How to solve puzzles with letters in a letter. How to solve puzzles
If you have nothing to do on long winter evenings, and the TV and computer are already tired, then start solving puzzles, because this is not only interesting, but also useful for brain training. But first, learn and remember the rules for solving.
In total, there are 16 tricks for compiling puzzles, but there are only two main rules. First, before you solve the rebus, remember that all the words that are encrypted in it are used only in the nominative case. Secondly, the picture can have several names, that is, if a chicken is drawn, then you can read it like a bird, and a leg like a paw, so when solving, do not forget about synonyms, as well as general and private meanings.
Now consider the main 16 tricks that are used when compiling a rebus.
- Commas are one of the most common tricks. If it is in front of the 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. How many commas, so many letters need to be removed. For example, if there are two commas before the word "car", then we remove "MA" and the word "TIRE" is obtained.
- Strikethrough letters, which 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.
- Strikethrough numbers indicate that you need to count the letters in the word and cross out that match the number in the count. For example, above the word Executioner there is a crossed out number 2, we remove the first A, we get CRYING.
- If the numbers are not crossed out, then take the letters from the word in a row and make a word out of 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 is indicated 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, be aware that in the figure the letters are arranged in random order, they can be rearranged.
- The arrow above the word, going from one number to another - the letters that correspond to the indicated numbers in the account, swap places.
- 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 confused, you will have to select the appropriate ones in meaning.
- Two letters - add the preposition "BEFORE" or "FOR", make a word.
- Interesting combinations in which one large letter is made up of several small letters. Then, when composing the word, you need to add the preposition "FROM". For example, a large B is made up of the letters A, we add FROM, we get a hut.
- If you don’t know how to solve a rebus with letters that are located on one large one, then put “ON”. For example, there are many small A on K, we add software, it turns out YET.
- If the letter is located under or above the word, then when guessing, the preposition "OVER" or "UNDER" is added.
- Sometimes you can find puzzles that use a musical staff and notes. In this case, only knowledge of the basics of music will help, that is, you need to guess which quarter the note is located on. It can be "do", "re", "mi", etc.
- The fraction is used as a preposition "NA", if the denominators are 2, then only half of the word is needed to solve.
- 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- this is a riddle in which the hidden word or phrase is depicted as a combination of drawings, symbols (letters, numbers, punctuation marks), and other signs. To solve puzzles, you need to know how to compose them. Here are the most common ones:
1. Using the technique: part of the searched 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 a combination of letters).
The rebus consists of a combination of letters DU and pictures CANCER. Together it turns out: FOOL.
Using the technique: part of the search word is a number.
This puzzle reads like R, ONE, A, and together it turns out: MOTHERLAND.
4. Using the method of permutation of letters.
The picture shows ROCKET. The first and third letters of its name must 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 above example, the comma is behind the picture. TABLE, we 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 method of replacing letters.
The substitution of a letter is indicated by the symbol "=" , for example, in the word ROSE FLOWER need to replace the letter R on To. It turns out: GOAT.
7. The 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 desired object 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 "car", "flower" and "plant". You need to choose the one that makes the most sense.
3. In a rebus, you can often see commas. If the comma is to the left of the picture and turned upside down, then this means that the first letter must be discarded from the name of the object in the picture, if to the right of the picture, then the last one. How many commas are worth, so many letters must be discarded.
For example, "forty" is drawn, but only "forty" should be read.
4. If objects or letters are depicted one inside the other, then their names are read with the addition of the union "in".
5. If behind some letter or object there is another letter or object, then it is necessary to read with the addition of the unions “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 chosen according to the meaning. In a rebus, such a combination can be depicted both with a horizontal line and without it.
For example: “under-s-ol” or “over-ol-s”, or “s-over-ol”, or “ol-under-s”
7. If for any letter another is written, then they read with the addition of the preposition "by".
For example: "po-r-t" or "t-po-r"
8. If one letter lies next to another, attached to it, tilted towards it, then they read with the addition of the preposition "y".
For example: "i-u-h" or "u-h-i":
9. If in the rebus the image of the object is turned upside down, then its name is read from the end. The object may not be turned over, but draw an arrow 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. The letter can be replaced by a number indicating the ordinal number of the letter in the word. If it is necessary to cross out several letters from the deciphered word, then several crossed out letters or numbers (serial numbers of letters) will be indicated. If the letters are consecutive, then a range may 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 “not” particle.
