The fourth trick in the series Math tricks In the section on free training in magic tricks, let’s start as in the previous trick, that is, suggest thinking of a number and adding half or most of it to it, then again adding half of the resulting amount or most of it.

But now, instead of demanding to divide the result by 9, offer to name by digit all the digits of the resulting result, except one, as long as this digit, unknown to the guesser, is not zero.

It is also necessary that the one who conceived the number should say the digit of the number that is hidden from him, and in which cases (in the first, in the second, or in the first and second, or neither) he had to add the majority of the number.

After this, to find out the intended number, you need to add up all the numbers that are named and add:

- 0 , if you never had to add most of the number;

- 6 , if only in the first case it was necessary to add most of the number;

- 4 , if only in the second case it was necessary to add most of the number;

- 1 , if in both cases it was necessary to add most of the number.

Further, in all cases, the resulting sum must be added to the nearest number that is a multiple of nine. This addition will be the hidden figure. Now, knowing all the numbers of the result, and therefore the entire result, it is not difficult to find the intended number. To do this, you need to divide the result by 9, multiply the quotient by 4 and, depending on the size of the remainder, add 1, 2 or 3 to the product.

Example 1. The number 28 was conceived. After the required actions were completed, the result was 63. The number 3 was hidden. Then the guesser completes the tens digit 6 given to him to 9 and receives the units digit 3. The result 63 was discovered. The required number is (63:9)x4 = 28.

Example 2. The number 125 was conceived. After performing all the required actions, the result was 282. Let's say, the hundreds digit is 2. It is reported: the tens and units digits are 8 and 2, respectively, and most of the number was added only in the first case.

Let's guess: 8+2+6=16. The closest multiple of nine is 18. So the hidden hundreds digit 18-16 = 2.

We determine (guess) the intended number: 282:9 = 31 (remainder 3); 31x4+1 = 125.

Example 3. Let the one who thought of a number say that the last result he received consists of three digits, the first digit being 1, the last digit 7, and most of the number had to be added in two cases.

Guess the intended number: 1+7+1=9. The complement of a number that is a multiple of nine is equal to zero or nine, but according to the condition, zero cannot be hidden, therefore, the hidden number is 9 and the whole result is 197. Divide 197 by 9; 197:9 = 21 (remainder 8). The intended number is 21 4+3 = 87.

Prove the trick. This is not difficult, especially for those who have understood the essence of the proof of the previous trick.

Focus 5

Let's continue math tricks to guess the intended number. Fifth mathematical trick. Think of some number (less than one hundred, so as not to complicate the calculations) and square it. Add any number to the number you have in mind (just tell me which one) and square the resulting amount. Find the difference between the resulting squares and report the result.

To guess the intended number, it is enough to divide half of this result by the number added to the intended one, and subtract half of the divisor from the quotient.

Example. Conceived 53; 53 squared = 53x53 = 2809. 6 is added to the intended number:

53 + 6 = 59, 59x59 = 3481, 3481 - 2809 = 672.

This result is reported.
Let's guess:

072:12 = 60, 0:2 = 3, 50 - 3 = 53.

The intended number is 53.
Find proof.

Focus 6

Sixth math trick. Invite your friend to think of any number in the range from 6 to 60. Now let him divide the conceived number first by 3, then divide it by 4, and then by 5 and report the remainders of the divisions. Using these remainders, using a key formula, you will find the intended number.

Let the remainders be R1, R2 and R3. Now remember this formula:

S=40R1 + 45R2 +36R3.

If it turns out S=0, then the intended number is 60; if S is not equal to zero, then the remainder of dividing S by 60 will give you the intended number. It will not be so easy for your friend who has thought of a number to figure out the guessing secret that you have.

Example. Conceived 14. Reported balances: R1=2, R2=2, R3=4.

Let's guess:

S = 40x2 + 45x2 + 36x4 = 314;
314:60 = 5

and the remainder is 14.

The planned number is 14.

There is no need to blindly believe a formula proposed without a conclusion. First make sure that it works flawlessly in all cases allowed by the trick's conditions, and then demonstrate the trick.

Focus 7

The seventh mathematical trick in the series math tricks to guess the intended number. Having understood the mathematical basis of the tricks presented here, you can modify them in every possible way, come up with other rules for guessing numbers, and diversify the questions proposed.

Here, for example, is such a topic. In the previous trick of guessing the intended number from its remainders after division, the numbers 3, 4 and 5 were proposed as divisors. Let's replace them with other divisors, for example, such as 3, 5, 7, and push the limits for the conceived numbers from 7 to 100. Factors in the key formula, of course, will also change. Match them to a new key formula suitable for the case.

Answer

S = 70R1 + 21R2 + 15R3, where R1, R2 and R3 are, respectively, the remainders from dividing the intended number by 3, 5 and 7. Guess the intended number. It is equal to the remainder of dividing S by 105 (if S = 0, then 105 is intended).

Focus “Phenomenal memory”.

To perform this trick, you need to prepare many cards, put its number on each of them (a two-digit number) and write down a seven-digit number using a special algorithm. The “magician” distributes cards to the participants and announces that he has memorized the numbers written on each card. Any participant names the number of the roll, and the magician, after thinking a little, says what number is written on this card. The solution to this trick is simple: to name a number, the “magician” does the following: adds the number 5 to the card number, turns over the digits of the resulting two-digit number, then each next digit is obtained by adding the last two; if a two-digit number is obtained, then the units digit is taken. For example: the card number is 46. We add 5, we get 51, rearrange the numbers - we get 15, we add the numbers, the next one is 6, then 5+6=11, i.e. take 1, then 6+1=7, then the numbers 8, 5. Number on the card: 1561785.

Focus “Guess the intended number.”

The magician invites one of the students to write any three-digit number on a piece of paper. Then add the same number to it again. The result will be a six-digit number. Pass the piece of paper to your neighbor, let him divide this number by 7. Pass the piece of paper further, let the next student divide the resulting number by 11. Pass the result further, let the next student divide the resulting number by 13. Then pass the piece of paper to the “magician”. He can name the number he has in mind. The solution to the trick:

When we assigned the same number to a three-digit number, we thereby multiplied it by 1001, and then, dividing it successively by 7, 11, 13, we divided it by 1001, that is, we obtained the intended three-digit number.

