad" situation. If the question in the example is "If you can find at least a few balls, four balls may be the same color", then we can answer "four" according to the most favorable situation. The problem now is "to ensure that there are four balls of the same color". The word "guarantee" requires us to analyze the problem from the most unfavorable situation.

2. There are 50 students going boating in the park, each big ship can take 6 people, and the rent is 10 yuan; Each boat can take four people and rent 8 yuan. So among many different chartering schemes, which one is the most economical?

Everyone in the big boat: 10÷6=5/3 yuan, and everyone in the small boat: 8÷4=2 yuan.

The rent of big ships is cheap, so rent as many big ships as possible: 50÷6=8+2.

Rent eight big boats, and there are two people left.

6+2=8=2×4

Two small boats are cheaper than two big ones.

So we rented 1 big boat less, and the remaining 8 people rented 2 small boats.

The most economical plan is to rent seven big boats and two small boats.

Rent: 7× 10+2×8=86 yuan.

3. Five people, A, B, C, D and E, take part in the table tennis competition. Every two people have to play a game, and only one game can be played. It is stipulated that the winner gets 2 points and the loser gets none. The known results are as follows: (1)A and E are tied for the first place; (2)B is the third place; (3)C and D are tied for fourth place, so how many points does B get?

Everyone can play 4 games, and one * * * can play 5×4÷2= 10.

If you win a game, you will get 2 points, and each person will get at least 0 points and at most 4×2=8 points.

Everyone's scores are: 0, 2, 4, 6 and 8.

Because AE tied for first place, no one can win, so no one can get 8 points.

Similarly, CD tied for fourth place, so there is no total negative, so everyone is 0.

Then the one tied for first place can only get 6 points, and the one tied for fourth place can only get 2 points.

B was the third place and got 4 points.

4. There are 15 students in one row. From the left, Kobayashi is 1 1. From the right, Xiao Gang is the 10. How many students are there between Xiao Lin and Xiao Gang?

Counting Xiao Lin and Xiao Gang, twice, the students who re-read are:

1 1+ 10- 15 = 6.

So there is 6-2=4 between Xiao Lin and Xiao Gang.

5. Black hen lays 2 eggs per day 1 egg, white hen lays 2 eggs per day 1 egg, and two chickens lay 2 eggs per day 1 egg. How many days will it take at least?

Black-bone chicken 1+2= 3 eggs a day, white chicken 1+ 1= 2 eggs a day.

The least common multiple of 2 and 3 is 6.

Can lay in 6 days: 6÷2+6÷3=5 eggs.

Oviposition requires 10 eggs: 10÷2×6= 12 days.

reconsider ...

After laying the last egg, black chickens should rest for 2 days and white chickens should rest 1 day.

* * * Rest time is 1 day.

So after laying 10 eggs, it takes at least12-1=11day.

6. A basket of radishes weighs 56 kilograms. Sell half the radish first, and then sell the remaining half. At this time, the basket weighs * * *17kg. How much does this basket of radishes weigh? How much does this basket weigh?

The radish sold for the second time accounts for (1-1/2) ×1/2 =1/4 of the total.

Two * * * sold together: 1/2+ 1/4=3/4, that is, 56- 17=39 kg.

Original radish weight: 39 ÷ 3/4 = 52kg.

Basket weight: 56-52 = 4kg

7. Xiao Qiang, Liang Xiao and Xiaojun practice basketball. A * * voted 150 times, * * * missed 64 times. As we all know, Xiao Qiang and Xiao Liangyi threw 48 balls, Liang Xiao and Jun Xiao threw 69 balls, and how many balls did Liang Xiao throw?

Three people and one * * * shot: 150-64=86 times.

Xiao Liang's score: 48+69-86=3 1 time.

8. Fill in 3, 6, 9, 12, 15, 18, 2 1, 24, 27 in the appropriate boxes, so that the sum of the three numbers in each horizontal, vertical and diagonal line will get 45.