For example: "no-bo":
12. If there are non-crossed-out numbers under the image of the 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 digits can also be specified if they are consecutive.
For example: instead of "rainbow", you need to read "dra"
13. If under the image of the object between the letters there is a sign "=", then this means that the first letter (or a combination of letters) must be replaced by the second letter (or a combination of letters)
14. If any letter consists of another letter, then read with the addition of "from"
15. In many cases, in rebuses, individual letter combinations “do”, “re”, “mi”, “fa”, “la”, “si” are depicted with the corresponding notes.
To learn how to compose and understand puzzles, it is worth understanding what they are.
Word "rebus" of Latin origin (lat. rebus, with the help of things, "Non verbis sed rebus" - "Not with words, but with the help of things"). The rebus originated in France in the 15th century, and the first printed collection of puzzles published in this country in 1582 was compiled by Etienne Taburo. In the time that has passed since then, the technique of compiling rebus problems has been enriched with a variety of different techniques.
So, rebus- this is one of the types of puzzles, a riddle for deciphering words. Encrypted according to certain rules in a rebus can be not only a single word, but also a proverb, saying, quote, riddle, and even a whole short story. Words and phrases in the rebus are depicted in the form of pictures, letters, numbers, notes and other various signs, the number of which is not limited. Solving the rebus is a whole science. When solving a rebus, it is necessary to write down all the signs in the form of a meaningful word or sentence. Although there are several types of puzzles (literary, mathematical, musical, sound, etc.), there are some general rules their compilation and interpretation.
rebus example
GENERAL RULES FOR SOLVING PUZZLES
A word or sentence is divided into such parts that can be depicted in the form of a picture or any sign. The rebus is read from left to right, less often from top to bottom. Punctuation marks and spaces in the rebus are not taken into account. If one word is guessed in the rebus, then it should, as a rule, be a noun, moreover, in the singular and in the nominative case. Deviation from this rule must be stipulated in the conditions of the rebus. If a sentence is guessed (proverb, aphorism, etc.), then, naturally, it can contain not only nouns, but also verbs and other parts of speech. In this case, the conditions of the rebus must contain the appropriate phrase (for example: “Guess the riddle”). The rebus must have a solution, and, as a rule, one. The ambiguity of the answer should be specified in the conditions of the rebus. For example: “Find two solutions to this puzzle.” The number of techniques used in one rebus and their combinations is not limited.
REBUSES IN PICTURES
The simplest option, when the rebus consists of two pictures to help you create a new word. The names of the objects depicted in the rebus should be read in the nominative singular or plural if several objects are depicted.
rebus 1
OX + WINDOW = FIBER
rebus 2
TRAIL + EXPERIENCE = TRAILER
rebus 3
EYE + FACES = EYE
From the last example, it can be seen that the picture in the rebus can have more than one name (eye and eye, bees and swarm, etc.); or the image may have a general or private name (a bird is a common name; a swift, a swallow, a chicken is a private name). If the depicted object has two meanings, then it is logically necessary to determine the appropriate one. This is the hardest part of puzzles.
If the picture turned upside down, which means that the word is read backwards.
rebus 4
Inverted NOSE = SLEEP
If to the right or left of the picture is one or more letters- this means that these letters should simply be added. Sometimes they are preceded by a "+" sign. Sometimes the desired object in the picture is indicated by an arrow.
rebus 5
FLASK + SA = SAUSAGE
rebus 6
Letter X + LION = SHED
REBUSES WITH COMMA
commas to the right or left of the picture means that in the word conceived with the help of the picture, you need to remove as many letters as there are commas. At the same time, commas in front of the picture indicate how many letters need to be removed at the beginning of the hidden word, commas at the end of the picture indicate how many letters need to be removed from the end of the word. Sometimes the commas to the left of the image are drawn upside down, although this does not play a fundamental role.
rebus 7
VOL K - K = VOL
rebus 8
GA MAC - GA = MAC
rebus 9
BA RAB AN - BA - AN = RAB
The arrow pointing to the left above the picture indicates that after the word is deciphered, it must be read backwards.
rebus 10
DRESSER - KO, read from right to left = HOUSE
REBUSES WITH LETTERS AND NUMBERS
If above the picture is strikethrough letter, and there is another one nearby, then this letter in the word must be changed to the specified one. If one or more letters are simply crossed out, then they must be removed from the given word. The "=" sign also serves to replace one of the letters with another.