Focus “Guess the crossed out number.”

Let someone think of some multi-digit number, for example, the number 847. Invite him to find the sum of the digits of this number (8+4+7=19) and subtract it from the conceived number. It turns out: 847-19=828. including the one that comes out, let him cross out the number - it doesn’t matter which one - and tell you the rest. You will immediately tell him the crossed out number, although you do not know the intended number and did not see what was done with it.

This is done very simply: you look for a number that, together with the sum of the numbers given to you, would form the nearest number that is divisible by 9 without a remainder. If, for example, in the number 828 the first digit (8) was crossed out and you were told the numbers 2 and 8, then, having added 2 + 8, you realize that the nearest number divisible by 9, i.e. 18, is not enough 8. This is the crossed out number.

Why does this happen?

Because if you subtract the sum of its digits from any number, then you will be left with a number that is divisible by 9 without a remainder, in other words, one whose sum of digits is divisible by 9. In fact, let in the conceived number a be the hundreds digit, b be the hundreds digit tens, c - units digit. This means that the total number of units in this number is 100a+10b+s. Subtracting the sum of the digits (a+b+c) from this number, we get: 100a+10b+c-(a+b+c)=99a+9b=9(11a+c), i.e. a number divisible by 9 When performing a trick, it may happen that the sum of the numbers given to you is itself divisible by 9, for example 4 and 5. This shows that the crossed out number is either 0 or 9. Then you must answer: 0 or 9.

Focus “Favorite number”.

Each of those present thinks of their favorite number. The magician invites him to multiply the number 15873 by his favorite number multiplied by 7. For example, if his favorite number is 5, then let him multiply by 35. The result will be a product written only with his favorite number. The second option is also possible: multiply the number 12345679 by your favorite number multiplied by 9, in our case this is the number 45. The explanation of this trick is quite simple: if you multiply 15873 by 7, you get 111111, and if you multiply 12345679 by 9, you get 111111111.

Trick: “Guess the intended number without asking anything.”

The magician offers students the following actions:

The first student thinks of some two-digit number, the second one assigns the same number to it on the right and left, the third one divides the resulting six-digit number by 7, the fourth one by 3, the fifth one by 13, the sixth one by 37 and passes on his answer to the person who has planned it. who sees that his number has returned to him. The secret of the trick: if you assign the same number to the right and left of any two-digit number, then the two-digit number will increase by 10101 times. The number 10101 is equal to the product of the numbers 3, 7, 13 and 37, so after division we get the intended number.

Fan competition - “Fun Score”. A representative is invited from each team. There are two tables on the board, on which numbers from 1 to 25 are marked in disarray. At the leader’s signal, students must find all the numbers on the table in order; whoever does it faster wins.

Focus “Number in an envelope”

The magician writes the number 1089 on a piece of paper, puts the piece of paper in an envelope and seals it. Invites someone, having given him this envelope, to write on it a three-digit number such that the extreme digits in it are different and differ from each other by more than 1. Let him then swap the extreme digits and subtract the smaller one from the larger three-digit number . As a result, let him rearrange the extreme digits again and add the resulting three-digit number to the difference of the first two. When he receives the amount, the magician invites him to open the envelope. There he will find a piece of paper with the number 1089, which is what he got.

Focus “Guessing the day, month and year of birth”

The magician asks students to perform the following actions: “Multiply the number of the month in which you were born by 100, then add your birthday, multiply the result by 2, add 2 to the resulting number, multiply the result by 5, add 1 to the resulting number, add 1 to the resulting number 0, add 1 more to the resulting number and finally add the number of your years. After that, tell me what number you got.” Now the “magician” has to subtract 111 from the named number, and then divide the remainder into three sides from right to left, two digits each. The middle two digits indicate the birthday, the first two or one - the month number, and the last two digits - the number of years; knowing the number of years, the magician determines the year of birth.

Focus “Guess the intended day of the week.”

Let's number all the days of the week: Monday is the first, Tuesday is the second, etc. Let someone think of any day of the week. The magician offers him the following actions: multiply the number of the planned day by 2, add 5 to the product, multiply the resulting amount by 5, add 0 to the resulting number at the end, and report the result to the magician. From this number he subtracts 250 and the number of hundreds will be the number of the planned day. Solution to the trick: let’s say it’s planned to be Thursday, that is, day 4. Let's perform the following steps: ((4×2+5)*5)*10=650, 650 - 250=400.

Focus “Guess the age”.

The magician invites one of the students to multiply the number of their years by 10, then multiply any single-digit number by 9, subtract the second from the first product and report the resulting difference. In this number, the “magician” must add the units digit with the tens digit to get the number of years.

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"The subject of mathematics is so serious that it is useful to seize the opportunity to make it a little entertaining"

B. Pascal

When we first met in a mathematics lesson, the teacher promised to guess the date of birth of each student in our class if we quickly and correctly performed the arithmetic operations she suggested. First, we had to multiply our birthday by 2, add 5 to the resulting number, multiply the resulting result by 50 and, finally, add the number of the month of our birth to the resulting number. After we told the resulting number to the teacher, she, as promised, guessed our date of birth and was mistaken only when we ourselves were to blame for the incorrect calculations. I really liked this trick. I also became interested in what lies at the heart of this trick. It was then that I decided that I would definitely research the issue of mathematical tricks, find out their secrets, make a selection of tricks and surprise and entertain my friends and acquaintances by demonstrating mathematical tricks in mathematics lessons, extracurricular activities and even at home parties.

I read in Internet sources that mathematical tricks do not receive special attention from either mathematicians or magicians. The first consider them simple fun, the second consider them too boring.

But, in my opinion, this is not at all true. Mathematical tricks have a deep meaning.

Mathematical tricks are experiments based on mathematical knowledge, on the properties of figures and numbers, presented in an extravagant form. To understand the essence of this or that experiment means to understand a small, but very important mathematical pattern.

A person's ability to guess numbers conceived by others seems amazing to the uninitiated. But if we learn the secrets of tricks, we will be able not only to show them, but also to come up with our own new tricks. And the secret of the trick becomes clear when we write down the proposed actions in the form of a mathematical expression, transforming which we obtain the secret of guessing.

In my work, I want to prove that mathematical tricks help develop memory, intelligence, the ability to think logically, improve mental calculation skills and, finally, simply increase students’ interest in mathematics, which should improve the quality of their knowledge.