24,03, 18

09, 15,2 1

12,27,06

9. There are 100 chickens and rabbits, and rabbits have 28 more feet than chickens. How many chickens and rabbits are there?

If 100 rabbits are rabbits, there are 100×4=400 rabbit feet and 0 chicken feet, with 400 rabbit feet more than chicken feet.

Every time 1 rabbit is reduced, 1 chicken is increased.

Rabbit feet decreased by 4 and chicken feet increased by 2.

The difference between rabbit feet and chicken feet is reduced by 4+2=6.

Chicken: (400-28)÷6=62

Rabbit: 100-62=38.

10, team A and team B with 96 people. If 8 people are transferred from team A to team B, and team B gives 36 people to team C, then the number of team A is twice that of team B. How many people were there in each team at that time?

Now the total number of Party A and Party B has decreased by 36, which is 96-36=60.

At this time, B has: 60÷(2+ 1)=20 people; A Yes: 20×2=40 people.

It turns out that A has: 40+8=48 people; B is: 96-48=48 people.

1 1, how many times does the number "1" * * appear in the number1,2,3, …, 132?

Unit:

1, 1 1,2 1,3 1,…… 13 1。 * * *: ( 13 1- 1) ÷ 10+ 1 = 14.

Ten:

10, 1 1, 12 ... 19,: 10

1 10, 1 1 1, … 1 19,: 10.

* * *: 10+ 10 = 20.

Hundreds of people:

100, 10 1,… 132。 a * * *: 132- 100+ 1 = 33。

1 This number, a * * * appears:

14+20+33=67 times

12. There are three people in Xiaoming's family. My mother is two years younger than my father. The age of the whole family adds up to just 70 this year. Seven years ago, the age of the whole family added up to just 50. How old is everyone in Xiaoming's family now?

The difference between the total age now and the total age seven years ago: 70-50=20 years old.

7×3=2 1 year

So Xiao Ming was not born seven years ago.

Xiaoming is 20-7×2=6 years old this year.

Mom and Dad are 70-6 = 64 years old this year.

Dad this year: (64+2)÷2=33 years old.

Mom this year: 33-2=3 1 year.

-+++++++++++ -

49 ways to ask and answer questions about the third grade Olympic Mathematics.

1. A road is 100 m long, and every 10 m is planted from beginning to end 1 plane tree. How many trees have been planted?

The road is divided into 100 ÷ 10 = 10, and * *10/tree is planted.

12 willows are arranged in a row, and 3 peach trees are planted between every two willows. How many peach trees have been planted?

3× (12- 1) = 33 trees.

How many times does it take to saw a 200 cm long piece of wood into 10 cm long pieces?

200 ÷ 10 = 20 segments, 20- 1 = 19 times.

4. It takes 10 seconds for ants to climb branches. How many minutes does it take to climb from the first section to the 13 section?

From the first segment to the 13 segment, it takes10× (13-1) =120 seconds, 120 ÷ 60 = 2 minutes.

5. Plant chrysanthemums around the garden and plant them every 1 meter 1 potted flower. * * * The flower bed is 20 meters long. How many pots of chrysanthemums do you need?

20/ 1× 1 = 20 pots

6. There are 250 poles from the power plant to the urban area, and the distance between every two poles is 30 meters. How far is it from the power plant to the city?

30× (250- 1) = 7470 meters.

7. Miss Wang keeps half of her monthly income in 20 yuan for living expenses and the rest in 50 yuan. At this time, there are still 40 yuan left to pay tuition and books for his children. How much does he earn this month?

[(40+50) ×2+20] ×2=400 (yuan) A: He earned 400 yuan this month.

8. After a person walked half the length along the big elevator, he walked the remaining half, leaving 1 km. Q: What is the total length of the big lift?

