Note what energy is encrypted in this puzzle. Exercise for the mind! Learning to solve puzzles

Number puzzles

Millions of people in all parts of the world love solving puzzles. And this is not surprising. “Mental gymnastics” is useful at any age. After all, puzzles train memory, sharpen intelligence, develop perseverance, the ability to think logically, analyze and compare.

Our whole life is a continuous chain of gaming situations. They can be significant, and sometimes they can be trivial, but both require us to make decisions. Even in Ancient Greece, the harmonious development of personality was unimaginable without games. And the games of the ancients were not only sports. Our ancestors knew chess and checkers, and they were no strangers to puzzles and riddles. Scientists, thinkers, and teachers have always been familiar with such games. They created them. Since ancient times, the puzzles of Pythagoras and Archimedes, the Russian naval commander S.O. have been known. Makarov and American S. Lloyd.

There is a type of puzzle that is called numerical. They are expressions that require an arithmetic solution, composed in the form of mathematical equalities, where numbers are replaced by other signs - letters, geometry figures, asterisks, etc.

Numerical puzzles mean those tasks in which it is necessary to use logical reasoning. They are the way to solve and decipher each symbol, which leads to the restoration of the numerical record.

Number puzzles are almost a thousand years old. They first appeared in China, then in India. In European countries, numerical puzzles were initially called crypt-arithmetic problems. Their appearance in Europe was first noted only in the twentieth century, despite the fact that the development of mathematics began many centuries ago.

When composing numerical puzzles, use the following rules. All numbers used are replaced with letters. If there are identical numbers in the problem, then the same number of letters is used. Intermediate stages of mathematical operations are indicated by asterisks. Based on these rules, several types of puzzles are distinguished. The first is puzzles in which all existing letters are replaced with numbers. In this case, an expression is encrypted that denotes everyday situations in the original presentation.

THREE BUNS

+TWO + WAS

FIVE IS A LOT

SNOW SEA SUMMER

+ SNOW + SEA + SUMMER

BLIZZARD OCEAN WARMTH

The entry may contain not only numbers, but also asterisks - this is the second type of puzzle. The third type is puzzles, in which almost all symbols are replaced by asterisks.

Numerical puzzles are very complex, and sometimes you come across ones that require a step-by-step long-term solution. Number puzzles are fascinating mathematical problems that greatly develop logic and intelligence.

Numerical puzzles can be composed of several rows of symbols, and between them a certain number of mathematical signs are placed, which are pointers for which actions need to be performed vertically and which horizontally.

1) TA+ IT = YEARS 2) KRA + OLI = IAYA

X - + X : -

EC x CH = LLAS L x AR = KYAI

LEAA + EC = LEETS OII + AL = RKA

Numerical puzzles are very popular not only in schools during regular lessons, but also at math olympiads. It is possible to solve numerical puzzles using computer programs, but incomparable pleasure can be obtained by a person who independently puzzles over the solution and eventually finds it.

The problems are presented in an entertaining way and are very interesting. They want to solve problems; they are captivated by their unusualness and non-obviousness of the answer. There is a desire to take even the difficult path of finding a solution. Entertaining and strict are quite compatible. Each independently solved task is perhaps a small victory, but still a victory.

How to solve mathematical puzzles and creep tariffs

In letter puzzles, each letter encrypts one specific number: identical numbers are encrypted with the same letter, and different numbers correspond to different letters.

In rebuses encrypted, for example, with asterisks, each symbol can represent any number from 0 to 9. Moreover, some numbers may be repeated several times, while others may not be used at all.

Before you start solving a mathematical letter puzzle (for example, a cryptarithm), make sure that no more than 10 different letters are used in it. Otherwise, such a puzzle will have no solutions.

Start solving the puzzle with the rule that zero cannot be the leftmost digit in a number. Thus, all the letters and signs with which the number in the rebus begins can no longer mean zero. The search for the necessary numbers will narrow.

When solving, use basic mathematical rules as a starting point. For example, multiplying by zero always gives zero, and when multiplying any number by one, we get the original number as a result.