Goal of the work: explore math tricks.

Tasks:

Study the literature on the topic under study.

Demonstrate a few tricks.

Explain them in terms of mathematics.

Attract the attention of classmates to study mathematics.

Subject of study: math tricks

Object of study:"secrets" of mathematical tricks

Research methods: study and analysis of literature on entertaining mathematics, independent modeling of mathematical tricks.

Practical significance: The material can be used in mathematics lessons and extracurricular activities, at mathematical evenings and holidays, and during mathematical competitions.

Chapter 1. History of the emergence of mathematical tricks.

Focus- a skillful trick based on deception of vision, attention with the help of a deft and quick technique, movement (Ozhegov’s dictionary)

The history of mathematical tricks.

The first document that mentions the art of illusion is an ancient Egyptian papyrus. It contains legends dating back to 2900 BC, the era of the reign of Pharaoh Cheops.

Initially, magic tricks were used by sorcerers and healers. The priests of Babylon and Egypt created a huge number of unique tricks using excellent knowledge of mathematics, physics, astronomy and chemistry. The list of miracles performed by the priests can include: thunderclaps, lightning flashes, temple doors opening by themselves, statues of gods suddenly appearing from underground, the sounding musical instruments themselves, voices.

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. Makarov and the American S. Loyd have been known.

We find the first mention of mathematical tricks in the book of the Russian mathematician Leonty Filippovich Magnitsky, published in 1703. We all know the great Russian poet M.Yu. Lermontov, but not everyone knows that he was a great lover of mathematics, he was especially attracted to mathematical tricks, of which he knew a great variety, and he invented some of them himself.

The enormous cognitive and educational value of intellectual games was repeatedly pointed out by K.D. Ushinsky, A.S. Makarenko, A.V. Lunacharsky. Among those who were interested in them were K.E. Tsiolkovsky, K.S. Stanislavsky, I.G. Erenburg and many other outstanding people.

I would especially like to mention the American mathematician, magician, journalist, writer and popularizer of science Martin Gardner.

He was born on October 21, 1914. Graduated from the Faculty of Mathematics of the University of Chicago. Founder (mid-50s), author and presenter (until 1983) of the “Mathematical Games” column of the Scientific American magazine (“In the World of Science”). Gardner interprets entertaining as a synonym for fascinating, interesting to learn, but alien to idle entertainment. Gardner's works include philosophical essays, essays on the history of mathematics, mathematical tricks and "comics", popular science sketches, science fiction stories, and intelligence problems.

Gardner's articles and books on entertaining mathematics gained particular popularity. Seven books by Martin Gardner have been published in our country, which captivate the reader and encourage independent research. “Gardner’s” style is characterized by intelligibility, brightness and persuasiveness of presentation, brilliance and paradoxicality of thought, novelty and depth of scientific ideas.

Among our compatriots I would like to mention the name of Ya. I. Perelman. Yakov Isidorovich Perelman did not make any scientific discoveries, did not invent anything in the field of technology. He did not have any academic titles or degrees. But he was devoted to science and for forty-three years he brought people the joy of communicating with science. It is with his books that the journey into the fascinating world of mathematics, physics, and astronomy begins. And it was his books that helped me write this work. Ignatiev E.I., Kordemsky B.A. made their enormous contribution to the popularization of mathematics. and many other Russian scientists, teachers, methodologists.

Mathematical tricks are interesting precisely because each trick is based on mathematical laws. Their meaning is to guess the numbers conceived by the audience. Millions of people in all parts of the world are addicted to mathematical tricks. And this is not surprising. “Mental gymnastics” is useful at any age. And tricks train memory, sharpen intelligence, develop perseverance, the ability to think logically, analyze and compare.

Chapter 2. Mathematical tricks

Focus “Guess the intended number.”

Let's ask any student to think of a number.

Then the student must multiply this number by 2, add 8 to the result,

divide the result by 2

and take away the intended number.

As a result, the magician boldly calls the number 4.

The solution to the trick:

The viewer thought of the number 7

1) 7●2 = 14 2) 14 + 8 = 22 3) 22/2 = 11 4) 11 - 7 = 4

The number X is guessed.

2) X●2 2) X●2 + 8 3) (X●2 + 8)/2 4) (X●2 + 8)/2 - X = X + 4 - X = 4

We got 4 regardless of the originally guessed number

Focus “Magic table”.

You see a table in which numbers from 1 to 31 are written in a special way in five columns.

I invite those present to think of any number from this table and indicate in which columns of the table this number is located.

After that I will tell you the number you have in mind.

The solution to the trick:

This table is compiled as follows: each column corresponds to a certain number, after calculating the sum of which the magician guesses the number you have chosen

For example: You thought of the number 27.

This number is in the 1st, 2nd, 4th and 5th columns.

It is enough to add the numbers located in the first row of the table in the corresponding columns, and we will get the intended number. (1+2+8+16=27).

Focus “Favorite number”.

Each of those present thinks of their favorite number.

I suggest he multiply the number 15873 by his favorite number multiplied by 7.

The solution to the trick:

1) 15873 * 7 = 111111. Thus, multiplying 15873 by 7 and by the favorite number, we get a number written only by the favorite number.

For example, favorite number is 5

1) 15873 *(7*5) 2) 15873 *35 = 555555.

4. Focus “Guess the intended day of the week.”

Let's number all the days of the week: Monday is the first, Tuesday is the second, etc.

Let someone think of any day of the week. I suggest you the following actions: multiply the number of the planned day by 2, add 5 to the product, multiply the resulting amount by 5, add 0 to the resulting number at the end, and report the result to the magician.

The solution to the trick:

Let's say Thursday is planned, that is, day 4.

Let's do the following: ((4×2+5)*5)*10 = 650,

650 - 250 = 400.

The number of hundreds shows the hidden day of the week.

By the way, the trick that our teacher showed us at the beginning of the school year for guessing the date of birth has the same secret.

Let the day of my birth (and this is a single or double digit number) X, and the number of the month of my birth at then we have:

(2 · X+ 5) · 50 + at= 100 · X + 250 + u. If you now subtract 250 from the result, you get a three or four-digit number, the last two digits of which indicate the month number, and the first one or two digits indicate the birthday.

