Classic articles on primary school mathematics puzzles and answers
Intelligence refers to the general psychological ability of living things. Refers to people's ability to know and understand objective things and solve problems by using knowledge and experience, including memory, observation, imagination, thinking and judgment. This ability includes the following points: understanding, judging, solving problems, abstract thinking, expressing thoughts, language and learning ability. When considering animal intelligence, intelligence? The definition can also be summarized as: the ability to effectively adapt to the environment by changing oneself, changing the environment or looking for a new environment. Intelligence, also called intelligence, is the ability of people to understand objective things and use knowledge to solve practical problems. Intelligence includes many aspects, such as observation, memory, imagination, analysis and judgment, thinking ability and adaptability. The level of intelligence is usually expressed by IQ, which is used to express the level of intellectual development. In particular, intelligence does not mean wisdom, but their meanings are different.
1, can you add symbols or brackets such as addition, subtraction, multiplication and division to the following puzzle to make it an equality formula?
1 2 3 4 5 = 1
1 2 3 4 5 =2
1 2 3 4 5 =3
1 2 3 4 5 =4
1 2 3 4 5 =5
1 2 3 4 5 =6
1 2 3 4 5 =7
1 2 3 4 5 =8
1 2 3 4 5 =9
1 2 3 4 5= 10
2. There are ten bags of apples, ten in each bag, and any one is the same weight; It is known that all nine bags of apples weigh 50 grams, and only one bag weighs 45 grams. Now there is only one lever to weigh, and I only need to weigh it once, so I will find out the bag of 45 grams of apples and ask how to weigh it. (Answer: First, number these ten bags of apples as 1 and 2. . . . 10, and take out the same number of apples from each bag and weigh them once. If it is a multiple of 50, it is the 10 package, otherwise a 5g short is the 9th package, and two short are the 8th package. . . )
3, 1.5 plus 5 (), plus two 5 plus ().
2. There are 1 piles of oranges, 2 piles of apples and 3 piles of pears, which add up to () piles.
The mother is 26 years older than her son. 1 year later, the mother is () years older than her son.
It takes 5 minutes to cook two eggs, and then it takes () minutes to cook four eggs.
5. Starting from 0, add 9 continuously, and after adding () times, their sum is 54.
6. Know □ +△ = 25□-○ =14△+◇ = 24△ +△ =16.
Calculate what □, △, ◇, ◇ stand for? Fill in the brackets.
□=( ) △=( ) ○=( ) ◇=( )
8. Put 10 pots of flowers on the round flower bed, with the spacing between every two pots of 1 m, and a circle of flower beds is () m long.
9. The clock strikes 2 at 2 o'clock, 2 seconds later, 5 at 5 o'clock, and () seconds later.
10. On Mingming's birthday, seven children were invited, each with a rice bowl, two with a vegetable bowl and three with a soup bowl. Please help him calculate, they use () bowls.
1, find a regular number:
4、8、 12、 16、20、( )、( )
3、 1、6、2、 12、3、( )、( )
2, a two-digit number, the sum of the number on the ten-digit number and the number on the one-digit number is 10. If the positions of these two digits are exchanged, the number obtained is 36 less than the original number, and the original two digits are ().
There are ***80 books on two shelves. Take eight books from the first shelf and put them on the second shelf. The number of books on the two shelves is equal. It turns out that there are () books on the first shelf.
4. There are 10 red beads and 10 black beads in the pocket. Now take at least () beads out of your pocket and make sure that the two beads are the same color.
A car goes from Nanjing to Shanghai, stopping at Zhenjiang, Changzhou, Wuxi and Suzhou along the way. The transportation department should prepare () different tickets for this car.
6. Grandpa is 74 years old. 10 years ago, his age was eight times that of his grandson, and this year he is () years old.
7. 1 Bottle of oil weighs 600g, half of the oil is eaten, and the bottles are weighed together, leaving 450g. There was () grams of oil in the bottle.
8, a cup of milk, Xiaomei first drank half a cup, filled the cup with cold boiled water, drank half a cup, and filled it with cold boiled water. Finally, Xiaomei drank it all and asked her to drink () a glass of milk.
9, 1 ~ 9, two different numbers at a time, the sum of these two numbers must be greater than 10, and there are () ways to take it.
10, an animal baby, grows 1 times every day, 16 days can grow 40 kg, and it takes () days to grow to 20 kg.
1 1. In order to welcome New Year's Day, the school hangs colored balls from left to right in the order of 4 yellow, 3 red 1 green, and asks if the 26th colored ball from left to right is () color.
