New math puzzles. Mathematical puzzles for children and adults. The easiest math puzzles
In this article we will look at the most interesting puzzles intended for children, but not every adult can master them. They managed to stupefy more than one Internet user and gained enormous popularity on the Internet, as did comic tests with answers - but how quickly can you cope with them? The correct answers are waiting for you at the end of the article!
Where does the bus go?
If we talk about the most popular children's tasks on the Internet, this is one of them. Here is a picture of a bus. Which way is he heading?
How many points are there?
More attentiveness tasks for the most eagle-eyed users: how many black dots do you see at the intersections of lines?
Which circle is bigger?
Now let's solve interesting graphic puzzles. Can you answer which of the yellow circles shown in the picture is larger?
Moving the matches
The following children's puzzles are also often given to first-graders to solve: they require you to move matches in a certain way to get a given figure.
Find the panda!
The Internet was also blown up by the following graphic puzzles by artists who placed an image of a panda in complex pictures and invited other users to find it. They hid the panda among a crowd of Star Wars stormtroopers, a metalhead gathering, and even tried to hide it among a myriad of massage tables. Check your attentiveness!
Japanese IQ test
But what kind of IQ test did the Japanese come up with? On the shore there is a man with two sons, a mother with two daughters and a policeman with a criminal. In front of them is a raft on which they need to get to the other side. Try to think about how they can be transported there, taking into account such interesting conditions:
- Only two people can fit on the raft at a time, and it cannot float without people at all.
- Children can only travel on the raft with an adult. But sons cannot remain alone with the girls’ mother, and daughters cannot remain alone with the boys’ father.
- And the criminal cannot be left alone with others without the supervision of a police officer.
Found the answer? If not, watch this interesting test in the video:
Right answers
This puzzle has two correct answers. The first is that the bus goes to the left, since on the other side, invisible to the viewer, there are doors through which passengers get inside. This answer is true for our roads with right-hand traffic. But for countries where traffic is on the left, the correct answer is to the right.
The picture shows parking spaces, and a car occupies one of them. If you turn the picture over, you will realize that you originally saw the numbers upside down. Therefore, the number under the car is 87. No matter how much you try to calculate some clever polynomial here, such interesting puzzles are not designed for algebraic logic, but rather for ingenuity.
Missing value = 2. To solve such children's puzzles, you need to put yourself in the shoes of the children. Do kids know how to solve complex equations and count arithmetic progressions? But they notice that the values in the columns depend on the number of circles in each set of numbers. Let's take, for example, the row 6855: in the number 6 there is one circle, and in the number 8 there are two, so the output is 1+2 =3, that is, 6855=3. And in row 2581 only the number 8 has two circles, so the solution is 2.
There are 12 points in total in the figure. But our brain is designed in such a way that it does not allow us to see them all at the same time, so at a time we can only notice three or four black dots.
The mugs are exactly the same! Such simple puzzles are built on visual illusion. The blue circles on the left side of the picture are large and some distance from the yellow one. The circles on the right side are small and stand close to the yellow circle, which is why it seems to us that it is larger than the first one.
Here's how to solve interesting children's puzzles with matches:
Unmasking the panda:
The more developed a child is at an early age, the easier it will be for him in high school and higher education institutions. Regular classes with preschool children and children in grades 1-2 help develop the ability to comprehend information, remember material, develop perception and thinking. Thanks to these qualities, the child will be able to reason, it will be easy for him to communicate with peers and with teachers.
In order to guide parents in the right direction in terms of when and what to teach their child, there is a wide variety of literature. One of the main directions is mathematical puzzles, which encourage the child to be smart and stimulate theoretical and practical knowledge. One of the sources of knowledge is our website, where math puzzles for children are presented in the form of interesting tasks and games.
Taking into account the different ages of children, on our website Childdevelop you can use math puzzles for schoolchildren in grades 1-2. For preschool children it will be important to download mathematical puzzle games. To understand the essence of logic exercises, the site has similar examples of puzzles for children.
Math puzzles to download and print for free
We offer convenient use of sections with practical tasks, where you can download mathematical puzzles for free. Accessible and quick, thanks to basic knowledge, mathematical puzzles for children and schoolchildren will become the main platform for easy receptivity of information and knowledge in high school.
Acquiring new knowledge through games will not only broaden the child’s horizons, but will also interest him, and soon he himself will ask to “play with him.” You, in turn, try to distribute mathematical puzzles for children from smallest to largest (from preschool age, and then mathematical puzzles for grades 1-2).