5. Focus “Familiar numbers”

After this, the magician immediately calls out the intended numbers.

The solution to the trick:

6. Focus

2. Ask a friend to write a number from 100 to 999. The only condition! The difference between the first and last digits must be greater than one. For example, the number 346 is suitable, since 6 - 3 = 3, and 3 is greater than 1. But the number 344 is not suitable, since 4 - 3 = 1.

3. Suppose your friend has already chosen a number and written it down. Your task is to rewrite this number in reverse order (346, and you write 643).

4. Now subtract the smaller number from the larger number (643 - 346 = 297).

6. Add both numbers (297+792).

The solution to the trick:

100a + 10b + c; a - c > 1.

100a + 10b + c - 100c - 10b - a = 99a - 99c = 99(a - c).

a - c = 2.99 * 2 = 198.198 + 891 = 1089,

a - c = 3.99 * 3 = 297.297 + 792 = 1089,

a - c = 4.99 * 4 = 396.396 + 693 = 1089,

a - c = 9.99 * 9 = 891.891 + 198 = 1089.

7. Focus

A circle of comrades who are not privy to the mathematical secret of Scheherazade's number can be amazed by the following trick.

Let someone write on a piece of paper - secret from the magician - a three-digit number, then let him add the same number to it again. The result is a six-digit number consisting of three repeating digits.

The magician invites the same comrade or his neighbor to divide - secretly from him - this number by 7: at the same time he warns that there will be no remainder. The result is passed on to another neighbor, who divides it by 11; there should be no remainder. The result obtained is passed on to the next neighbor, who is asked to divide the number by 13 (again without a remainder).

The result of the third division is transmitted to the first comrade with the words:

Here is the number you have in mind.

The solution to the trick:

This beautiful arithmetic trick, which gives the impression of magic to the uninitiated, can be explained very simply. Attaching it to a three-digit number itself means multiplying it by 1001 (Scheherazade’s number), that is, by the product 71113. It is clear that if you first multiply the intended number by 1001, and then divide it by 1001, then you will get it yourself.

This focus can be changed. Suggest division by 7, then by 11, and then by the intended number. Then we can say with confidence that the result will be 13.

8. Trick “Guess the result of calculations without asking anything”

Let's write some number between 1 and 50 on a piece of paper and hide it without showing the participants the trick.

In turn, let each participant write whatever number he wishes, greater than 50 but greater than 100, and, without showing you, do the following:

will add 99 - x to its number, where x is the number you wrote on a piece of paper (you will calculate this difference in your head and tell the participants of the trick the finished result);

cross out the leftmost digit in the resulting sum and add the same digit to the remaining number;

the resulting number will be subtracted from the number originally written down by him.

As a result, all participants will get the same number, exactly the one you wrote down and hid.

The solution to the trick:

My number X , Where " X" more than 1 but less than 50.

Intended number at , Where " y" greater than 50 but less than or equal to 100.

y - (y + 99 - x - 100 + 1) = y - y - 99 + x + 100 - 1 = x.

9. Focus modeled by myself.

Guessing the house and apartment number of a participant in the trick.

Add 8 to the house number, multiply the result by 8, multiply the result by 125, add the apartment number to the result. Tell me how much you got, and I will tell you your house number and apartment number.

The secret of the trick:

(X + 8) * 8 * 125 + Y - 8000 = 1000X + 8000 + Y - 8000 = 1000X + Y.

The last one, two, three digits are the apartment number, the first 1 - 2 digits are the house number.

Conclusions.

Previously, I did not understand the significance of mathematical tricks because I knew little about them. I learned that the secret to solving many tricks is equations. While doing research, I became convinced that mathematical tricks are interesting to schoolchildren.

Thanks to my work, I increased my knowledge and also realized that magic tricks sharpen the ability to think logically, analyze and compare.

In addition, I realized that my current knowledge is not enough to understand the nature of many of the tricks I encountered while researching the topic. This applies to knowledge of algebra and geometry. Therefore, I will continue to study math tricks in future classes.

Conclusion

There is an interesting parable.

“Once upon a time there was an old man who, when he died, left 19 camels to his three sons. He bequeathed half 1/2 to his eldest son, a fourth to his middle son, and a fifth to his youngest. Unable to find a solution on their own (after all, the problem in “whole camels” has no solution), the brothers turned to the sage.

O wisest one! - said the elder brother, - my father left us 19 camels and ordered us to divide them among ourselves: the eldest - half, the middle - a quarter, the youngest - a fifth, but 19 is not divisible by 2, 4, or five. Can you, O venerable one, help our grief, for we want to fulfill the will of our father?

“There is nothing simpler,” the sage answered them. - Take my camel and go home.

The brothers of the house easily divided 20 camels in half, into 4 and into 5. The eldest brother received 10 camels, the middle one 5, and the youngest 4 camels. At the same time, one camel (10 + 4 + 5 = 19) remained extra. The brothers returned to the sage and complained:

Oh, sage, again we did not fulfill the will of our father! This camel is superfluous. “Not superfluous,” answered the sage, “this is my camel.” Return him and go home.” “There are no unsolvable problems. There is always a way out” (folk wisdom)

Mathematical tricks are varied. In many mathematical tricks, numbers are veiled by objects related to numbers. They develop skills in quick mental calculation, calculation skills, because... you can guess small and large numbers, awaken the imagination, surprise, fascinate, develop the creative principles of the individual, artistic abilities, stimulate the need for creative self-expression. Mathematical tricks promote concentration. The magic of magic can wake up the sleepy, stir up the lazy, and make the slow-witted think. After all, without unraveling the secret of the trick, it is impossible to understand and appreciate all its charm. And the secret of focus most often has a mathematical nature.

Literature

Perelman, Ya.I. Interesting arithmetic. Numbers and tricks / Ya.I.Perelman. - M.: OLMA Media Group, 2013

Perelman, Ya.I. “Living Mathematics”, D.: VAP, 1994

Kordemsky, B.A. Mathematical savvy. - M.: Science. Ch. ed. physics and mathematics lit., 1991

Ignatiev E.I. In the kingdom of ingenuity - M.: Science. Ch. ed. physics and mathematics lit., 1984

M. Gardner “Mathematical miracles and mysteries” - Moscow: “Nauka”, 1988

Application

Focus 1: “Familiar numbers”

Write down the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 in sequence on a piece of paper. Ask one of the students to add in their mind any three numbers following one another. And the result is to be named.