Very often, mathematical puzzles are examples of adding two numbers. If, during addition, the sum has more characters than the terms, then the sum begins with “1”

Pay attention to the sequence of arithmetic operations. If a number puzzle consists of several rows of characters, it can be solved both vertically and horizontally.

Don't be afraid to make mistakes. Perhaps they will tell you the right course of action. Don't neglect the brute force method. Some puzzles will require a long step-by-step solution, but in the end you will be rewarded with the correct answer and an excellent workout for your intelligence.

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, which means B+B is greater than 10 and C is equal to 1. Replace the characters 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.

If you have nothing to do on long winter evenings, and are already tired of TV and the computer, then start solving puzzles, because it is not only interesting, but also useful for training your brain. But first, study and remember the rules for solving.

There are a total of 16 techniques for composing puzzles, but there are only two main rules. Firstly, before you solve the rebus, remember that all the words that are encrypted in it are used only in the nominative case. Secondly, a picture can have several names, that is, if a chicken is drawn, then you can read it as a bird, and a leg as a paw, so when solving, do not forget about synonyms, as well as general and particular meanings.

Now let's look at the main 16 techniques that are used when composing a puzzle.

• Commas are one of the most common techniques. If it is in front of a word, then you need to remove the letters at the beginning, and if it is upside down after the picture or letters, then the last ones. There are as many commas as there are letters that need to be removed. For example, if there are two commas before the word “car”, then we remove “MA” and get the word “TIRES”.
• Crossed out letters that are located next to the rebus or at the top mean that they need to be found in the word and removed. If the letters are repeated, then you need to cross out everything.
• Crossed out numbers indicate that you need to count the letters in the word and cross out those that match the number. For example, above the word EXECUTIONER there is a crossed out number 2, remove the first A, you get CRYING.
• If the numbers are not crossed out, then take the letters from the word and make a word from them.
• The “=” sign says that you need to change the letter in the word that comes before this sign to the one after it. The same thing is meant by the arrow, which is located between the two letters.
• If the “=” sign is crossed out, then put “NOT” between the letters. Before you solve puzzles with such a symbol, know that in the picture the letters are arranged in any order and can be rearranged.
• An arrow above a word, going from one number to another - the letters that correspond to the indicated numbers are swapped.
• The word is upside down - read it not from left to right, but vice versa.
• The “+” sign is the preposition K, but this is not enough, since the syllables are often mixed up, you will have to select the ones that are suitable for the meaning.
• Two letters - add the preposition “BEFORE” or “FOR”, make up a word.
• Interesting combinations in which several small letters are formed into one large one. Then, when composing a word, you need to add the preposition “FROM”. For example, a big B is made up of the letters A, add IZ, and you get IZBA.
• If you don’t know how to solve a puzzle with letters that are located on one big one, then put “PO”. For example, there are many small A on K, we add PO, it turns out BYE.
• If the letter is located under or above the word, then when solving, the preposition “ABOVE” or “UNDER” is added.
• Sometimes you can find puzzles that use the stave and notes. In this case, only knowledge of the basics of music will help, that is, you need to guess on which quarter the note is located. It can be “do”, “re”, “mi”, etc.
• The fraction is used as the preposition “ON”; if the denominators are 2, then only half of the word will be needed to solve it.
• If at the end of the rebus there is an arrow pointing to the beginning, then after all the manipulations, read the word backwards.

Rebus is a riddle in which the hidden word or phrase is depicted as a combination of pictures, symbols (letters, numbers, punctuation marks), and other signs. To solve puzzles, you need to know the techniques for composing them. Here are the most common ones:

1. Using the technique: part of the search word is a picture.

The rebus consists of two pictures, which can be called as BANK And MOUTH. Search word: BANKRUPT.

2. Using the technique: part of the searched word is a letter (or letter combination).

The rebus consists of a letter combination DU and pictures CANCER. Together it turns out: FOOL.

Using the technique: part of the search word is a number.

This rebus reads like R, ONE, A, and together it turns out: HOMELAND.