There is no point in saying that it is more profitable to use free literature. Today, not every parent will be able to buy books for every developmental period. Therefore, the Childdevelop website makes it possible to use the necessary knowledge absolutely free of charge. Choose for yourself what is better: “cognitive math puzzle to print for free” or buy the same book “math puzzle”?
Zhuravskaya Anastasia
The purpose of this work is to study various mathematical puzzles, their classification and application in mathematics lessons.
Download:
Preview:
Municipal budgetary educational institution "School No. 3"
Competition of design and research works in mathematics
Research project
Mathematical puzzles, games and their application in mathematics lessons
Prepared by:
7th grade student
Zhuravskaya Anastasia
Supervisor:
Babina Marina Sergeevna
Mathematic teacher
g.o. Semenovsky
2017
annotation
The purpose of this work is to study various mathematical puzzles, their classification and application in mathematics lessons.
Tasks:
- Study various examples of intelligence tasks;
2. Consider ways to solve them;
3. Classify tasks by type.
Methods used in this study:
1. Study and synthesis
2. Analysis and synthesis
Why am I interested in this particular topic? It all started with an ordinary puzzle that I recently saw on the Internet.In less than a month, this puzzle collected tens of thousands of reposts and comments on social networks, becoming the subject of attention and controversy of almost half a million people. It is not as simple as it might seem at first glance. But it’s not as complicated as it might seem the second time.
Puzzles as a branch of entertaining mathematics
The puzzle is...The element of play that makes fun math fun can take the form of a puzzle, a competition, a magic trick, a paradox, a fallacy, or a simple math problem with a “secret”—some unexpected or funny twist of thought. Whether all these cases relate to pure or applied mathematics is difficult to decide. On the one hand, entertaining mathematics should certainly be considered pure mathematics without the slightest admixture of utilitarianism. On the other hand, it undoubtedly belongs to applied mathematics, since it meets the eternal human need for play. Probably, such a need underlies even pure mathematics. There is not much difference between the delight of a neophyte who has managed to find the key to a complex puzzle, and the joy of a mathematician who has overcome yet another obstacle on the way to solving a complex scientific problem. Both are engaged in the search for true beauty - that clear, well-defined, mysterious and delightful order that underlies all phenomena. It is not surprising, therefore, that pure mathematics is sometimes difficult to distinguish from entertaining mathematics. Thus, in topology, the problem of four colors remained unsolved until recently, although more than one page was devoted to it in many books on entertaining mathematics.
No one will deny that flexagons are very entertaining toys, however, the analysis of their structure very soon comes up against the need to use the higher sections of group theory, and articles about flexagons can be found on the pages of many purely specialized mathematical journals.
Creative mathematicians are usually not ashamed of their interest in entertaining problems and puzzles. Topology has its origins in Euler's work on the seven bridges of Königsberg. Leibniz spent a lot of time solving a puzzle that has experienced a rebirth under the name “Check your level of development (IQ).” The greatest German mathematician Hilbert proved one of the main theorems in the traditional field of entertaining mathematics - cutting figures. A. Turing, the founder of modern computer theory, examined the game invented by S. Lloyd in 15 in his article on solvable and insoluble problems.
P. Hein said that, while visiting Einstein, he saw in the owner’s bookcase a whole shelf filled with mathematical toys and puzzles. It is not difficult to understand the interest that all these great minds had in the mathematical game, for creative thinking, which finds reward in such trivial problems, is akin to the type of thinking that leads to mathematical and scientific discovery in general. After all, what is mathematics if not the systematic attempt to find better and better answers to the puzzles that nature poses to us?
The educational value of engaging mathematics is now widely recognized. This is emphasized by magazines intended for mathematics teachers and new textbooks, especially those written from “modern positions.” Thus, even in such a serious book as “Introduction to Finite Mathematics,” the presentation is often enlivened by entertaining problems.
There is hardly a better way to arouse the reader's interest in the material being studied. A mathematics teacher who reprimands students for playing tic-tac-toe in lecture would have to stop to ask himself whether this game is not of more mathematical interest than his lecture. Indeed, an analysis of the game of tic-tac-toe in seminar classes can serve as a good introduction to some areas of modern mathematics.
Examples of puzzles
Puzzles with matches
You need to move only one match in the arithmetic example “8+3-4=0” laid out with matches so that the correct equality is obtained (you can also change the signs and numbers).
Answer: This classic math match puzzle can be solved in several ways. As you may have guessed, the matches need to be moved so that different numbers are obtained.