For example, he will choose 5, 6 and 7. In this case, the sum will be 18.

After this, I immediately call out the intended numbers.

The secret of the trick:

To do this trick you just need a little intelligence.

When they call the sum (5+6+7) = 18, divide it in your head by 3. In our case, you get 6. This is the desired average figure. The number in front of it is 5, and after it is 7. The whole effect of this trick is in the lightning-fast response.

Focus 2

1. Write the number 1089 on a piece of paper and put it aside temporarily (without showing it to anyone).

2. Ask a friend to write a number from 100 to 999. The only condition! The difference between the first and last digits must be greater than one. For example, the number 346 is suitable, since 6-3=3, and 3 is greater than 1. But the number 344, for example, is not suitable, since 4-3=1. It's clear? If not quite, read first))

3. Suppose your friend has already chosen a number and written it down. Your task is to rewrite this number in reverse order (346, and you write 643). Ready?

4. Now subtract the smaller number from the larger number (643-346=297).

5. Now write down the resulting answer in reverse order (it was 297, it will become 792).

6. Add both numbers (297+792).

7. Voila! Show me your piece of paper with the magic number 1089. You knew in advance what the answer would be! Indeed, 297+792=1089! Hocus Pocus!!! The most interesting thing is that this algorithm always works!

Math tricks (1-3)

In this section we will give free training in tricks with which you will surely surprise your comrades, friends, loved ones and we will start this section with mathematical tricks.

The main theme of mathematical tricks is guessing the intended numbers or the results of operations on them. The whole “secret” of these tricks is that the “guesser” knows and can use the special properties of numbers, but the “thinker” does not know these properties).

Mathematical tricks are interesting because each trick has its own mathematical interest and consists in “exposing” its theoretical foundations, which in most cases are quite simple, but sometimes are cunningly disguised.

You can check the feasibility of each trick using any example, but to justify most arithmetic tricks it is most convenient to resort to algebra. At first, you can omit the “proofs” of the tricks and limit yourself to only mastering their content for showing it to your friends. But the proofs will not be difficult for those who like to think and are familiar with the rudiments of algebra.

Only the basic framework of mathematical tricks is given here, since their practical design may vary depending on the conditions and place, as well as on your taste, wit and invention.

Guessing the intended number (7 tricks)

Focus 1 .

First math trick with numbers.
Think of a number. Subtract 1. Double the remainder and add the originally intended number. Tell me the result. I will guess the intended number.

Guessing method.
Add 2 to the result, and divide the sum by 3. The quotient is the intended number.
Example.
Conceived 18; 18- 1 = 17; 17x2 = 34; 34 + 18=52. Let's guess: 52 + 2 = 54; 54:3=18.
Proof. We denote the intended number by the letter x. We carry out the required actions:

x- 1; 2(x-1); 2(x- 1) + x;

Result

2x - 2 + x = 3x - 2.

Adding 2, we get 3x, and dividing by 3, we get the intended number x.

Focus 2.

The second trick from the "mathematical tricks" series.
Invite your friend to think of a number. Then make him alternately multiply and divide the number he has in mind several times into different numbers arbitrarily assigned by you. Let him not tell you the result of his actions.

After several multiplications and divisions, stop and ask the person who thought of a number to divide the result he received by the number he thought of, then add the number he thought of to the last quotient and tell you the result. Based on this result, you immediately guess the number your friend had in mind.

The secret is very simple. The guesser himself also needs to think of an arbitrary number (for example, 1) and perform all the multiplications and divisions assigned to him, up to division by the originally conceived number. Then, in the particular, he will end up with the same number as the other person who conceived it, even though their originally conceived numbers were different. After this, the guesser must subtract his own result from the result reported to him. The difference will be the desired number.

Example. The intended number is 7. Multiplied by 12. The result (84) is divided by 2. The resulting number (42) is multiplied by 5. The result (210) is divided by 3. The result is 70, and after dividing by the intended number and adding the intended number -17.

At the same time, you “in your head” thought of the number 1. Multiply by 12, you get 12. Divide by 2, you get 6. Multiply by 5, you get 30. Divide by 3, you get 10. Subtracting 10 from 17, you get the desired number 7.

Note 1. To enhance the effect, you can give the person who conceived the number the opportunity to assign numbers by which he would like to multiply and divide the resulting results, as long as he tells you these numbers every time.

Note 2. It is not necessary to alternate multiplications and divisions. You can assign some multiplications first and then some divisions, or vice versa.

Prove this arithmetic trick, that is, show “in letters” that the trick works for any given number.

Focus 3.

Let's continue our free training in magic tricks and show you an interesting mathematical trick with numbers.
To teach this trick, we accept or agree to call the majority of an odd number that part of it that is 1 more than the other. Thus, the number 13 has a major part equal to 7, and the number 21 has a major part equal to 11.

Think of a number. Add to it half of it, or, if it is odd, then most of it. To this amount add half of it or, if it is odd, then most of it. Divide the resulting number by 9, tell the quotient, and if you get a remainder, then say whether it is greater than, equal to, or less than five. Depending on the answer to the question, the intended number is equal to:

Quadruple the quotient if there is no remainder;
- quadruple quotient +1 if the remainder is less than five;
- quadruple quotient + 2 if the remainder is five;
- quadruple quotient + 3 if the remainder is more than five;

Example. Conceived 15. Carrying out the required actions, we have:

15 + 8 = 23, 23 + 12 = 35, 35: 9 = 3 (remainder 8). Reported: “quotient three, remainder greater than five.”

Let's guess: 3 4 + 3 = 15. 15 is intended.

Prove this mathematical trick too. When thinking about the proof, I advise you to take into account that any integer (that is, intended) can be represented in one of the following forms:

4n, 4n + 1, 4n + 2, 4n + 3,

where the letter n can be given meanings: 0, 1, 2, 3, 4, ...

Continued Free training in magic tricks:

Number in envelope

Simple Arithmetic

1. Write down how many days a week you want to make love.
2. Multiply this number by 2.
3. Add 5 to the resulting number.
4. Multiply the amount by 50.
5. If you already had a birthday this year, add 1750; if not, add 1749.
6. Subtract your year of birth from the resulting number.
7. Add 7 to the resulting number.
The first digit of the resulting number is the number of days per week on which you want to make love. The last two are your age.