rebus 11
O R YOL \u003d Donkey
rebus 12
BA BARREL - BA = BARREL
rebus 13
KORO B A = CROWN
If the crossed out letter(s) stands as an independent figure, then it must be read with the addition of the “not” particle.
rebus 14
NOT UCH
Numbers can be used instead of a picture. If part of the word in the rebus is represented by a number, then the number is pronounced as a numeral.
rebus 15
Number SEVEN + letter I = FAMILY
rebus 16
STO number + letter L \u003d TABLE
Keep in mind that a number can have more than one name.
rebus 17
ONE + FORK = FORK
rebus 18
Letter W + QOL + letter A = SCHOOL
rebus 19
Letter P + ONE + AR KA \u003d MELLE
rebus 20
ON VAR + figure TWO + L EU \u003d BASEMENT
Several identical letters or other images in a row mean that you need to try to count them.
rebus 21
SEVEN letters I = FAMILY
rebus 22
THREE CATS + letter F = JERSEY
rebus 23
PAIR of letters D = PARADE
Numbers next to the picture are used to number the letters in a word. The number indicates the place of the letter in the given word, and the order in which the numbers are written determines the new place of this letter.
rebus 24
PINE = PUMP
rebus 25
PAINTER = GAUGE
If there are fewer numbers than letters in the hidden word, this means that only the specified number of letters must be selected from the hidden word.
rebus 26
A LL IGAT O R = GUITAR
The use of crossed out numbers means that the corresponding letters must be removed from the hidden word.
rebus 27
PAL AT KA = STICK
If two numbers with arrows pointing in different directions are shown next to the picture, it means that in the word it is necessary to swap the letters indicated by the numbers.
rebus 28
Z A M OK \u003d SMAMA
Roman numerals may also be used.
rebus 29
Forty A = FORTY
The use of fractions is not excluded. When a fraction is used in a rebus, it is unraveled as "ON"(divide by). If a fraction with a denominator 2 is used in the rebus, then this is unraveled as "FLOOR"(half).
rebus 30
Z divide by K \u003d SIGN
rebus 31
Gender of letter E = FIELD
crossed out sign "=" between pictures should be read as "NOT".
rebus 32
And not Y \u003d hoarfrost
PUZZLES BY THE TYPE "LETTERS IN A LETTER", "LETTERS ON OR UNDER THE LETTER"
Often in rebuses, letters are drawn placed in an unusual perspective relative to each other (one inside the other, one under or above the other, one runs towards the other, one goes out of the other, etc.). This means that it is necessary to describe a drawing or letter combinations using prepositions, unions: “I”, “B”, “K”, “U”, “C”, “FOR”, “FROM”, “ON”, “ON” , "BEFORE" and others.
If objects, numbers or letters are depicted one in the other, then their names are read with the addition of a preposition "AT" before or between titles.
rebus 33
In the letter O, the letter Z = WHO
rebus 34
The letter Z in the letter O + the letter H \u003d CALL
If one object is depicted after another, then their names are read with the addition of a preposition "FRONT" or "PER".
rebus 35
Behind the letter L, the letter P \u003d ZALP
Usage horizontal bar between pictures, letters or numbers placed one below the other means the use of prepositions "ON", "ABOVE", "UNDER".
rebus 36
On the letter C, the letter T \u003d NAST
rebus 37
Under the letter C cok \u003d HOOP
rebus 38
C letter H letter E + letter G \u003d SNOW
Who among us is not familiar with puzzles? These entertaining ciphers are familiar to everyone from young to old. In puzzles, words are encrypted using a sequence of pictures and different symbols, including letters and numbers. The word "rebus" is translated from Latin as "with the help of things." The rebus originated in France in the 15th century, and the first printed collection of puzzles published in this country in 1582 was compiled by Etienne Taburo. In the time that has passed since then, the technique of compiling rebus problems has been enriched with a variety of different techniques. To solve the rebus, it is important not only to know what is drawn, but also to take into account the location of the drawings and symbols relative to each other, and this is achieved by practice. There are some unspoken rules by which puzzles are made up, and it is easier to solve them also according to the same rules, and the rules are as follows:
General rules for solving puzzles
The word or sentence in the rebus is divided into parts, which are depicted in the form of a picture or symbol. The rebus is always read from left to right, less often from top to bottom. Spaces and punctuation marks are not read. What is drawn in the pictures in the rebus is read in the nominative case, usually in the singular, but there are exceptions. If several objects are drawn, the arrow indicates which part of the entire image is used in this rebus. If not one word is guessed, but a sentence (proverb, catchphrase, riddle), then in addition to nouns there are verbs and other parts of speech. Usually this is specified in the task (for example: “Guess the riddle”). The rebus must always have a solution, and one. The ambiguity of the answer should be specified in the conditions of the rebus. For example: “Find two solutions to this puzzle.” The number of techniques used in one rebus and their combinations is not limited.