First way. From the figure eight we move the lower left match to the middle of the zero. It turns out: 9+3-4=8.
Second way. From the number 8 we remove the upper right match and place it on top of the four. As a result, the correct equality is: 6+3-9=0.
Third way. In number 4, we turn the horizontal match vertically and move it to the lower left corner of the four. And again the arithmetic expression is correct: 8+3-11=0.
There are otherscreative
ways to solve this example in mathematics, for example, with a modification of the equal sign 0+3-4 ≠ 0, 8+3-4 > 0, but this already violates the condition.
Rearrange the three matches so that the fish swims in the opposite direction. In other words, you need to rotate the fish 180 degrees.
To solve the problem, we will move the matches that make up the lower part of the tail and body, as well as the lower fin of our fish. Let's move 2 matches up and one to the right, as shown in the diagram. Now the fish swims not to the right, but to the left.
Puzzles – crosswords:
Horizontally: 3. What is the name of the chord passing through the center of the circle? 5. What kind of figure is this, consisting of all points of the plane located at a given distance from a given point? 7. In which triangle are the angles at the base equal? 9. What is the name of a triangle in which all three angles are acute? 10. What is the name of the side of a right triangle that lies opposite the right angle?
Vertically: 1. What is the name of the ray that divides an angle in half? 2. What is used to depict a circle in a drawing? 4. What is the name of a segment connecting two points on a circle? 6. What are two lines in a plane called if they do not intersect? 8. What is the name of a triangle in which one of the angles is obtuse?
Rebuses
A rebus is a riddle, a puzzle consisting of a combination of letters, words, numbers, pictures and punctuation marks. Puzzles promote the development of thinking, train intelligence, logic, intuition, and ingenuity. They help expand your horizons, remember new words and objects. Trains visual memory and spelling. Unlike an ordinary riddle, where only a verbal description in poetry or prose is used, rebuses combine several methods of perception, both verbal and visual.
There are several main types of puzzles:
1. In the form of pictures and illustrations.
2. Word puzzles.
3. Mathematical puzzles.
There are certain rules for solving puzzles.
1. A comma at the very beginning of a word indicates that you need to remove the first letter in this word, and a comma at the end means that you need to remove the last letter in the word. Two commas - remove two letters. In the word mosquito we remove the last two letters AP, in the word iron we remove the first letter U and the last letter G.
2. Crossed out numbers indicate that the letters standing in this place are removed. In the word five we remove the second and third letters, that is, YAT. If letters are crossed out, they are also removed from the word.
3. Numbers that are not crossed out indicate that the letters in places 2 and 3 must be swapped. In the word iron, the letters T and Y are swapped YUT. Now we read the word in full.
This picture encrypts the word PERPENDICULAR.
4. If the picture is upside down, then the word guessed using the picture is read from right to left. The word read is not turnip, but aper. The first letter A is removed. In the word stump, the last letter b is removed. The word whale is read backwards. In the word chair, the first two letters ST are removed. The names of all objects depicted in the rebus are read only in the nominative case.
5.An “arrow” or an “equals” sign indicates that one letter must be replaced by another. In our case, in the word tick, the letter T must be replaced with the letter D. Now the word can be read in full.
The word EAST is encrypted in this picture.
6.Letters, words or pictures can be depicted inside other letters, above other letters, under and behind them. Then prepositions are added: IN, ON, ABOVE, UNDER, FOR. Our letter O contains the number STO, so it turns out B-O-STO-K.
The word MAP is encrypted in this picture.
7.The numbers under the picture indicate that from this word you need to take the letters located in places numbered 7,2,4,3,8 and compose them in the order in which the numbers are located. In the word cheesecake you need to take the letters 7-K, 2-A, 4-P, 3-T, 8-A. You can read the word.
Let's try to solve a few puzzles in the field of mathematics.
PROOF
Examples of puzzles:
Hypotenuse
Median
Chord
Puzzles with weights
Diamonds and scales
The box contains 242 diamonds, of which one is of natural origin, the rest are copies made in a laboratory (artificial). The masses of artificial diamonds are the same, the mass of natural diamonds is slightly less. Come up with a system of actions to isolate a natural diamond using five weighings on a cup scale without weights or weights.
Answer
We place 81 diamonds on the scales. This weighing selects 81 or 80 diamonds. The second time we place 27 diamonds from the selected group on the scales. This weighing selects 27 or 26 diamonds. The third time we place 9 diamonds from the selected group on the scales. So we select 9 or 8 diamonds. The fourth time we put 3 diamonds on the scales, and 3 or 2 diamonds stand out. Finally, for the fifth time, we put one diamond on the scale and determine which one is natural.