Guess the crossed out number

You stand with your back to the board. The participant writes down any six-digit number on the board. You ask him to write a new number from the digits of the original number rearranged in any order. Then the smaller number is subtracted from the larger number. The resulting difference is multiplied by any number. In the resulting product, one non-zero digit is arbitrarily crossed out. Then the participant must tell you in random order all the uncrossed out numbers. You guess the crossed out one.

The Secret of Focus . If the numbers are rearranged and the smaller one is subtracted from the larger one, then the resulting difference is divided by 9. It is clear that the product must also be divisible by 9. The sum of the digits of this product must also be divided by 9. When they call you the numbers, you mentally add them up. After all the numbers are told to you, you must figure out which number to add to your sum so that the resulting number is divisible by 9. As you proceed, you can always add up the numbers of the resulting subtotal to make counting easier. For example, if you have a sum of 25 and need to add 6, then you can add 6 not to 25, but to 7 (2 + 5). As a result, you can get not 13, but 4 (1 + 3).

Mysterious squares

The person showing stands with his back to the audience, and one of them selects any month on the monthly table calendar and marks a square containing 9 numbers on it. Now it is enough for the viewer to name the smallest of them, so that the person showing immediately, after a quick count, announces the sum of these nine numbers.

Explanation. The person showing needs to add 8 to the named number and multiply the result by 9

Guess the date of birth

So, first you need to choose a “victim”, then ask her to count to herself:
1. Multiply your birthday (to yourself) by two.
2. Add 5 to the result.
3. Multiply the result by 50.
4. Add the number of the month in which you were born.

Ask the person to say the number. Then just subtract 250 from the result, and you're done. You will get 4 or 3 digits. The first 2 (can be one digit) are the day, and the last two are the month .

Tricky leaf

You select 5 participants from the audience and give them identical pieces of paper. Let the first of them write any two-digit number on a piece of paper and show this number to the second. The second participant must add the same number to the right and left of this number and divide this number by 3. He writes the result on a piece of paper (only the result!), shows it to the third participant, then folds the piece of paper and gives it to you. The third viewer divides the number he saw by 7, writes the result on a piece of paper, shows it to the fourth viewer, folds the piece of paper and gives it to you. The fourth viewer divides the number by 13, writes the result on a piece of paper, shows it to the fifth viewer, folds the piece of paper and gives it to you. The fifth spectator divides the number by 37, writes the result on a piece of paper, adds it up and gives it to you. You take the same piece of paper, without looking at the received pieces of paper, write the original number, fold your piece of paper, go up to the first spectator and show his piece of paper to the rest of the spectators. Then you take out your piece of paper, unfold it and, having told the number to the audience, show it.

The secret of focus. If you add the same number to the left and right of any two-digit number, you get a number that is 10,101 times larger than the original. 3 7 13 37 = 10 101. Therefore, the number written on the piece of paper for the fifth participant coincides with the number written down for the first participant. You show this piece of paper to the audience (anything can be written on your piece of paper).

Number in envelope

The magician writes the number 1089 on a piece of paper, puts the piece of paper in an envelope and seals it. Invites someone, having given him this envelope, to write on it a three-digit number such that the extreme digits in it are different and differ from each other by more than 1.

Let him then swap the extreme digits and subtract the smaller one from the larger three-digit number. As a result, let him rearrange the extreme digits again and add the resulting three-digit number to the difference of the first two. When he receives the amount, the magician invites him to open the envelope. There he will find a piece of paper with the number 1089, which is what he got.

Mathematical tricks from simple to complex: diving into the tempting world of numbers.

Focus 1: “Familiar numbers”

Write down the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 in sequence on a piece of paper. Ask one of the students to add in their mind any three numbers following one another. And the result is to be named. For example, he will choose 5, 6 and 7. In this case, the sum will be 18. After this, the teacher immediately names the intended numbers.

The secret of the trick:

Introduction

By learning magic tricks, a person develops artistry and creativity. Mathematical tricks focus children's attention on the mathematics lesson, thanks to the entertaining essence of the trick combined with the mathematical nature of the secret (once having shown the trick, the child can be encouraged to take active actions in the lesson under the pretext of revealing the secret). The whole point of watching a magic trick is to find the answer and enjoy the “magical actions.”

Event goals

Arouse students' interest in mathematics and instill a love for it. Raise students' spirits. Explain what mathematical tricks are, why they are needed, teach children several of them.

Progress of the event

To begin with, the teacher says a few words about mathematical tricks, asks the children a few questions: “Do you like magic tricks?.. What tricks do you know, can you perform?.. Do you want to learn new tricks?” - etc. After a short discussion, it is worth showing a mathematics presentation on the topic of mathematical tricks.

After being shown , you should start demonstrating tricks. There are many different types of mathematical tricks, we will give just a few examples.

Focuses:

Day of the week on the palm
Let's number each day of the week (Monday - 1, Tuesday - 2, etc.). Any student can guess one of the days (a number from 1 to 7), the teacher suggests multiplying the guessed number by 2, then adding 5, multiplying the sum by 5, and adding a zero at the end. The class is informed of the result, from which 250 is subtracted. As a result, the number of hundreds will correspond to the guessed day

The secret of the trick: Let’s substitute “x” for the day number:

((2x+5)*5)*10=(10x+25)*10=100x+250

100x+250-250=100x. Therefore, the number of hundreds always corresponds to the day number.

Note: Tricks of this type are the most common of all mathematical tricks, so you shouldn’t fill the event with them only.

Phenomenal memory

The teacher writes a very long number series (22-26 numbers) on a piece of paper and states that he can list all the numbers in the series in the same order from memory. Once done, you can repeat the trick to prove that the number series is completely arbitrary (there really shouldn’t be any pattern to it).

The secret of the trick: All the numbers in the row are just familiar phone numbers (you can take the last 4-7 numbers from each number).

Note: As can be seen from the example, some mathematical tricks use ordinary tricks.

Intuition, or the magic nine

One student (or all at once) writes a number from 3 different digits, and next to it - a number from the same digits, but in reverse order. The smaller number is subtracted from the larger number. Not seeing the result, the teacher says that in the middle of the answer received there is nine (if the answer has a two-digit number, then write it as 0...). And indeed, the nine stands where the teacher predicted.