1× 2× 2 = 4km

9. Party A is processing a batch of parts. On the first day, half of this pile of parts and 10 pieces were processed, and on the second day, the remaining half and 10 pieces were processed, leaving 25 pieces untreated. Q: How many parts are there in this batch?

(25+10) × 2 = 70, (70+10) × 2 =160. Comprehensive formula: (25+10) × 2+10× 2.

10. A caterpillar grows from a larva to an adult, doubling every day. 16 days can grow to 16 cm. How many days can it grow to 4 cm?

16 ÷ 2 ÷ 2 = 4 (cm),16-1=14 (days)

1 1. A bucket of water, pour out half of it for the first time, then pour it back into the bucket for 30 kg, pour out the remaining half of the water in the bucket for the second time, and pour out 180 kg for the third time, with 80 kg left in the bucket. How many kilograms of water are there in the bucket?

180+80 = 260 (kg), 260× 2-30 = 490 (kg), 490× 2 = 980 (kg).

12. There are 200 books on the shelves A and B. There are three times fewer books on the shelf A than on the shelf B, and there are 16 books. How many books are there on shelves A and B?

Answer: B: (200+16) ÷ (3+1) = 54 (Ben); A: 54×3- 16= 146 (Ben).

13. Xiaoyan spent 185 yuan bought a suit. How much are the coat and trousers?

Pants: (185-5)÷(2+ 1)=60 yuan;

Coat: 60×2+5= 125 (Yuan).

14. The sum of the ages of Party A, Party B and Party C is 94 years old. Party A is twice as old as Party C, five years old, and Party B is twice as old as Party C. 19 years old Q: How old are Party A, Party B and Party C respectively?

If everyone's age doubles, then the sum of three people's ages is 94×2= 188. If A minus 5 years old and B minus 19 years old, then the sum of their ages is188-5-19 =164 (years old). At this time, A's age is half that of C, that is, C's age is twice that of A. Similarly, C's age is twice that of B, so at this time, the ages of A and B are164 ÷ (1+1+2) = 4 1 (years old. The original age of A is (4 1+5)÷2=23 (years old), and the original age of B is (4 1+ 19)÷2=30 (years old).

15. Xiaoming and Xiaohua finish fishing. Xiao Ming said, "If you give me 1 fish you caught, my fish is twice as big as yours. If I give you 1, we will be the same. " Please work out how many fish each of them caught.

Xiaoming is more than Xiaohua 1×2=2. If Xiaohua gives Xiaoming 1 fish, then Xiaoming has 2+ 1×2=4 fish, and Xiaohua has 4÷(2- 1)=4 fish. It turns out that Xiaohua has fish 4+ 1=5 (strips) and Xiaoming has fish 5+2=7 (strips).

16. Xiao Fang went to the stationery store to buy 13 Chinese books and 8 arithmetic books, and spent 10 yuan. As we all know, the price of six Chinese books is equivalent to the price of four arithmetic books. Q: How much are 1 Chinese books and 1 arithmetic books?

8÷4×6= 12, that is, the price of eight arithmetic books is equal to 12. Therefore, the original language value of 1 0× 1 00 ÷ (13+12) = 40 (points), and the arithmetic value of1is 40× 6 ÷.

17. Find the pattern and fill in the appropriate numbers in the brackets. 75, 3, 74, 3, 73, 3, (), ().

Answer: 72, 3.

18 Find the pattern and fill in the appropriate numbers in brackets. 1, 4, 5, 4, 9, 4, (), ().

Odd terms form the sequence 1, 5, 9 ..., and each period is 4 more than the previous period; Even items are all 4, so13,4 should be filled in.

19. Find the pattern and fill in the appropriate numbers in the brackets. 3, 2, 6, 2, 12, 2, (), ().

24,2。

20. Find the pattern and fill in the appropriate numbers in brackets. 76, 2, 75, 3, 74, 4, (), ().

Answer: To split the original series into two columns, you should fill in: 73, 5.