How to solve puzzles from pictures
They name all objects sequentially from left to right in the nominative singular.
Answer: track experience = tracker
Answer: ox box = fiber
Answer: eye of the face = outskirts
If the object is drawn upside down, its name should be read from right to left. For example, a “cat” is drawn, you need to read “current”, a “nose” is drawn, you need to read “dream”. Sometimes reading directions are shown with an arrow.
Answer: dream
Often an object drawn in a rebus can be called differently, for example, “meadow” and “field”, “leg” and “paw”, “tree” and “oak” or “birch”, “note” and “mi”, in such cases, you need to select a suitable word, such that the rebus has a solution. This is one of the most important difficulties in solving puzzles.
Answer: oak rava \u003d oak grove
How to solve puzzles with commas
Sometimes the name of the item depicted cannot be used in its entirety and one or more letters at the beginning or end of the word must be dropped. Then a comma is used. If a comma is to the left of the figure, the first letter is discarded from its name, if it is to the right, the last. How many commas are worth, so many letters are discarded.
Answer: ho ball k = hamster
For example, 3 commas and a “feeder” are drawn, you only need to read the “fly”; “sail” and 2 commas are drawn, you only need to read “steam”.
Answer: Umbrella p = pattern
Answer: li sa to por gi = boots
How to solve puzzles with letters
Such letter combinations as before, above, on, under, behind, at, y, in, as a rule, are not depicted in puzzles, but are identified from the corresponding position of letters and drawings. Letters and letter combinations from, to, from, from, to, and are not shown, but the relationship of letters or objects, or direction.
If two objects or two letters, or letters and numbers are drawn one into the other, then their names are read with the addition of the preposition "in". For example: “v-o-yes”, or “v-o-seven”, or “no-v-a”. A different reading is possible, for example, instead of "eight" you can read "seven-in-o", and instead of "water" - "yes-in-o". But such words do not exist, therefore such words are not a solution to the rebus.
Answers: v-o-yes, v-o-seven, v-o-lx, v-o-ro-n, v-o-mouth-a
If one object or symbol is drawn under another, then we decipher it with the addition of “on”, “above” or “under”, you need to choose a preposition according to the meaning. Example: “fo-na-ri”, “under-at-shka”, “above-e-wa”.
Answers: for-on-ri, under-at-shka, over-e-wa
If behind any letter or object there is another letter or object, then you need to read with the addition of “for”. For example: “Ka-za-n”, “za-ya-ts”.
Answer: for-i-ts
If one letter lies next to another or is leaning against it, then they read with the addition of "y" or "k". For example: “L-u-k”, “d-u-b”, “o-k-o”.
Answers: onion, oak
If a letter or syllable consists of another letter or syllable, then read with the addition of "from". For example: “from-b-a”, “b-from-he”, “out-of-y”, “f-from-ik”.
Answers: hut, bison
If another letter or syllable is written throughout the letter, they read with the addition of “by”. For example: “po-r-t”, “po-l-e”, “po-i-s”. Also, "by" can be used when one letter with legs runs over another letter, number or object.
Answer: Poland
Answers: belt, field
If an object is drawn, and a letter is written next to it, and then a letter is crossed out, this means that this letter must be thrown out of the word. If there is another one above the crossed out letter, then this means that it is necessary to replace the crossed out one with it. Sometimes in this case an equal sign is placed between the letters.
Answer: laz
Answer: raspberry z Mont \u003d lemon
How to solve puzzles with numbers
If there are numbers above the picture, this is a hint in what order to read the letters from the name of the subject. For example, 4, 2, 3, 1 means that the fourth letter of the name is read first, then the second, followed by the third and first.
Answer: brig
The numbers can be crossed out, which means you need to discard the letter corresponding to this order from the word.
Answer: horse ak LUa bo mba = Columbus
Quite rarely, the action of the letter is used in rebuses - it runs, flies, lies, in such cases, the corresponding verb in the third person of the present tense must be added to the name of this letter, for example, “y-runs”.