12, Xiaohong and Xiaoming live in the same building. Xiaohong lives on the third floor and Xiaoming lives on the sixth floor. It takes 12 seconds for Xiaohong to walk home from the first floor, and () seconds for Xiaoming to get home at the same speed.
/Kloc-Class 0/3 and Class 2 (2) rowed 44 people. Each big ship can take six people, and the rent is 10 yuan. Each boat can take four people and rent 8 yuan. If you are a tour leader, you have to rent () a big boat and () a small boat, and the rent is () yuan.
14, five ropes should be tied into one, and one * * * should be tied into a knot (); A rope should be cut into four sections and cut () times.
15. Grandma gave Dongdong and Xiaohong candy, and each of them ate four, leaving 1. Everyone takes 5 capsules, the difference is 1 capsule. Grandma took out () candy.
1-5 Question tip:
1, find a regular number:
4、8、 12、 16、20、(24)、(28)
Tip: The law is 4 (which number is 4) or the previous number plus 4.
3、 1、6、2、 12、3、( )、( )
Hints: 3, 1, 6, 2, 12, 3, (24), (4), except for the flashing ones, everything else is twice as large as the previous ones.
2, a two-digit number, the sum of the number on the ten-digit number and the number on the one-digit number is 10. If the positions of these two digits are exchanged, the number obtained is 36 less than the original number, and the original two digits are ().
Tip: For a two-digit number, exchange numbers between numbers to get a new two-digit number. The difference between the original number and the new number must be a multiple of 9. This difference divided by 9 is the digital difference (greatly reduced) between numbers and numbers. This is 36? 9=4, that is to say, the difference between the original digit and the decimal digit is 4 (greatly reduced), and their sum is 10, so the problem becomes a sum-difference problem. The original number was 73.
There are ***80 books on two shelves. Take eight books from the first shelf and put them on the second shelf. The number of books on the two shelves is equal. It turns out that there are () books on the first shelf.
Tip: One * * * is 80 copies, and the last two are equal, both of which are 40 copies. After taking 8 books from the first shelf, there are 40 books, so there are 40+8=48 books. The second shelf has only 40 books after getting 8 books, so there are 40-8=32 books. Here I ask how many books were in the first shelf, which should be 48. Other solutions, as long as reasonable, should be affirmed.
4. There are 10 red beads and 10 black beads in the pocket. Now take at least () beads out of your pocket and make sure that the two beads are the same color.
Tip: This is the most basic principle problem of pigeon coop, and there are three of them. When parents or teachers guide you, don't put the numbers too big at once. Start small, such as "You have two red beads and two black beads in your pocket. Now, take out at least () beads from your pocket and make sure that the two beads are the same color. " Then gradually enlarge. Guide children to understand the exact meaning of the words "only ensure".
A car goes from Nanjing to Shanghai, stopping at Zhenjiang, Changzhou, Wuxi and Suzhou along the way. The transportation department should prepare () different tickets for this car.
Hint: This is a combination problem. Considering the reality of primary school students, there are only four stops here, and it is one-way driving. Let the students actually sort with four different numbers, but it is very important to guide them to pay attention to the order at the beginning of the first time. It is 4+3+2+ 1= 10.
1. My brother has 4 apples, my sister has 3 apples and my brother has 8 apples. After my brother gave it to my brother 1, my brother ate three apples. Who has more apples at this time?
Xiaoming is 6 years old and Xiao Qiang is 4 years old. How old is Xiaoming two years later?
Students line up to do exercises. There are four people in front of Xiaoming and four people behind him. How many people are there in this team?
4. There is a book. Xiaohua read two pages on the first day, and then read two more pages every day than the day before. How many pages did he read on the fourth day?
Students line up to do exercises, counting from the front, Xiao Ming ranks fourth, counting from the back, and Xiao Ming ranks fifth. How many people are there in this team?
6. There are eight rubber balls. If every boy sends one, there will be two more. If every girl sends one, there will be two less. How many boys and girls are there?
7. The teacher gave each of the nine outstanding students a flower and 1 red flower. How many red flowers does the teacher have?
8. There are five students throwing sandbags. If the teacher gives each person two sandbags, the difference is 1. How many sandbags does the teacher have?
9. There were nine books just now. Dad bought him five more, and Xiaoming borrowed two. How many books were there just now?
10. A group of pupils, eight students are taller than Li Ping and nine students are shorter than him. How many students are there in this group?
1 1. After Xiao Lin ate eight cookies, Xiao Lin now has four cookies. How many biscuits did Xiao Lin eat?