4. Using the technique of rearranging letters.

The picture shows ROCKET. The first and third letters of its name need to be rearranged. It turns out: COACH.

5. Using the technique of skipping letters.

The missing letter is indicated by a comma. She can stand in front of the picture or behind it. In the example above, the comma is behind the picture. TABLE, skip the last letter, we get: ONE HUNDRED.

If there are several commas, then there are also several missing letters, for example: BARREL.

6. Using the technique of replacing letters.

Substitution of a letter is indicated by the symbol "=" , for example, in the word ROSE letter needs to be replaced R on TO. It turns out: GOAT.

7. Use of prepositions “in”, “for”, “on”, “above”, “under”, “from”, etc.
This is one of the most difficult techniques, especially when combined with others. Some examples:

Searched words: WHO, HARE, PEOPLE.

1. The names of all objects depicted in the rebus are read only in the nominative case. It is possible that the required item in the figure is indicated by an arrow.

2. Quite often, an object depicted in a rebus may have not one, but two or more names. It can also have one general and one specific meaning, for example, “auto” and “machine,” “flower” and “plant.” You need to choose the one that makes sense.

3. You can often see commas in a rebus. If the comma is to the left of the picture and inverted, then this means that the first letter of the name of the object in the picture must be discarded; if to the right of the picture, then the last letter. How many commas are there, so many letters need to be discarded.

For example, “forty” is drawn, but only “forty” needs to be read.

4. If objects or letters are depicted one within the other, then their names are read with the addition of the conjunction “in”.

5. If behind a letter or object there is another letter or object, then it is necessary to read with the addition of the conjunctions “for” or “before”.

6. If one object or letter is depicted under another, then it is necessary to read with the addition of the words “on”, “above”, “under”. The required option is selected according to its meaning. In a rebus, such a combination can be depicted either with or without a horizontal line.

For example: “under-s-ol” or “over-ol-s”, or “s-over-ol”, or “ol-under-s”

7. If another letter is written after one letter, then read it with the addition of the preposition “by”.

For example: “po-r-t” or “t-po-r”

8. If one letter lies next to another, is attached to it, is tilted towards it, then it is read with the addition of the preposition “y”.

For example: “i-u-ch” or “u-ch-i”:

9. If in a rebus the image of an object is turned upside down, then its name is read from the end. The object may not be turned over, but an arrow can be drawn from right to left.

10. If there is a crossed out letter under the depicted object, this means that this letter is not used when deciphering. A letter can be replaced with a number indicating the serial number of the letter in the word. If it is necessary to cross out several letters from a deciphered word, then several crossed out letters or numbers (ordinal numbers of letters) will be indicated. If the letters are consecutive to each other, then a range can be specified.

An example is given that from the word “bus” only “obus” should be used. All three options are the same.

11. If the crossed out letter(s) stands as an independent figure, then it must be read with the addition of the particle “not”.

For example: “no-bo”:

12. If there are uncrossed numbers under the image of an object, this means that the letters of the encrypted image are read in the order indicated by the numbers and only those letters whose serial number is indicated by the number. A range of numbers may also be specified if they are consecutive.

For example: instead of “rainbow”, you need to read “dra”

13. If there is an “=” sign between the letters under the image of an object, this means that the first letter (or combination of letters) must be replaced with the second letter (or combination of letters)

14. If any letter consists of another letter, then read with the addition of “from”

15. In many cases, in puzzles, individual letter combinations “do”, “re”, “mi”, “fa”, “la”, “si” are represented by the corresponding notes.

Ready? Go!

2.

3.

4

5.

6.

And here you have to puff a little longer: you need to unravel whole proverbs:

7.

8.

9.

Well, the last task for real pros! Guess what phrase is encrypted here:

10.

How to solve puzzles? Let's remember a few rules:

1. The names of all objects depicted in the pictures should be read in the nominative case.

2. Commas before a picture or word mean how many letters need to be removed from the beginning of the word.

3. Commas (usually upside down) after a picture or word indicate how many letters need to be removed from the end of the word.