Math games
Math games
All the above puzzles keep our interest alive in the classroom. But most of all I like it when our lesson takes the form of a game. Our teacher often uses games in lessons on generalizing and systematizing knowledge. Then repeating everything is easy and simple, the class is divided into teams, we compete, and get grades. There are no indifferent people in such lessons.
Often at the beginning of the lesson we repeat previously studied material in the form of “Our own game”. Any student can choose a question from the table for a certain score. If a student does not answer, the right to answer passes to another student. The collected points are summed up and you can get a grade for repetition.
In the form of a fairy tale game, we reinforced actions with decimal fractions in the 6th grade. We practice examples and prepare for the test.
Conclusion
This project was written based on my own experience. Personally, I find it more interesting in class when we not only learn something new and practice this knowledge by solving all sorts of problems, but also have the opportunity to play, compete, and show that I can complete the task faster and better than anyone else.
Also, entertaining mathematics develops thinking, trains intelligence, logic, intuition, and ingenuity.
List of studied literature
1. Gardner Martin "Math Puzzles and Fun"
2. B.A.Kordemsky. Mathematical savvy. Moscow. State publishing house of technical and theoretical literature. 1957
3. “Extracurricular work in mathematics”, Alkhova Z.N., Makeeva A.V., Saratov: “Lyceum”, 2002
4. “Tasks for ingenuity” Sharygin I.F., Shevkin A.V., Moscow “Enlightenment” 2003
6. http://riddle-middle.ru/zagadki/s_podvohom/
7. http://www.toybytoy.com/game/Puzzle
8. http://puzzlepedia.ru/100.html
9. http://www.e-crossword.ru
The dates are in the range from 14 to 19. The numbers 18 and 19 appear once. If the birthday is on these dates, then Bernard would immediately say the month.
If Cheryl told Alfred she was born in May or June, then the birthday could be May 19th or June 18th. Since Alfred knows for sure that Bernard does not know the answer, it means that we are not talking about May or June. That leaves July or August.
In July and August there are still dates in the range from 15 to 17, and 14 occurs twice. If the birthday were on the 14th, then Bernard, after Alfred’s remark, would still not be able to give an exact answer. So, we are not talking about the 14th. The remaining dates are July 16, August 15 and August 17.
If Cheryl had told Alfred that she was born in August, then after Bernard’s answer, Alfred could not have known the exact date of birth - after all, 2 whole dates fall in August.
So Cheryl was born on July 16th.
This problem was shown to Kong by a friend's niece. She played a prank on the TV presenter, saying that the puzzle was intended for 10-year-old schoolchildren.
The debate about how to solve a “simple” problem became serious. After 2 days, when most of the participants gave up, it turned out that the task was an Olympiad task for 14-year-old schoolchildren.
Mathematical comic puzzles and joke problems for primary schoolchildren
1. The housewife was carrying 100 eggs in a basket. And the bottom fell out (read not “a bottom”, but close to the word “one”). How many eggs are left in the basket? (No one)
2. There were 50 pears growing on the pear tree, and 12 less on the willow tree. How many pears grew on the willow tree? (Pears do not grow on willow)
3. Which is lighter: 1 kg of cotton wool or 1 kg of iron? (Equal)
4. A chicken weighs 2 kg on two legs. How much does a chicken weigh on one leg? (2 kg).
5. Vasya and Sasha played checkers for 4 hours straight. How many hours did each of them play? (4 hours).
6. There were 2 magpies, 3 sparrows and 2 squirrels sitting on the tree. Suddenly two sparrows fluttered and flew away. How many birds are left on the tree? (3 birds).
7. How many ends do two and a half sticks have? (6)
8. A flock of ducks was flying. The hunter killed one. How many ducks are left? (One, the rest flew away)
9. There is an oak tree in the field. There are 3 apples on the oak tree. A good fellow was driving along and picked one. How many apples are left? (Not a single one, apples don’t grow on oak trees)
10. We have a very friendly family: seven brothers have one sister. How many children are there in total? (8)
11. Two men walked from the village to the city, and three more men and one woman met them. How many men walked from the village to the city? (2)
12. Grandmother bought two pairs of shoes, three apples and five pears at the market. The grandmother gave one pair of shoes to her granddaughter. How many fruits did grandma buy? (8)
To two bunnies at lunchtime
2 neighbors arrived.