12. After my brother gave my brother five pencils, there were six left. How many pencils does my brother have?
13. There are 8 boys in the Second Squadron, and there are as many girls as boys. How many students are there in the second squadron?
14. Dahua and Xiaogang each have 10 pictures. After Dahua gave Xiaogang two, how many more did Xiaogang have than Dahua?
15. Mother cat gave Xiaobai 5 fish and Xiaohua 4 fish, and Xiaobai and Xiaohua * * * ate 6 fish. How many people are there?
16. The students borrowed balls from the gym, nine from Class One and six from Class Two. How many balls were lost in the gym?
17. After taking out five white balls and five flower balls from the bag, there are 10 white balls and five flower balls left. How many white balls and flowers are there in the bag?
18. Fangfang made 14 flowers, Jingjing made 8 flowers, and Fangfang gave Jingjing several flowers. Are there as many flowers as they have?
19. Mom bought some duck eggs and 12 eggs. I ate eight eggs, and there were as many eggs left as duck eggs. How many eggs did mom buy?
20. There are 10 sheep on the grass. Three white goats escaped and seven black goats came. How many sheep are there now?
2 1.6 pupils bought idioms with 14 yuan, 17 yuan, 18 yuan, 2 1 Yuan, 25 yuan and 37 yuan respectively. When I looked at the pricing, I found that there was not enough money, but the money of Party A, Party B and Party C together could just buy two pieces, and the money of Party D and Party E together could just buy 1 piece. The price of this idiom is () yuan.
22. What does each stand for?
○ + □ = 15
○ ? □ =56
○=( )
□=( )
23. Find a rule to fill in the blanks:
4、8、 12、 16、20、( )、( )
3、 1、6、2、 12、3、( )、( )
24, a two-digit number, the sum of the number on the ten-digit number and the number on the one-digit number is 10. If the positions of these two digits are exchanged, the number obtained is 36 less than the original number, and the original two digits are ().
25. There are 80 books on two shelves. Take eight books from the first shelf and put them on the second shelf. The number of books on the two shelves is equal. It turns out that there are () books on the first shelf.
26. There are 10 red beads and 10 black beads in the pocket. Now take at least () beads out of your pocket and make sure that the two beads are the same color.
On the 27th, a car went from Nanjing to Shanghai, stopping at Zhenjiang, Changzhou, Wuxi and Suzhou along the way. The transportation department prepared () different tickets for this car.
28. Grandpa is 74 years old. 10 years ago, his age was eight times that of his grandson, and this year he is () years old.
29. 1 Bottle of oil weighs 600g, half of the oil is eaten, and the bottles are weighed together, leaving 450g. There was () grams of oil in the bottle.
30, a cup of milk, Xiaomei drank half a cup first, filled the cup with cold boiled water, drank half a cup, and filled it with cold boiled water. Finally, Xiaomei drank it all and asked her to drink () a glass of milk.
3 1 and 1 ~ 9, two different numbers are taken at a time, and the sum of these two numbers must be greater than 10, and there are () ways to take them.
32, an animal baby, every day 1 times, 16 days can grow 40 kilograms, and it takes () days to grow to 20 kilograms.
33. In order to welcome New Year's Day, the school hangs colored balls from left to right at the school gate in the order of 4 yellow, 3 red 1 green, and asks if the 26th colored ball from left to right is () color.
Xiaohong and Xiaoming live in the same building. Xiaohong lives on the third floor and Xiaoming lives on the sixth floor. It takes 12 seconds for Xiaohong to walk home from the first floor, and () seconds for Xiaoming to get home at the same speed.
There are 44 students in Class Two (2) rowing. Each big ship can take six people, and the rent is 10 yuan. Each boat can take four people and rent 8 yuan. If you are a tour leader, you have to rent () a big boat and () a small boat, and the rent is () yuan.
36. Weave five ropes into one, and tie a knot with a * * * (); A rope should be cut into four sections and cut () times.
37. Grandma gave Dongdong and Xiaohong candy, and each of them ate four, leaving 1. Everyone takes 5 capsules, the difference is 1 capsule. Grandma took out () candy.
38. Find a rule to fill in
4 9 16 25 ( ) ( ) ( ) ( )
39. In division, the divisor is 6. Xiao Ming turns the ten digits and single digits of the dividend upside down, and the quotient of division is 4. The correct bonus for this problem is ().
40.6 Children get together, each with a rice bowl, two with a vegetable bowl and three with a soup bowl. Bowls should be prepared for this party.