How to solve puzzles with notes
Often in rebuses, individual syllables corresponding to the names of notes - “do”, “re”, “mi”, “fa” ... are depicted with the corresponding notes. Sometimes the generic word "note" is used.
Notes used in composing puzzles
Answers: beans, minus
Hello everyone!
How about a mental warm-up? Do you like to guess crossword puzzles and think about logic puzzles in your spare time? People have been turning complex into fascinating for a very long time, drawing abracadabra and intricate schemes. Puzzles for deciphering hidden words, or in the common people - puzzles - this is a whole art that lives according to its own rules for compiling and unraveling.
Do you know how to solve puzzles or encrypted riddles for you - a dense forest? It turns out that there are techniques and techniques here that allow you to “turn on the brain”. So, let's get acquainted - a mysterious rebus.
Lesson plan:
Where did the puzzle come from?
A bit of history. The logical training of the mind came to us from France. There they were solved with pleasure back in the 15th century, the Prussian King Frederick himself was not averse to straining his brain.
From Latin, the word is translated as "with the help of things." And indeed, it is with the use of pictures of all kinds of objects, letters and numbers that puzzle lovers make riddles.
In 1582, the French even published the first collection, which introduced the whole of Europe to entertaining logic in pictures. In our native Russia, puzzles appeared only by the end of the 19th century - we once had problems to solve! Thanks to the Rebus magazine, they became one of the entertainments for the inhabitants of that era.
It turns out that the modern Russian puzzle is already over a hundred years old, and it is still popular, and the improvement of the used methods of “hide and seek” is an endless and limitless affair. New riddles today - a wide variety of "taste and color", for too smart and simpler.
What are the puzzles?
Words in logical riddles are encrypted in different ways.
The simplest drawn puzzles usually hide one or two words at the most, they can be solved in “one-two-three”, but tasks of three or more elements are much more difficult to solve, but even more interesting.
Rebuses can even write down sayings and proverbs, phrases and quatrains! Imagine Pushkin's letter from Tatyana to Onegin in the form of pictures! That would be interesting! And what a masterpiece it would look!
And puzzles will be a great, beautiful and interesting addition to your school research projects. For example, like or .
Solving the unsolvable, or general rules for puzzles
If you combine all the rules for solving logical puzzles together, you get a special set that helps you choose the right path to a solution.
- Each hidden word is divided into parts, depicted by a picture or with the help of signs. These parts are usually read from left to right, but it happens that vice versa and even from top to bottom.
- The hidden lonely word is usually a noun in the singular nominative case. There are exceptions to the rules, but hints are given for this.
- When a rebus is a whole sentence, then, of course, not only nouns live there, but also verbs and adjectives, in general, other parts of speech. For such puzzles, the compilers specifically make an indication like "guess the proverb."
- The puzzle must have one solution. If there are several of them, a reference is also made to this.
So, armed with a paper sheet with a pencil, we write out each guessed image, follow all the instructions for them, add the resulting parts. Voila! You have found the correct answer!
And now let's go through the main types of puzzles and how to solve them.
Pictures with letters and numbers
There are several methods that allow you to easily solve such problems:
Drawings with commas and signs.
Riddles with commas and pictures, as well as using other characters, they are also solved according to their own rules:
Letter puzzles
Often here the letters are drawn from different angles - inside each other, near, one under the other - all these are techniques that allow you to hide the hidden word:
Try your strength!
Have you studied the instructions for the order of guessing puzzles? Now put the theory into practice! Here's a proverb for you:
Well, how are you doing? Waiting for answers in the comments!
Well, since we did a good job, you need to have a good rest! Yeralash! For all! look and smile)
On this I say goodbye to you, I’ll also go tell fortunes, I’ll do exercises for the mind!
Always yours, Evgenia Klimkovich.
Numerical puzzles
Millions of people in all parts of the world love to solve puzzles. And this is not surprising. “Mind 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 an uninterrupted chain of game situations. They are significant, but they are trifling, but both of them require us to make decisions. Even in ancient Hellas, without games, the harmonious development of the personality was not conceived. And the games of the ancients were not only sports. Our ancestors knew chess and checkers, puzzles and riddles were not alien to them. Such games at all times were not alienated by scientists, thinkers, teachers. They created them. Since ancient times, the puzzles of Pythagoras and Archimedes, the Russian naval commander S.O. Makarov and the American S. Loyd.