Hares sat in the garden
How many carrots did you eat? (20).
Masha and Tanya are not bored:
Drink 3 cups.
Sashka ran to the girls
He drank 3 cups at once.
How many cups are there at the table?
Did the three of you drink? (9 cups).
Ivan came to the zoo
I found monkeys there.
2 played on the sand,
3 sat on the board,
10 backs were warm.
How many together, have you counted? (15 monkeys).
There are five Natashas in our class,
Two Seryozhas and five Sashas.
There is Alenka and Kondrat.
How many children are there in the class? (14 guys).
The cherry is finally ripe
Ten cherries on it
For two of my friends.
The tangerine is ripening:
One for each of them.
How much fruit for the guys?
Have you prepared a good garden? (12).
Here under the roof in our house
3 crows settled in,
2 tits, 5 jackdaws.
Just a whole kindergarten!
There are two more mice living there.
How many birds are there under our roof? (10).
We carried chairs into the hall
And 3 legs were broken off.
If there were 5 chairs,
There are five guys in our house,
They love to play everything.
How many sandals do they need?
(Five pairs, or 10 sandals).
21. Three swallows flew out of the nest. What is the probability that after 15 seconds they will be in the same plane? (Answer: 100%, because three points always form one plane).
22. There are two coins on the table; in total they give 3 rubles. One of them is not 1 ruble. What coins are these? (Answer: 2 rubles and 1 ruble. One is not 1 ruble, but the other is 1 ruble).
23. How fast should a dog run so as not to hear the clink of a frying pan tied to its tail? (Answer: If you think that she needs to run at supersonic speed, then you are mistaken - the dog just needs to stand still).
24. A satellite makes one revolution around the Earth in 1 hour 40 minutes, and another in 100 minutes. How can it be? (Answer: 1 hour 40 minutes = 100 minutes).
25. The roof of one house is not symmetrical: one slope makes an angle of 60 degrees with the horizontal, the other makes an angle of 70 degrees. Suppose a rooster lays an egg on the ridge of a roof. In which direction will the egg fall - towards a flatter or steeper slope? (Answer: Roosters don't lay eggs.)
26. There is an elevator in a 12-story building. Only 2 people live on the ground floor; from floor to floor the number of residents doubles. Which button in the elevator of this building is pressed most often? (Answer: Regardless of the distribution of residents by floor, button “1”).
27. Two wallets contain two coins, and one wallet contains twice as many coins as the other. How can this be? (Answer: One wallet lies inside another).
28. The son of the professor’s father talks to the father of the professor’s son, and the professor himself does not participate in the conversation. Could this be possible? (Answer: Yes, maybe, if the professor is a woman).
29. Two sons and two fathers ate 3 eggs. How many eggs did each person eat? (One egg each).
30. There were 5 tanks with fuel in the warehouse, 6 tons each. Fuel was released from two tanks. How many tanks are left? (5).
31. Imagine that you are the captain of a football team. There are 8 football teams in the region, each with 11 members. The players on your team are 2 years younger than their captain, while the players on the other team are only 1 year younger. How old is your team captain? (As many years as the person answering).
32. A pair of horses ran 20 km. How many kilometers did each horse run? (20 km).
33. When the magpie turns 4 years old, what will happen to it? (He will live for five years.)
34. If it is raining at 11 o’clock at night, is it possible that the weather will be sunny 48 hours later? (No, because it will be night).
35. It takes 1 hour to cook 1 kg of meat. How long will it take to cook 0.5 kg of meat? (1 hour).
36. Marina had a whole apple, two halves and 4 quarters. How many apples did she have? (3).
37. 6 sparrows were sitting in the garden bed, 5 more flew to them. The cat crept up and grabbed one sparrow. How many sparrows are left in the garden? (One who was grabbed by the cat. The rest flew away).
38. The boy wrote the number 86 on a piece of paper and said to his friend: “Without making any notes, increase this number by 12 and show me the answer.” Without thinking twice, the comrade showed the answer. Can you do this? (Turn the piece of paper upside down).
39. There were 4 rabbits in the cage. Four guys bought one of these rabbits and one rabbit remained in the cage. How could this happen? (One rabbit was bought along with a cage)
40. Ducks were flying: one in front and two behind, one behind and two in front, one between two and three in a row. How many ducks were there in total? (Three ducks, one after another).
41. One old man was asked how old he was. He replied that he was a hundred years old and a few months old, but he only had 25 birthdays. How could this be? (This person was born on February 29, that is, he has a birthday once every four years).