4 1. Students need to move 10 sets of desks and chairs to decorate the venue. Two people carry a table and two chairs each. Please make a careful calculation. You should arrange for () students to move all at once.
42. physical education class in our class. The whole class stands in four rows, with the same number of people in each row. I stand in the first row. I am the third on the left and the seventh on the right. Excuse me, do you know there are () people in our class?
43. Wang read a story love letter. He read five more pages before he was halfway through, 15 pages. How many pages did Wang read?
44. There are seven five-pointed stars in the rectangular box. Divide it into seven pieces with three straight lines, and each piece must have a five-pointed star. How to divide it?
☆ ☆ ☆
☆
☆ ☆ ☆
45. One day, a young man came to Boss Wang's shop and bought a present. The cost of this gift is 18 yuan, and the list price is 2 1 yuan. As a result, the young man took out 100 and bought this gift. Boss Wang didn't have any change at that time, so he changed 100 yuan from the neighborhood and gave it to the young man 79 yuan. But later, the neighborhood found that this 100 yuan was counterfeit, and Boss Wang had no choice but to return this 100 yuan to the neighborhood. The question now is: How much did Boss Wang lose in this transaction?
46. Divide the clock face into three parts with two straight lines (note that three parts are not four parts), so that the sum of each part is equal. Where should the straight line be drawn and how should it be divided?
47. A hunter came home with a sheep, a wolf and a cabbage and met a river on the way. There is only one boat by the river, but it is too small. At most, you can only take the hunter and another thing across the river at a time. But when the hunter is away, the wolf will eat the sheep and the sheep will eat the cabbage. Excuse me, how to safely transport wolves, sheep and cabbage across the river?
48. A cake baking tray can only bake two cakes at a time. It takes three minutes to bake one side. Q: How many minutes does it take to bake three cakes?
49. The difference between mom and dad is 50 kg, and the two children weigh 30KG. Everyone meets a river and wants to cross it, but the ship weighs 85 kilograms. How can they all cross the river?
50. A guest went to the bakery and bought three cakes, which took 16 minutes to finish. A cake should be baked on both sides, and 1 noodle should be baked for 5 points. A * * * has two pots. How can I bake the cake according to the requirements of the guests?
5 1. A river has 1000 red fish, 1000 goldfish, and there are three bears on the shore. If 1 red fish = 10 goldfish, the bear will eat 500 red fish or 5000 goldfish every day, and all goldfish will eat 500 small fish and red fish every day.
52 .. 1 well has 1 frog, and the depth of the well is 5m. It climbs 3 meters every day and slides 2 meters at night. When can this frog climb out of this well?
53. How to plant 10 trees in 5 rows with 4 trees in each row?
54. I bought 50 cream cakes, 8 of which were packed in a box. How many boxes should I use at least?
Selected Questions and Answers of Math Puzzle in Primary School
1. Plant trees around a square site, with 10 trees on each side and one tree at each vertex. There are * * * trees around this site.
The coach from Jinan to Beijing has five stops, so this coach from Jinan to Beijing needs to prepare () different tickets.
The sum of 3.751+752+753+754+755+756+757 is ().
There are several students in a row. From left to right, Xiao Qiang is the fifth, from right to left, and Xiao Qiang is the third. There are () students in this row.
5. There are 70 baskets of cabbages and radishes in the food market, with more cabbages than radishes 18 baskets. Then, cabbage () basket and radish () basket are shipped.
6. Cut out the largest square on a rectangular paper with a length of 10 cm and a width of 8 cm. The circumference of this square is () cm.
7. There are two numbers 340 and 150, and their sum is much worse than their ().
8. In a division formula, the sum of dividend, divisor and quotient is 2 12, and the known quotient is 2, so the dividend is ().
9. Give pencils to eight students. There are some left over from five people, and six people are not enough. There is as much left as there is not enough. A * * has () pencils.
10, the third grade students planted 80 trees, the fourth and fifth grades planted twice as many trees as the third grade, and the third grade planted () trees.
Answer:
1, (36) 2, (6) 3, (5278) 4, (7) 5, (44 and 26)
6、(32) 7、(300) 8、( 140) 9、(44) 10、( 174)
Simplified Q&A on Math Puzzles in Primary Schools
1, for example 1: You let the workers work for you for 7 days, and the workers' remuneration is a gold bar. Gold bars are divided into seven consecutive parts. At the end of each day, you must give them some gold bars. If you are only allowed to break the gold bars twice, how can you pay the workers?