The secret of the trick: Since only 1 and 3 digits change places, then for a larger number, the digit in the units place will always be smaller, which means that you will need to take 1 from the tens place, and when you need to subtract the tens, from the hundreds place (to understand, try solving in a column) . For example, 653-356=297.

Note: The secrets of the most interesting mathematical tricks usually cannot be guessed at first glance, and the trick itself is difficult to attribute to any subgroup.

Conclusion

Mathematical tricks are a great way to make children fall in love with the subject they are studying and understand all the splendor of its properties and rules.

Math tricks 4-7
Guessing the intended number

Focus 4.

The fourth trick in the seriesMath trickssection Let's start as in the previous trick, that is, suggest thinking of a number and adding half or most of it to it, then again adding half of the resulting amount or most of it.

But now, instead of demanding to divide the result by 9, offer to name by digit all the digits of the resulting result, except one, as long as this digit, unknown to the guesser, is not zero.

It is also necessary that the one who conceived the number should say the digit of the number that is hidden from him, and in which cases (in the first, in the second, or in the first and second, or neither) he had to add the majority of the number.

After this, to find out the intended number, you need to add up all the numbers that are named and add:

- 0 if you never had to add most of the number;
- 6, if only in the first case it was necessary to add most of the number;
- 4, if only in the second case it was necessary to add most of the number;
- 1, if in both cases it was necessary to add most of the number.

Further, in all cases, the resulting sum must be added to the nearest number that is a multiple of nine. This addition will be the hidden figure. Now, knowing all the numbers of the result, and therefore the entire result, it is not difficult to find the intended number. To do this, you need to divide the result by 9, multiply the quotient by 4 and, depending on the size of the remainder, add 1, 2 or 3 to the product.

Example 1. The number 28 was conceived. After the required actions were completed, the result was 63. The number 3 was hidden. Then the guesser completes the tens digit 6 given to him to 9 and receives the units digit 3. The result 63 was discovered. The required number is (63:9)x4 = 28.

Example 2. The number 125 was conceived. After performing all the required actions, the result was 282. Let's say, the hundreds digit is 2. It is reported: the tens and units digits are 8 and 2, respectively, and most of the number was added only in the first case.

Let's guess: 8+2+6=16. The closest multiple of nine is 18. So the hidden hundreds digit 18-16 = 2.

We determine (guess) the intended number: 282:9 = 31 (remainder 3); 31x4+1 = 125.

Example 3. Let the one who thought of a number say that the last result he received consists of three digits, the first digit being 1, the last digit 7, and most of the number had to be added in two cases.

Guess the intended number: 1+7+1=9. The complement of a number that is a multiple of nine is equal to zero or nine, but according to the condition, zero cannot be hidden, therefore, the hidden number is 9 and the whole result is 197. Divide 197 by 9; 197:9 = 21 (remainder 8). The intended number is 21 4+3 = 87.

Prove the trick. This is not difficult, especially for those who have understood the essence of the proof of the previous trick.

Focus 5.

Let's continuemath tricksto guess the intended number. Fifth mathematical trick. Think of some number (less than one hundred, so as not to complicate the calculations) and square it. Add any number to the number you have in mind (just tell me which one) and square the resulting amount. Find the difference between the resulting squares and report the result.

To guess the intended number, it is enough to divide half of this result by the number added to the intended one, and subtract half of the divisor from the quotient.

Example. Conceived 53; 53 squared = 53x53 = 2809. 6 is added to the intended number:

53 + 6 = 59, 59x59 = 3481, 3481 -2809 = 672.

This result is reported.
Let's guess:

072:12 = 60, 0:2 = 3, 50 - 3 = 53.

The intended number is 53.
Find proof.

Focus 6.

Sixth math trick. Invite your friend to think of any number in the range from 6 to 60. Now let him divide the conceived number first by 3, then divide it by 4, and then by 5 and report the remainders of the divisions. Using these remainders, using a key formula, you will find the intended number.

Let the remainders R 1 , R2 and R3 . Now remember this formula:

S=40R1 +45R2 +36 R3 .

If it turns out S=0, then the intended number is 60; if S is not equal to zero, then the remainder of dividing S by 60 will give you the intended number. It will not be so easy for your friend who has thought of a number to figure out the guessing secret that you have.

Example. Conceived 14. Remains reported: R1 =2, R2 =2, R3 =4.

Let's guess:

S = 40x2 + 45x2 + 36x4 = 314;
314:60 = 5

and the remainder is 14.
The planned number is 14.

There is no need to blindly believe a formula proposed without a conclusion. First make sure that it works flawlessly in all cases allowed by the trick's conditions, and then demonstrate the trick.

Focus 7.

The seventh mathematical trick in the seriesmathematical tricks for guessing the intended number. Having understood the mathematical basis of the tricks presented here, you can modify them in every possible way, come up with other rules for guessing numbers, and diversify the questions proposed.

Here, for example, is such a topic. In the previous trick of guessing the intended number from its remainders after division, the numbers 3, 4 and 5 were proposed as divisors. Let's replace them with other divisors, for example, such as 3, 5, 7, and push the limits for the conceived numbers from 7 to 100. Factors in the key formula, of course, will also change. Match them to a new key formula suitable for the case.

Answer.
S=70R1 +21R2 +15R3 , where R1 , R2 and R3 - respectively, the remainders from dividing the intended number by 3, 5 and 7. We guess the intended number. It is equal to the remainder of dividing S by 105 (if S = 0, then 105 is intended).

Trick about Rhinoceros

(cool trick..to show those who don’t believe in magic tricks, but who know EVERYTHING :)))

Think of a number from 1 to 10. Did you think of it?

You got a two-digit number.

Add the first digit of this two-digit number to the second. Example: if the number is 21, then you need to add 2+1. .Next: folded?

Subtract 4 from the result.

Now think of a letter for this number in alphabetical order. That is, if you get 1, then this is the letter A; 2-letter B; 3-B; 4-G, etc.

Now you have made a wish and keep a letter in your head, remember this letter and wish for a European country.

See the answer below...

Answer: There are no rhinoceroses in Denmark!!! Ha ha ha...

