Mathematical puzzles with numbers and letters. Mathematical puzzles

Mathematics is one of the most difficult sciences, which gives schoolchildren a lot of trouble during their studies. At the same time, mental calculation skills and various mathematical techniques must be mastered by every person, since without this knowledge it is simply impossible to live in the modern world.

Long and complex mathematics lessons, especially in the lower grades, tire children excessively and do not allow them to fully assimilate information. To prevent this from happening, kids need to provide the necessary information in the form of a fun game, for example, in the form of mathematical puzzles.

Such puzzles can vary in difficulty level, so you can start solving them as early as kindergarten. In addition, children almost always really like puzzles, and you don’t have to force your child to study. In this article we will tell you the benefits of mathematical puzzles for children and offer several examples for boys and girls of different ages.

What are math puzzles and why are they so useful for children?

Mathematical puzzles are of different levels of complexity, which are compiled using graphic elements. Solving such riddles is an extremely exciting activity that you can spend more than one hour doing. In addition, older children enjoy composing mathematical puzzles for their classmates and friends, and this also allows them and contributes to the development of logical thinking.

In cases where the puzzles are quite complex riddles, boys and girls have to seriously “rack” their brains to find the correct answer. In the process of this exciting activity, children develop innovative thinking. In the future, this skill will be useful for finding possible ways out of different life situations.

Finally, mathematical puzzles give children a boost of excellent mood, and if the child solves them not alone, but in the company of friends or relatives, they additionally contribute to socialization and strengthening relationships.

Examples of mathematical puzzles for preschoolers

Mathematical riddles for preschoolers should be the simplest. They usually include 2-3 elements, and their answer is a simple mathematical term or the name of a number. In particular, the following puzzles are suitable for children of senior preschool age:

Mathematical puzzles for grades 1-4

Primary school students are already familiar with numbers and some other mathematical terms, so they can use them to create and solve various puzzles. At this age, riddles are most often used, the text of which contains numbers and other similar elements. Moreover, the answer to such puzzles can be anything, including those not related to mathematical science.

At the same time, mathematical terms can also be encrypted in such problems, but in this case they are quite complex concepts that primary schoolchildren have yet to become familiar with. The following mathematical puzzles with answers are suitable for students in grades 1, 2, 3 and 4:

Mathematical puzzles for students in grades 5-9 with answers

For secondary school students, especially those in grades 8-9, math puzzles should already be quite complex - so that the children would have to work hard to decipher them. Otherwise, such problems will not be able to interest and captivate schoolchildren for a long time, and therefore will be absolutely useless.

Such puzzles can vary in difficulty level, so you can start solving them in kindergarten. In addition, children almost always really like puzzles, and you don’t have to force your child to study. In this article we will tell you the benefits of mathematical puzzles for children and offer several examples for boys and girls of different ages.

What are math puzzles and why are they so useful for children?

Examples of mathematical puzzles for preschoolers

Mathematical puzzles for grades 1-4

Mathematical puzzles for students in grades 5-9 with answers

LogicLike knows how to diversify math classes: first of all, by solving entertaining math puzzles at the 4th grade level.

Examples of simple tasks with answers

Traditionally, we start by analyzing the solution to the problem from the previous publication - “Math puzzles with answers for grades 2 and 3.” Next, you will find new interesting mathematical puzzles for addition and subtraction with solutions and answers, developed by the methodologists of the Center for the Development of Logic “LOGIC”.

Rebus 1. Arithmetic rebus table for ingenuity

Calculate the price of a police car.

Based on the same amounts (A) in the bottom row and first column, we establish that the prices of red and blue cars are equal.

Let's look at the top and middle lines. We conclude that the police car is 4 money more expensive than the blue car.

Taking the price of blue as x (then the price of the police car is x + 4), we create an equation using the top line:
x + (x + 4) + x = 70 x + x + x = 66 x = 22
Price of a police car: 22 + 4 = 26.

Answer: 26.

Rebus 2. With numbers from 0 to 5

The same numbers are encrypted with the same letters, different ones with different letters. This problem uses only 6 digits - from 0 to 5.

What number is encrypted behind the word “BARK”?

The correct answer is found by checking each of the signs.

If we subtract an equal number from a number, we get 0. Let's start the solution using the above thesis. L - L = Y, which means Y = 0. The largest number is 5. From the conditions of the problem it is known that Y = 4, which means E = 5, A = 1. The remaining numbers 2 and 3 are encrypted behind the letters L and M. > L. Accordingly, M = 3, and L = 2.

352 − 142 = 210

Answer: 210.

All these puzzles are part of the LogicLike educational platform. Register and continue solving problems online.