2 1. Find the pattern and fill in the appropriate numbers in the brackets. 2, 3, 4, 5, 8, 7, (), ().

Answer: Split the original series into two columns, which should be:16,9.

22. Find the pattern and fill in the appropriate numbers in brackets. 3, 6, 8, 16, 18, (), ().

Answer: 6 = 3× 2, 16 = 8× 2, that is, the even term is twice the odd term before it; And 8 = 6+2, 18 = 16+2, that is, from the third item, the odd item is 2 more than the even item before it, so it should be filled in: 36, 38.

23. Find the pattern and fill in the appropriate numbers in brackets. 1, 6, 7, 12, 13, 18, 19, (), ().

Answer: To split the original series into two columns, you should fill in: 24, 25.

24. Find the rules and fill in the appropriate numbers in brackets. 1, 4, 3, 8, 5, 12, 7, ().

Answer: Odd terms form a series of 1, 3, 5, 7, …, and each series is 2 more than the previous series; Even-numbered items make up the series 4, 8, 12, …, and each item is 4 more than the previous one, so you should fill in: 16.

25. Find the pattern and fill in the appropriate numbers in brackets: 0, 1, 3, 8, 2 1, 55, (), ().

Answer: 144377.

26. A, B, C and D won the top four in a competition. It is known that D is not the highest ranking, but it is higher than both B and C, and C is not higher than B. Q: Where are they?

Answer: D is not the highest ranking, but it is higher than B and C, so it is the second, and A is 1. C is not ranked higher than B, so B is the third and C is the fourth.

27. The weight of an elephant equals the weight of four cows, the weight of one cow equals the weight of three ponies, and the weight of one pony equals the weight of three piglets. Q: How many piglets does an elephant weigh?

Answer: 4×3×3=36, so the weight of an elephant is equal to the weight of 36 piglets.

28. There are three people, A, B and C. One likes watching football, the other likes watching boxing and the other likes watching basketball. It is known that A doesn't like watching basketball, and C doesn't like watching basketball and football. One ticket for football, boxing and basketball. Please give them tickets according to their hobbies.

Answer: C doesn't like watching basketball and football. He should be given a boxing ticket. A doesn't like watching basketball. You should get a football ticket. Finally, the basketball ticket should be given to B.

29. There is a pile of iron and copper, each with exactly the same weight and each with exactly the same weight. Three iron bars and five copper bars weigh 2 10g. Four iron blocks and 10 copper blocks weigh 380 grams. Q: How much does each piece of iron and copper weigh?

Answer: Four iron blocks and 10 copper blocks * * * weigh 380 grams, so two iron blocks and five copper blocks * * * weigh 380÷2= 190 (grams). While three iron blocks and five copper blocks * * * weigh 2 10g, so 1 iron blocks weigh 2 10- 190=20 (g). 1 copper weight (190-20×2)÷5=30 (g).

30. One of the three people A, B and C did a good deed. They each said a word, only one is true. A said, "B did it." B said, "I didn't do it." C said, "I didn't do it either." Q: Who did something good?

Answer: If A does a good deed, then what B and C say is true, which contradicts that only one sentence is true. If B does something good, then what A and C say is true and contradictory. The good thing is done by C. At this time, both A and C are wrong, and only B is true, so the good thing is done by C.

3 1. Cut a rectangular cardboard with a length of 8 cm and a width of 3 cm on each of the four corners. What is the circumference of the rest?

Answer: (8+3)×2=22 (decimeter)

32. Calculation:18+19+20+21+22+23.

The original formula =( 18+23)×6÷2= 123.

33. Calculation:100+102+106+108+/kloc-0+12+65438.

The original formula = (100+114) × 8 ÷ 2 = 856.

34.995+996+997+998+999

The original formula =(995+999) ×5÷2=4985.