4. Crossed out letters mean that such letters need to be removed from the word. If there are several such letters in a word, then all of them are crossed out.

5. Crossed out letter numbers mean that it is necessary to cross out only letters with the corresponding serial number from the beginning of the word.

6. An equality of type I=E means that in a word all letters I should be replaced with E. If an equality of type 1=C is indicated, then only the first letter should be replaced with C. (P=S SAW - POWER)

7. The use of an arrow going from one letter to another also serves to indicate the corresponding replacement of letters. A-P

8. The numbers 3,1,4,5 above the picture mean that from the word you must use only letters numbered 3,1,4,5 and in the order of the numbers.

9. A picture turned upside down means that the word needs to be read backwards.

10. If a fraction is used in the rebus, then it is deciphered as “NA” (divide BY). If a fraction with a denominator of 2 is used, then this is deciphered as “FLOOR” (half).

11. In puzzles, when encrypting, notes are often used. Indicate their name.

12. If the pictures are placed one below the other, then this is deciphered as “ON”, “ABOVE”, “UNDER”.

13. A letter made up of other letters is deciphered as “IZ”. If we depict a large “A” with small letters “B”, we get “FROM B A”

14. A letter written on top of another stands for “PO.”

15. If one letter is depicted behind another letter, then this is deciphered as “FOR” or “BEFORE”.

16. If an arrow pointing to the left is drawn above the picture, then you first need to decipher the word, and then read it backwards.

17. The crossed out "=" sign between pictures should be read as "NOT" (Example: "C" is NOT equal to "G").

Well, now the answers:
1. St. Petersburg
2. Supermarket
3. Beginning
4. Tournament
5. Classic
6. Compote
7. God protects those who are careful
8. Out of sight, out of mind
9. Language will bring you to Kyiv
10. If you are suddenly bitten by a crocodile, all you have to do is press hard on its eyes and it will let you go.

Rebus is an exciting puzzle game that develops ingenuity, logic and the ability to find the unusual in a picture. These puzzles will be of interest to both adults and children, as some of them have a very high level of difficulty. They are used in schools to teach the child to quickly use data, process it and arrange it in the right position. Often a rebus of letters or words has several spelling options and you need to choose the most suitable sound, which allows you to develop memory and vocabulary. Only the child who has enough words in his memory so that he can recognize and understand them can take on solving puzzles. Simpler problems are given to children from the second grade, when they already know the alphabet and numbers well; a younger child simply will not understand how to solve it. You need to start with picture puzzles, they are considered simpler; letter puzzles and note puzzles will be more difficult. They will only be possible for a child with special knowledge.

Rebuses have a rich history; they appeared even before writing. After all, it was with the help of pictures that ancient people tried to convey to others the meaning of certain events. Nowadays, puzzles are used as entertainment and a game that will captivate the whole family. In order to solve them, you need to remember a number of rules in order to understand what is read and in what order.

What could a rebus be?

A rebus is a picture that can show:

• letters;
• numbers;
• arrows;
• Pictures;
• fractions;
• notes;
• commas and periods.

They can be upside down, located in each other and in different positions in the picture. All such puzzles are divided by difficulty level. The simplest ones can be read very easily, for example, “Bumblebee” and “Table”:

You will have to think about more complex pictures.

And there are those for which you will have to be patient with pen and paper.

But for all of them there are certain rules by which puzzles are solved. If you figure it out, even the most complex proverb puzzles will yield and become understandable.

How to read a rebus?

The rebus itself is a whole picture; before you start solving it, you need to understand whether there are any special rules for reading it. If they are not there, then the words or phrases are read as usual, from left to right, but if they are, then this must be taken into account. There are two main signs:

Arrows from right to left indicate that a word or several words should be read in reverse: from right to left.