Olympiad puzzles in mathematics for 4th grade students

Rebus 3. What is encrypted behind the “dacha”?

Identical numbers are indicated by the same letters, different numbers - by different ones.

What number is hidden behind the word “DACHA”?

When solving, we proceed from the fact that P H = 5, therefore, due to the transition through the ten, A = 2, and H = 6 and L = 1.
D is even, since there is no transition through ten. D ≠ 0, D ≠ 2, D ≠ 6.
If we assume that D = 4, then P = 2 = A, and this option is impossible.

Therefore, D = 8, and P = 4.

4126 + 4126 = 8252.

Answer: 8252.

Rebus 4. Long division

Determine which numbers are hidden behind the asterisks and restore the original form of the division example (before the numbers were hidden by the asterisks).

1. Find the number *7*.
The number *7* is obtained if 2 (the first digit of the quotient) is multiplied by the divisor *5.
2 × *5 = *7*
2 × 5 = 10 – at the end of the number (in the units place) there will be 0. Remember 1 ten.
We are looking for the number by which we need to multiply 2 to get a two-digit number with the number 6 at the end. Only 8 fits.
So 2 x 85 = 170.

Einstein's problem

There are 5 houses on one street. People of different nationalities live in different houses. Everyone drinks their own drink, has a favorite type of recreation and has their own pet.
It is known that:
1. The British man lives in a red house.
2. The Swede has a dog.
3. The Dane drinks tea.
4. The green house stands to the left of the white one, close to it.
5. The owner of the green house drinks coffee.
6. The one who reads novels has birds.
7. The owner of the yellow house loves to walk.
8. The owner of the middle house drinks milk.
9. A Norwegian lives in the first house.
10. The person who watches TV lives next to the owner of the cats.
11. The one who keeps horses lives next to the one who likes to walk.
12. Anyone who listens to music drinks kvass.
13. The German solves problems.
14. A Norwegian lives next to the blue house.
15. The one who watches TV has a neighbor who drinks water.
Who keeps the fish?

At a school quiz, participants were asked 20 questions. For a correct answer, the student was given 12 points, and for an incorrect answer, 10 points were deducted. How many correct answers did one student give if he answered all the questions and scored 86 points?

Place 7 full barrels, 7 half-filled barrels, and 7 empty barrels on three trucks so that all trucks have the same weight of cargo.

There are pencils on the table. Two players take turns taking 1, 2 or 3 pencils. The one who takes the last pencil loses. How should a beginner play to win if there are 8 pencils on the table? Will the first be able to win if the second plays correctly, if there are 9, 10, 15 pencils on the table?

There are 33 people in our class, and everyone is friends with exactly 5 classmates. Could this be possible?

8 girlfriends decided to exchange photographs so that each of them ended up with photographs of other girlfriends. How many photos will this require?

Nina lives on the 4th floor, and Tanya lives on the 2nd. Nina climbs 60 steps. How many steps does Tanya climb?

Instructions

Before you start solving complex problems, practice with a simple example: CAR+CAR=CONSTRUCTION. Write it down in a column, it will be easier to solve. You have two unknown five-digit numbers whose sum is a six-digit number, so B+B is greater than 10 and C is equal to 1. Replace the symbols C with 1.

The sum A+A is a single-digit or two-digit number with a unit at the end, this is possible if the sum G+G is greater than 10 and A is equal to either 0 or 5. Try to assume that A is equal to 0, then O is equal to 5 , which does not satisfy the conditions of the problem, because in this case B+B=2B cannot equal 15. Therefore, A=5. Replace all A's with 5's.

The sum O+O=2O is an even number and can be equal to 5 or 15 only if the sum H+H is a two-digit number, i.e. H is more than 6. If O+O=5, then O=2. This solution is incorrect, because. B+B=2B+1, i.e. O must be an odd number. So O is equal to 7. Replace all O's with 7's.

It is easy to see that B is equal to 8, then H = 9. Replace all letters with the found numeric values.

Replace the remaining letters in the example with numbers: G=6 and T=3. You got the correct equality: 85679+85679=171358. The rebus has been solved.

When subtracting, also start with units. If the number of one or another digit being reduced is less than the number being subtracted, then borrow 1 ten or a hundred from the next digit, etc. and do the calculations. Put a dot over the number you borrowed from so you don’t forget. When performing actions with this digit, subtract from the reduced number. Write the result below the horizontal line.

Check the calculations are correct. If you added, then subtract one of the terms from the resulting sum, you should get the second. If you subtracted, then add the resulting difference with the subtrahend, you should get the minuend.

note

The digits of the numbers must be located one below the other.