There is such a kind of puzzles, which are called numerical. They are expressions that require an arithmetic solution, compiled in the form of mathematical equalities, where numbers are replaced by other signs - letters, geometry figures, asterisks, etc.
Numerical puzzles mean those puzzles in which it is necessary to use logical reasoning. They are the way to solve and decipher each character, which leads to the restoration of the numerical record.
Numerical puzzles are almost a thousand years old. They first appeared in China, then in India. In European countries, numerical puzzles were first 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 compiling puzzles of a numerical type, the following rules are used. All used numbers are replaced by letters. If there are identical numbers in the task, respectively, the same number of letters is used. Intermediate stages of mathematical operations are indicated by asterisks. There are several types of puzzles based on these rules. The first is puzzles in which all available letters are replaced with numbers. At the same time, some expression is encrypted that denotes everyday situations in the original presentation.
THREE BUN
+TWO + WAS
FIVE LOTS
SNOW SEA SUMMER
+ SNOW + SEA + SUMMER
blizzard ocean heat
The entry may contain not only numbers, but also asterisks - this is the second type of puzzles. The third type is puzzles, in which almost all characters are replaced by asterisks.
Numerical puzzles are very complex, sometimes there are those that require a phased long-term solution. Numerical puzzles are fascinating mathematical problems that greatly develop logic and quick wits.
Numerical puzzles can be made up of several rows of symbols, and between them a certain number of mathematical signs are placed, which are pointers to what actions need to be performed vertically and which horizontally.
1) TA + IT \u003d YEARS 2) KRA + OLI \u003d IAYA
X - + X : -
EU x CH = LLAS L x AR = KYAI
LEAA + EC = LEEC OII + AL = RKA
Numerical puzzles are very popular not only in schools in regular lessons, but also in mathematical Olympiads. You can solve numerical puzzles with the help of computer programs, but a person who puzzles over the solution on his own and eventually finds it can get incomparable pleasure.
The tasks presented in an entertaining way are very interesting. I want to solve them, they captivate with their unusualness, non-obviousness of the answer. There is a desire to make even a difficult path of finding a solution. Amusement and severity are quite compatible. Each independently solved task is perhaps a small, but still a victory.
How to solve mathematical puzzles and creep tariffs
In alphabetic puzzles, each letter encrypts one specific number: the same numbers are encrypted with the same letter, and different letters correspond to different numbers.
In puzzles encrypted, for example, with asterisks, each character 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 starting to solve the mathematical letter puzzle(e.g. cryptarithm), make sure it uses no more than 10 different letters. Otherwise, such a rebus will have no solutions.
Start solving the rebus with the rule that zero cannot be the leftmost digit in a number. Thus, all letters and signs with which the number in the rebus begins can no longer mean zero. The circle of search for the necessary numbers will narrow.
In the course of the decision, start from the basic mathematical rules. For example, multiplying by zero always gives zero, and when multiplying any number by one, we will get the original number as a result.
Very often, mathematical puzzles are examples of adding two numbers. If, when adding, the sum has more signs than the terms, then the sum starts with "1"
Pay attention to the sequence of arithmetic operations. If a numerical rebus 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 iteration method. Some puzzles will require a long step-by-step solution, but in the end you will be rewarded with the right answer and an excellent warm-up for your quick wits.
Before you start solving complex problems, practice on a simple example: CAR + CAR = COMPOSITION. Write it in a column, so it will be more convenient to decide. You have two unknown five-digit numbers, the sum of which is a six-digit number, so B + B is greater than 10 and C is 1. Replace the characters C with 1.
The sum of A + A is a one-digit or two-digit number with a unit at the end, this is possible if the sum of G + G is greater than 10 and A is either 0 or 5. Try to assume that A is 0, then O is equal to 5 , which does not satisfy the conditions of the problem, since 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, it can be equal to 5 or 15 only if the sum of H + H is a two-digit number, i.e. N more than 6. If O+O=5, then O=2. This solution is incorrect, because B + B \u003d 2B + 1, i.e. O must be an odd number. So O is equal to 7. Replace all O with 7.
It is easy to see that B is equal to 8, then H=9. Replace all letters with the found numerical values.
Replace the remaining letters in the example with numbers: G=6 and T=3. You got the correct equality: 85679+85679=171358. Rebus solved.