35.:( 1999+ 1997+ 1995+…+ 13+ 1 1)-( 12+ 14+ 16+…+ 1996+ 1998)

The number of items in the first bracket is (1999-11) ÷ 2+1= 995, so the original formula = (1999-1998)+

36. Find Law 2, 1, 4, 2, 6, 4, 8, 10, 16, (12), (32)

Even terms are more than 2 times, and odd terms are 2 times.

32, 16,48,24,72,(36),( 108)32÷2= 16,32+ 16=48,48÷2=24,48+24=72,72÷2=36,72+36= 108

37. A book * * * has 150 pages. It is necessary to sort out the page numbers of this book (342). From page 1 to page 9, 9 digits are required; From page 10 to page 99, 2× 90 = 180 is required; From page 100 to page 150, it takes 3× 5 1 = 153.

So * * * needs 9+ 180+ 153 = 342.

◆ When one basket is put into four baskets of apples, the basket weighs 28kg. Pour out three baskets of apples, each weighing 10kg, and one weighing (4) kg.

Three baskets of apples weigh 28- 10 = 18kg.

1 apple basket weight 18 ÷ 3 = 6 kg.

The weight of a basket 10-6 = 4 kg.

38. Square vegetable fields with a side length of12m. If we want to double its area, how many meters will it add on one side and on the other? (writing process)

The expanded area is 12× 12× 2 = 288 square meters.

After expansion, the length of one side is12+4 =16m.

After deployment, the length of the other side is 288÷16 =18m.

So 18- 12 = 6m is added.

39. The school flower 156 yuan bought three chairs and four tables. As we all know, two tables can buy five chairs. How much is a chair? How much is a table? (writing process)

Because two tables can buy five chairs, and two× 2 = four tables can buy five× 2 =10 chairs.

Because you need 156 yuan to buy three chairs and four tables, you need 10 = 13 chairs * *.

So a chair is 156 ÷ 13 = 12 yuan.

It takes 12× 5 = 60 yuan to buy five chairs.

It takes 60 ÷ 2 = 30 yuan to buy a table.

40. There is an island where there are two kinds of people, one is honest and the other is a liar. One day, a tourist went to the island and met people on three islands, A, B and C, and asked them who was an honest man and who was a liar. A said, "Both B and C are liars." B said, "I am an honest man." C said, "B is a liar." There are (2) liars among these three people.

Because what B and C say is contradictory, there must be honest people and liars among them.

So a is also a liar.

So, two of the three liars.

4 1, 40 pears are allocated to 3 classes, 20 pears are allocated to 1 class, the rest are allocated to 2 classes and 3 classes on average, and 2 classes are allocated to (10).

42. Seven years ago, my mother was six times older than my son. My son is 12 years old and my mother is (37) years old.

43. The students have a radio practice contest, and the whole class is arranged in six equal rows. Xiaohong is in the second row. From the beginning, she stood in the fifth position, and from the back, she stood in the third position. There are (42) students in this class.

44. There is a string of colored beads arranged in the order of "2 red, 3 green and 4 yellow". The 600th one is (yellow).

45. Wrap the rope around the tree three times, more than 30 cm. If you circle the tree four times, the difference is 40 cm. The circumference of the tree is 70 cm, and the rope is 240 cm long.

46. A snail climbed to the bottom of the well at a depth of12m, climbed 3m every hour, and then slipped 2m. It takes (65,438+00) hours for the snail to climb out of the wellhead.

47. Saw a wooden stick with a length of 10 meter, and it takes 2 minutes to saw each section. It will take (4) minutes if this stick is sawed into five equal parts.

48. Three cats ate three mice in three days. At this rate, nine cats can eat (9) mice in nine days.

49. ┖ ┴ ┴ ┴ ┴ ┴ ┴ ┴ ┴ ┴ ┚ There are () line segments in * * in the figure. ┖┴┴┴┴┴┴┴┴┴┴┚ There are (55) line segments in the diagram * *.