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 in the crowd of stormtroopers from " Star Wars”, in a gathering of metalheads, and even tried to hide her among the 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

There can be two correct answers to this puzzle. 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 valid for our roads with right-hand traffic. But for countries where traffic left-handed, the correct answer is 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:

All puzzles with answers and solutions.

These puzzles are mainly for older children school age. Joke problems, riddle problems, comic stories and challenging mathematical problems develop students' curiosity and intelligence. At the same time, children develop intuition, guesswork, and speed of thinking. Children exhibit particular mental activity when achieving a game goal.

Here is an entertaining mathematical material of varying degrees of difficulty. It may also be of interest to adults.

MATH PUZZLES

Squirrel and nuts

A squirrel, stocking up for the winter, came across a large pile of nuts. She worked for three nights, filling her nest with nuts. How many nuts disappeared from the pile if on the first night the squirrel carried away half as many nuts as on both subsequent nights (combined), and on the last night one less nut than on both previous nights?

(For 9 nuts. On the first night - 3, on the second - 2, on the third - 4)

How many cats?

The room has four corners. There is a cat in each corner. Opposite each cat are three cats. There is one cat on each cat's tail. How many cats are there in the room?

(There are only four cats in the room)

Cat and mice

The cat Vaska is sleeping, and in a dream he sees that he is surrounded by twelve gray mice and one white one. Vaska hears a voice in his sleep: “You must eat every thirteenth mouse, counting all the time in one direction, so that the white mouse is eaten last.” Vaska thought: which mouse should I start with?

Help the cat solve the problem.

(You should start counting from the sixth mouse, counting clockwise from the white mouse (not counting it). To determine which mouse to start counting from, draw 12 dots and one cross on the circle and start counting from there. Cross out each dot and cross , when it's his turn. Do this until there is only one dot left. Replace it with a white mouse, and a cross will indicate which gray mouse to start with)

How many are there?

Vanya has as many brothers as sisters, and his sister has half as many sisters as brothers. How many sisters and how many brothers are there in that family?

(3 sisters and 4 brothers)

All my ducks

Vanya watches the ducks swimming in the village pond.

One duck swims in front of two ducks, another duck swims between two ducks, and one duck swims behind two ducks. “We’ve never had so many ducks in our village pond,” Vanya thinks. How many ducks does Vanya see?

(The boy sees 3 ducks in the pond)

Two shepherds

Two shepherds, Ivan and Peter, met. Ivan says to Peter: “Give me one sheep, then I will have exactly twice as many sheep as you!” And Peter answers him: “No! It’s better if you give me one sheep, then we’ll have equal numbers of sheep!”

How many sheep did each person have?

(It is clear that Ivan has more sheep. But how much more does he have than Peter? If Ivan gives one sheep not to Peter, but to someone else, will both shepherds have equal numbers of sheep? No, because they have equal shares would only be if Peter received this sheep. This means that if Ivan gives one sheep not to Peter, but to a third party, then he will still have more sheep than Peter, but how much more? It is clear that by one sheep, because if you now add one sheep to Peter's flock, then both will have the same amount. It follows that, as long as Ivan does not give any of his sheep to anyone, he has two more sheep in his flock than Peter. Now Let's start with Peter. As we found, he has two fewer sheep than Ivan. This means that if Peter gives, say, one of his sheep not to Ivan, but to someone else, then Ivan will have three more sheep, than Peter. But let it be Ivan who gets this sheep, and not a third party. It is clear that then he will have four more sheep than Peter has left. But the problem says that Ivan in this case will have exactly twice as many sheep, than Peter's. This means that four is exactly the number of sheep that Peter will have left if he gives one sheep to Ivan, who will have eight sheep. And before the expected return, it means that Ivan had 7, and Peter had 5 sheep)

Camel division

The old man, who had three sons, ordered that after his death they should divide the herd of camels that belonged to him so that the eldest took half of all the camels, the middle - a third and the youngest - a ninth of all camels. The old man died and left 17 camels. The sons began dividing, but it turned out that the number 17 is not divisible by 2, 3, or 9. At a loss as to what to do, the brothers turned to the sage. He came to them on his own camel and divided it according to his will. How did he do it?

(The sage embarked on a trick. He added his camel to the herd for a while, then there were 18 of them. Dividing this number, as stated in the will (the eldest brother received 18 x 1/2 = 9 camels, the middle one 18 x 1/3 = 6 camels , youngest 18 x 1/9 = 2 camels), the sage took his camel back (9 + 6 + 2 + 1 = 18). The secret is that the parts into which the sons were to divide the herd according to the will do not add up amount to 1. Indeed, 1/2 + 1/3 + 1/9 = 17/18)

Pack animals

A mule and a donkey, loaded with sacks, walk side by side. The mule says to the donkey: “I will carry twice as much as you if I take your bag. And if you take my bag, then we will both carry the same amount.”

Zhuravskaya Anastasia

The purpose of this work is to study various mathematical puzzles, their classification and application in mathematics lessons.

Download:

Preview:

Municipal budget educational institution"School No. 3"

Competition of design and research work 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:

1. 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.This puzzle has collected tens of thousands of reposts and comments on social networks in less than a month, 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, because 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, founder modern theory computers, reviewed 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 its reward in such trivial problems, is akin to the type of thinking that leads to mathematical and general scientific discovery. 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.

Hardly exists The best way awaken 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 the points of the plane located on given distance from this 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 right triangle, lying opposite a 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 natural origin, the rest are copies of it, made in the 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 consolidated actions with decimals in 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 activities 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 more developed a child is at an early age, the easier it will be for him in high school and higher education. educational institutions. Regular activities with children preschool age 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. It will be relevant for preschool children to download math games puzzles. 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).

About what is more profitable to use free literature, not worth talking about. 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”?