In linear algebra and geometry, the concept vector defined differently. In algebra vector om is the element vector nogo space. In geometry vector om is an ordered pair of points in Euclidean space - a directed segment. Above vector We have defined linear operations - addition vector ov and multiplication vector but for a certain number.

Instructions

The work vector and a for a number? is called a number?a such that |?a| = |?| * |a|. Obtained by multiplying by a number vector parallel to the original vector y or lies on the same straight line with it. If?>0, then vector s a and ?a are unidirectional if? vectors a and?a are directed in different directions.

Video on the topic

A rebus is a special riddle in which the desired word is enclosed in pictures containing various letters and numbers. In the pictures you can also see other signs that will help you read the word correctly. Solving puzzles is a very exciting activity that will help you warm up before difficult work. To solve the puzzle, you must remember a number of simple rules.

Instructions

The names of any objects depicted in the picture are read only in the nominative case.

Sometimes a drawing may have several names (for example, paw or leg). An item can also have a specific or general name. For example, a flower is a general name, but a specific name is a tulip or a rose. Therefore, if you can correctly guess the object shown in the picture, then consider that the hardest part is over. The simplest and most popular method of solving puzzles is to decipher the pictures in parts. That is, you first need to write down all the names of the objects in order, and then put the text together from them.

One or more inverted commas can be drawn to the right or left of the object - this means that one or more letters need to be removed at the beginning or end of the word, respectively.

If there are numbers above the picture, the letters in the word must be read in a certain order - exactly in the order in which the numbers appear.

Crossed-out letters may be written above the picture; therefore, they must be excluded from the name of the object and from the text.

The use of an arrow drawn from one letter to another serves to indicate the appropriate substitution of letters (for example, A-P).

Einstein's problem

Task 1.

Task 2.

Place 7 full barrels, 7 half-filled barrels, and 7 empty barrels on three trucks so that all trucks have the same weight of cargo.

Task 3.

Task 4.

There are 33 people in our class, and everyone is friends with exactly 5 classmates. Could this be possible?

Task 5.

8 girlfriends decided to exchange photographs so that each of them ended up with photographs of other girlfriends. How many photos will this require?

Task 6.

Nina lives on the 4th floor, and Tanya lives on the 2nd. Nina climbs 60 steps. How many steps does Tanya climb?

Rebus is a logic game in which you have to guess the answer from a picture. The latter depicts objects, animals and plants, letters and numbers. Their relative position matters. Even for fidgets, puzzles can be a fun activity if presented in a playful way. For example, you can offer to teach your child how to solve spy codes.

And from the simplest picture puzzles for preschool age to relatively complex ones. We assure you: if your child gets carried away and learns to use logical thinking, over time you will learn from him how to solve riddles in pictures.

Puzzles have been invented on a huge variety of topics. The main thing is that every word, letter and object that serves as an answer to the picture is already familiar to the baby.

How to solve puzzles for children with letters in pictures?

If you are interested in puzzles, then most likely you know the benefits of these logic puzzles. They develop memory, intelligence, speed of thinking, the ability to navigate a situation and apply the knowledge already acquired.

To teach a 6-7 year old child how to solve problems correctly, first explain to him the rules. There is no need to insist that he remember everything at once. Most likely, you don’t know them all yourself. It’s better to explain one or two things a day and support them with thematic tasks. The latter can be printed (more convenient for outdoor activities) or shown from the monitor. In subsequent classes, it is also better not to offer too much material. It is important to explain to the child that first he needs to correctly identify and name the object shown in the picture. And only then apply the rules in relation to this word.

So, let's read the basic rules! In particular, we will determine what a comma, a strikethrough, an inverted object and other subtleties mean in pictures.

What does a comma mean at the beginning or end of a rebus?
A comma at the bottom or at the top before the picture means that one letter at the beginning must be dropped from the name of the depicted object. Accordingly, we see two commas - we discard the first two letters. These icons are very common.
What does an inverted comma at the beginning or end mean?
The rules for inverted commas are similar to the rules for regular commas (see previous paragraph).
What do the crossed out and added letters mean?
A crossed out letter in the picture means that it needs to be excluded from the name of the drawn object (and another one must be added, if indicated). Added to the left or right of the picture - you need to add it to the word at the beginning and at the end.
What do the numbers in the puzzles mean?
Numbers can have two meanings. Do they stand above the word? To guess the answer, you need to rearrange the letters from place to place in the indicated order. The name of a number can be part of a word (often “one hundred”, “five” are used). A crossed out number means that the letter with that serial number must be excluded from the word. It should be remembered that some numbers, as well as objects, can have several names (unit - “count”, “one”, “one”).
What does the plus sign and the equal sign mean?
If there is a plus sign between words (symbols), then they need to be added to each other. Sometimes “+” means the preposition “to”; the necessary one is chosen according to the meaning. The equal sign (for example, A=K) indicates that all the letters “A” in the word should be replaced with the letters “K”.
Vertical or horizontal line in tasks?
A horizontal line means “under”, “over”, “above” and “on” at the same time, depending on the context. Used with letters or pictures, when one part is drawn below the line, the other above. Sometimes denotes a fraction (half of something, that is, “half-”).
Arrangement of letters in the picture and prepositions
It is important to look at the relative position of the letters. If they are placed one inside the other, it means that the preposition “in” is added to their names. One letter is drawn after another - meaning the preposition “behind” or “before”.
The object in the picture is drawn upside down? To get the answer, you need to read the word backwards. Children 6-7 years old can easily turn short words in their minds. True, the number of such tasks is quite limited.