Xiao Pu (now working in minimally invasive surgery, I encountered this problem last year): This problem is relatively simple compared with other minimally invasive problems, but it still makes my head bigger. That's how I did the problem. If it is broken twice, it will be divided into three parts. I divided the gold bars into three parts: 1/7, 2/7 and 4/7. In this way, I can give it to him on 1 that day1/7; The next day, I gave him 2/7 to get back1/7; On the third day, I will give him 1/7, plus the original 2/7 is 3/7; On the fourth day, I gave him 4/7 gold bars and asked him to find out 1/7 and 2/7 gold bars. On the fifth day, give him1/7; The sixth day is the same as the second day; 1/7 restored him on the 7th day.
Example 2: Now Xiaoming's family has crossed a bridge. It's dark when crossing the bridge, so there must be a light. Now it takes 1 second for Xiaoming to cross the bridge, 3 seconds for Xiaoming's brother, 6 seconds for Xiaoming's father, 8 seconds for Xiaoming's mother and 12 seconds for Xiaoming's grandfather. At most two people can cross the bridge at a time. The speed of crossing the bridge depends on the slowest one. The light turns on for 30 seconds and then goes out. Ask Xiaoming how to cross the bridge.
Reference answer: This puzzle is actually to examine the ability of candidates to solve problems under restricted conditions. Specific to this topic, many people often think that Xiao Ming should go into battle lightly, which saves the most time, but in the end he can't find a solution. But in another way of thinking, we can decide who will come and go according to the specific situation, as long as we make some slight changes: the first step, Xiaoming crosses the bridge with his brother and Xiaoming comes back, which takes 4 seconds; In the second step, Xiaoming crossed the river with his father and his younger brother came back, which took 9 seconds. The third step, mom and grandpa cross the river, and Xiaoming comes back, which takes 13 seconds; Finally, Xiao Ming and his younger brother crossed the river in 4 seconds, with a total time of 30 seconds. How thrilling!
3. Topic Xiaohong's mother bought 48 jellies. Xiaohong's mother said to Xiaohong: If you can divide these jellies into four parts, so that the first part adds 3, the second part subtracts 3, the third part multiplies 3 and the fourth part divides 3, and the results are consistent, then you can eat these jellies. Xiaohong thought for a long time and finally came up with this problem. Do you know how to divide the smart ones?
answer
The four copies are 12, 6, 27 and 3 respectively. Suppose these four jellies are all X, then the first one is X+3, the second one is X3, the third one is 3X, and the fourth one is X/3, and the total is 48, so X=9. So we can know how much each one is.
4. Push back and skillfully turn it into a coin
Ever heard of coin games? If you haven't heard of it, get familiar with the rules of the coin game first! The coin withdrawal game is a game played by two people. Each participant is required to take several coins in turn, and whoever gets the last coin wins. Let's play a game of taking coins.
Game 1: There are 15 coins on the table, and two players (you and one of your classmates) take several coins in turn. The rule is that each person takes at least 1 coin and at most 5 coins at a time. Whoever gets the last one will win all 15 coins.
The game has started, and you must be thinking: Is there any way to ensure that you win? If so, what is the method? Now imagine yourself in a winning state. It's your turn to take coins. There are no more than five coins on the table. At this time, you can take all the coins on the table at once and become the winner. Now, can you move forward from this final state and find a state so that as long as your opponent is in this state, no matter how many coins he takes, you will be in an ideal winning state? It is not difficult to find that if your opponent has six coins on his desk, no matter how much he takes (from 1 to 5), there will be at least 1 and at most five coins left on the desk, so the victory must belong to you. In other words, whoever takes the ninth coin (15-6 =) wins. Therefore, the winning situation of the game 1 is the same as that of the next game 2.
Game 2: There are 9 coins on the table. Two players (you and one of your classmates) take turns to take a few coins. The rule is that each person takes at least 1 block and at most 5 pieces, and whoever gets the last piece wins 15 coins.
From the backward analysis of the first 1 game, we can easily know that the outcome of the second game is the same as that of the third game.
Game 3: There are three coins on the table. Two players (you and one of your classmates) take some in turn. The rule is that each person takes at least 1 block and at most 5 pieces, and whoever gets the last piece wins 15 coins.
In the third game, you only need to be the first to take three coins from the table to win. It can be seen that if you want to win the game of 1, as long as you take the three coins on the table first, you will definitely win.
Think about it: play the following game with your children by using the best strategy above: put 30 coins on the table, and two players (you and one of your classmates) take several in turn. The rule is that everyone takes at least two coins at a time and at most six coins, and whoever gets the last one wins all 30 coins.
Trust you, you will win.
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