Rules for solving the rebus

The image itself includes letters, numbers and pictures that must be read and combined in a certain order. Therefore, they look not only at what is drawn, but also at how it is done. If there is a picture in the rebus, they select a word that goes with it, here you need to turn on your imagination and remember that sometimes it can be a jar, and sometimes what lies in it. All other elements are “read” in order, taking into account some rules:

Numbers, signs and commas

Very often the image is accompanied by commas, equal signs, minus signs or a row of numbers. This talks about what to do with the letters that make up a word. All actions can be seen in the pictures below, in which a “flower” is drawn, which must be turned into a “current”.

If there are commas near the picture, you need to look where they are and count them. When they appear before a word, the first letters are subtracted; if after it, then the last ones, in the amount of commas.

Sometimes there are crossed out letters next to the picture, this indicates that they need to be removed from the word.

And when there are “=”, “+” or “-” next to each other and additional letters or a picture, this indicates that this action needs to be done with the word. Letters are added either before the word or at the end. But sometimes "+" or "-" indicate that you need to add "to" or "from". We must always remember this.

The numbers next to the word indicate in what order and what letters should be taken.

Large numbers and signs

Large numbers and signs drawn in a rebus the size of the main pictures are perceived as a word or action. When they are present, different letters or syllables are added to the word.

• a large “+” indicates that you need to add “to”, “with” or “and”;
• a large “-” indicates that you need to add “from”;
• a number adds those letters that are in the word that signifies it.

For example, there are three pictures above: R + C = rice, ok-mol = hammer, 100l = table.

How to solve letter puzzles?

Sometimes a rebus consists of only one letter, which is drawn in different shapes and positions. The same decision rules apply to them:

• if the letter is drawn in a letter, then add: “in”;
• if the letter is above the letter, add: “above” or “on”;
• if the letter is under the letter, “under” will be added;
• if the letters are drawn from letters, you should definitely indicate this by adding “from”.

For example:

In the letter “O” we have “ron” written, that is, it should be read as “crow”.

The letters “S”, “D” and “T” grabbed the handles together, so the letter “i” is added between them - and we get the word “sits”.

This suggests that you need to add “on” to the sentence.

The letter “E” contains the letters “TKE”, that is, it is read as “v+e+tke” - “branch”.

All that remains is to connect all the words and we get: a crow is sitting on a branch. Letter puzzles allow you to develop your imagination well and learn to quickly form words.

How to solve puzzles with notes

Puzzles with notes are designed for those children who study music and it is not difficult for them to determine which note is drawn in the picture. To solve the puzzle, take seven notes and use their names.

This is the note "C" and "m", read as "house".

And these are “fa” and “sol”, that is, “beans”.

Such puzzles help you quickly remember how to write notes and quickly, subconsciously use them.

How to solve complex puzzles made from pictures, letters and numbers?

Puzzles are divided by level of difficulty. They mean not only words, but also phrases. If the picture seems too complicated, don’t be shy to take a pen and paper and break it down into its components. When you need to guess not just one word, but a proverb or a well-known phrase, the author usually writes about it. Let's take, for example, a rebus:

and let's try to solve it. We remember that rebuses are read from left to right like words in a book; if there are no additional icons, and this rebus does not have them, then you should start from the right.

From the letter “E” the letters “la” move away, that is, the whole picture needs to be read as “s+e+la”, that is, we get the first part: “sela”

Here we see that the letters “ha” are holding the letter “m” in their hands and we get the following combination “m+u+ha”. Of course, you can also read “u+ha+m”, but, in my opinion, the fly is still better.

This is a large jar of delicious jam, since there are no commas, numbers or symbols next to it, this indicates that the entire word must be used in its entirety, without changes.

And this indicates what is being added – “on” or “above”. In our case, “on” is more suitable.

As a result of the fact that the complex picture was decomposed into simple elements, we received a simple rebus from the words: village + fly + jam + on. As a result, we get the phrase: “A fly sat on the jam.”

In each case, it is worth turning on your imagination and learning to quickly use the rules - and then complex puzzles will not be so difficult. The main thing is to always be careful and not lose any elements.

As you know, a person is not born, they become one, and the foundations for this are laid in childhood. A significant role in the development of a person as an intellectual individual is played by his mental abilities and ingenuity, which need to be developed from an early age.