Most often, puzzles use several rules simultaneously. It is believed that at the age of 6-7 years, children are already familiar with letters and clearly know their names. If a younger student has not yet encountered commas, teaching him a new symbol will not be particularly difficult.

Examples of puzzles in pictures for children 6-7 years old with answers

Children 6-7 years old and younger perceive material much better in connection with some memorable event. Puzzles about animals will be solved with delight if you offer them to your child the next day after visiting the zoo. A first-grader girl who is eager to enroll in a music school will be interested in musical puzzles. And a child, a boy impressed by the planetarium, will like pictures about space.

About animals and birds

When giving children a task about birds or animals, make sure that they have already encountered such animal names and also understand everything that is shown in the picture.

Puzzles about family, about mother

Who is the sweetest for a child, if not mommy! And who does he happily meet every time, except mom and dad? Children will really enjoy recognizing and guessing their grandparents, sisters and other relatives in the encrypted pictures. Print or draw brighter pictures and start having fun while teaching your child at the same time!

About sports, about health

Puzzles about work, health, sports, professions and many others can be used as thematic game aids. Is there a lesson or conversation planned on one of the topics in the graduating group of kindergarten, first grade of school or at home? A riddle in the form of a picture will allow you to learn the material better than an ordinary faceless story. Kids will be interested in the non-standard presentation of the material.

Puzzles based on fairy tales

Fairy tales with familiar characters, modern or classic cartoons are an inexhaustible source of inspiration. If your child is not very interested in logical riddles, you can try to get him interested in guessing his favorite characters. There are many more mysteries on this topic than are given as an example. Knowing your child’s interests and favorite fairy tales, you can create puzzles in the form of applications yourself.

A rebus is a riddle in which the desired word or phrase is depicted as a combination of figures, signs, letters, i.e. "objects". One of the main difficulties when solving puzzles is the ability to correctly name the object depicted in the picture and understand how the fragments of the picture relate to each other. It is necessary to take into account the presence of synonyms; the letter “fraction” can be read in different ways. In addition to knowing the rules, you also need ingenuity and logic.

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Slide captions:

Municipal educational institution "Secondary school in the village of Yurlovka, Saratov district, Saratov region" Vostrikova I.O. Rebuses

Find the missing figure?

Which person should be used instead of a question mark? ?

Collect a FLOWER

How many triangles? 8

Top Beam Rebuses

Puzzles Problem Diameter

Rebuses Sign Five

Puzzles Diagonal Square

Puzzles Addition Subtraction

Puzzles Section A Cuba

Puzzles T i=a Point Eight O 7

Puzzles A D Two

Addition problems In all problems, express an integer with the numbers 1, 2, 3, etc., applied once and arranged sequentially. Example. Write the number 19 using the first four digits. Answer: 19 = 12 + 3 + 4 1. Express the number 24 using the digits 1 to 5. 24 = 12+3+4+5 2. Express the number 30 using the numbers 1, 2, 3, 4, 5 and 6. 30 = 12+3+4+5+6 3. Write the number 37 using one, two, three and four. 37 = 1+2+34 4. Express the number 45 using the numbers 1 to 8. 45=12+3+4+5+6+7+8 5. Express the number 46 using the numbers 1, 2,3 and 4. 46 =12+34 6. Represent the number 55 using the first seven digits. 55=1+2+34+5+6+7 7. Draw the number 69 using numbers from 1 to 5. 69 = 1+23+45 8. Write the number 100 in two ways using 1,2,3,4, 5,6 and 7. 100 = 1+23+4+5+67 9. Express the number 102 with the digits from 1 to 6 100 = 1+2+34+56+7 102 = 12+34+56 10. Represent the number 333 using all the numbers. 333=1+234+5+6+78+9