When a child is ready to solve puzzles

One of the most effective ways to develop a person and increase his intellectual level is to solve puzzles and rebuses. Before using letters and pictures and introducing the child to other mind games, you should make sure that the little person is already ready for this - he has learned to talk and identify images. You should start with the simplest picture puzzles. It is necessary to complicate the tasks as the baby grows up and the level of his mental abilities develops.

Types of puzzles

There are a huge variety of different puzzles. All of them can be divided into categories:

1. Picture puzzles. The puzzle is hidden in the images of this or that object. When deciphering, the name of the item should be read exclusively in the nominative case. There are situations when the object shown in the picture has several names or meanings. For example, “bus” and “transport”, “cat” and “animal”. In this case, you need to choose the clue word that is more suitable in meaning.
2. Letter puzzles consist exclusively of letters. They can be arranged in a variety of ways, which is fundamental when composing such a puzzle.
3. Picture + letter. How to solve puzzles with letters and pictures? The main key to solving this rebus is the image, and the letters indicate that to get the only correct answer you need to slightly adjust the name of the depicted object.
4. The “picture+number” rebus is an analogue of the “picture+letter” rebus, only here the picture is complemented by numbers, the number of which may vary.
5. Puzzles with commas. Quite often, picture riddles use a comma, regular or inverted. How to solve puzzles with commas? This sign indicates that to get the answer you need to shorten the name of the object drawn in the picture, discarding the first or last letter.

The right approach to raising children is those parents who involve their children in solving puzzles from an early age. Solving such puzzles contributes to the development of logical, creativity and originality, ingenuity, concentration, and attention.

But how can you make sure that your child likes this kind of “mental exercise”? Here are some simple but effective tips:

1. Patience, patience and more patience! This is very important, since children are characterized by eternal restlessness and haste.
2. If you see that a child cannot solve puzzles, do not torture yourself or him! Wait a while, it is possible that the baby will soon show interest in this activity.
3. Puzzles should be chosen taking into account the age category of the baby. So, if a child can only read, then you should choose picture puzzles or letter puzzles; if the child already knows how to count, it would not be superfluous to explain to him how to solve puzzles with numbers, etc.
4. At the stage of involving the baby in “mind games,” it is recommended to give preference to the simplest picture puzzles. It is very important that they are colorful.
5. Forcing a child to solve puzzles by force is strictly prohibited, since such an approach can completely discourage the child from engaging in activities of this kind. The most effective approach to solving puzzles is considered to be a game one.
6. Don't ignore the puzzles with answers. The child can solve such puzzles on his own without the help of his parents. The baby will determine the solution path himself, starting from the answer.
7. You should follow the rules that will help you figure out how to solve puzzles with letters and pictures, as well as with numbers or commas.

Learning to solve puzzles

A set of special rules will help you learn how to solve puzzles correctly:

Rebus - do it yourself!

You need not only to know how to solve puzzles with letters and pictures, but also to learn how to compose them yourself or together with your child. This will be another exciting task in which your child will be able to express himself.

To create a logic puzzle yourself, use the following recommendations:

1. Review all puzzle rules.
2. You should start with the simplest puzzles. At this stage, you can clearly explain to the baby how to encrypt this or that word in the puzzle. For example, write the number “7” and the letter “I” - the answer will be the word “family”.
3. Explain to your child that the same word can be the answer to several different puzzles. For example, let’s take the same word “family”, it can be encrypted in the rebus “7Ya” and “yayayayayaya”.
4. In order for the child to enjoy the process of training memory and logical thinking, he wants to return to composing and solving puzzles again and again, provide him with a field for amateur activities.
5. Take clean sheets of paper, bright markers and magazines (from which you can cut out individual parts of the future puzzle), glue. For example, we found a picture in a magazine with a picture of a cup - we cut it out, glue it onto a landscape sheet, and under the picture we write “W=Y” with a felt-tip pen. The puzzle has been created! The answer is a seagull.

Have fun and useful activities!