After all the mathematical calculations, you get 9, then 5. This is the letter D. There is one country for the letter D - Denmark.

The rest must be brought up and
Play! It’s like I can read minds, etc.

In order to surprise your friends and family by performing magic tricks, you don’t need to have super-dexterous hands and mysterious magic props. It is enough to know the secrets of interesting tricks based on mathematics.

Mathematical tricks: secrets and solutions

1. NINE

On the table in the shape of a nine (see picture) you need to lay out 12-20 coins. Twelve is the minimum number. From those present, a person is selected who will make a wish. To avoid errors in calculations, you can organize a collegial riddle from several, or even all those present. You stand with your back to the audience.

Rice. 3 Nine

The guesser thinks of a number that is greater than the number of coins that make up the “leg” of the nine. The maximum value of the number is theoretically unlimited, but common sense should still be used. To avoid possible jokes, its value can be limited in advance. After this, the guesser counts out as many coins as he has planned in the following way: starting from the “leg” from the bottom up, and then further, counterclockwise around the ring. After he counts out the intended number of coins, the counting is repeated. You should start exactly with the coin where the previous count stopped. But now the guesser counts the coins from one to the intended number along the ring clockwise. Under the coin on which the count has ended, the wisher hides, for example, a small, inconspicuous piece of paper.

You turn to the audience, make “magic passes” over the table looking at the audience, and pick up the hidden coin.

THE SECRET OF FOCUS. Everything is very simple. The fact is that regardless of what exact number is intended, the count ends in any case in the same place. To begin with, perform this trick yourself in your mind with any number, and you will know what kind of coin it will be. If you are asked to repeat a trick, the nine should be modified by removing or adding a few coins to the leg. This technique will allow you to change the position of the “hidden” coin.

2 . Heads or tails?

Another coin trick is based on the difference between heads and tails. A handful of change is laid out on the table. You ask one of the spectators to turn over coins at random, one at a time. Each inversion should be accompanied by the word “is.” These actions should be done behind your back. The same coin can be turned over several times. At the end, the wisher covers one of the coins with his hand. You turn around and name exactly how the coin is lying - “heads” or “tails” up.

THE SECRET OF FOCUS. The whole point of the trick is in your preparation. After the coins are scattered, it is necessary to count the number of “eagles”. For each “is” you need to add one to this number. It all depends on the final number. If it turns out to be even, then the number of “eagles” in the final combination is even, if the sum is odd, then the number of “eagles” is odd. The position of the hidden coin will be “spoken” by the open ones.

This trick can be done with any identical objects that can be placed in one of two possible ways.

As you already understand, the above tricks, like all mathematical tricks, are based on the properties of figures and numbers, and their secrets lie in the exact reflection of a certain mathematical pattern.

It sounds like magic...but it's actually math! Do you want to become a magician? Thanks to this book, you will always have mathematical tricks in your arsenal. With a pencil and paper you can do the most incredible things. For example, correctly guessing a person’s age, reading someone’s thoughts, making accurate predictions, demonstrating your amazing memory. This book will allow you to acquire “sleight of hand”, teach you everything listed above, and even more. In it you will find tips on how to prepare your audience for a particular focus. And best of all, you will learn the secrets of these amazing tricks. Go for it!

Focus with marked dates

The trick starts like this. The viewer is asked to open a monthly report card for any month and circle one date of his choice in each of the five columns. (In the case when the numbers are located in six columns, which is very rare, the sixth column is not taken into account.) In this case, the person showing stands with his back to those present.

Still not turning around, he asks: “How many Mondays do you have circled?”, then: “How many Tuesdays?” etc., going through all the days of the week. After the seventh and final question, the person showing announces the sum of the circled numbers.

The secret of focus. The sum of the numbers in a line that begins with the first day of the month is always 75 (except for February in non-leap years). Each marked number in the next line increases this amount by 1, in the next line by 2, etc.; each marked number in the previous line reduces the mentioned amount by 1, in the line preceding it by 2, etc. Let, for example, the first day of the month fall on Thursday and one Monday, one Thursday and three Saturdays are circled; the person showing performs a mental calculation:

75 + 3 * 2 - 1 * 3 = 78

and announces the result.

Of course, the person showing must know in advance what day the first day of the month chosen by the viewer falls on.

1. Based on the principle of mathematical trick.

(Einstein as a mathematician-magician).

Tricks are based on deceiving people in the hope that this deception will not be immediately noticed. They are harmless in that the magician does not even assume that they will definitely believe him. The only hope is that the essence of his trick will not be immediately revealed. Magic is a kind of entertainment, nothing more.

It is very difficult to understand whether Einstein considered himself a magician. It is possible that he believed in his genius and had absolutely no gift for self-criticism. After all, he tried to put even his best friend at that time in a mental hospital himself, without the support of the Academies of Sciences, for criticizing his article. This is instead of checking for the hundredth time to see if there is an error in it. It is not known whether he checked his article at least once after its publication. But, as you know, it is much more difficult to find your own mistake.

The disadvantage of Einstein's critics is that they usually refute the conclusions of the “theory of relativity”, instead of looking for errors in the work itself, which is much simpler. I have already done similar work once, but this time I decided to approach Einstein’s “work” from a different angle. There is no need to do math at all. Einstein's mistakes, of course, are not mathematical, but logical.

What is a “mathematical trick”? I will give an example that is familiar to me from school, although the text I am citing may be somewhat different.

Guess the number

Ask someone to think of any number, then subtract 1 from it, multiply the result by 2, subtract the number from the product and tell you the result. By adding the number 2 to it, you will guess what you have planned.

Guess the date of birth

Multiply the number of your birth by 2, add 5, multiply by 50 and add the serial number of the month. Subtract 250 from the number you get and get your birthday and month.

Guess the result of actions on an unknown number

Someone came up with a number. You ask to multiply it by 2, then add 12 to the product, divide the amount in half and subtract the intended number from it. Whatever number is intended, the result will always be 6.

Today I want to offer you a mathematical focus from the series "Entertaining tasks". With this trick you can surprise your friends. If you don't know when your friends' birthday is, you can guess their date of birth using some simple mathcalculations. You can, of course, just ask any person when their birthday is. But it’s much more interesting to surprise a person, entertain, amuse or simply make an impression with the help of mathematics.

Surprise your friend by guessing his date of birth without asking her!

What needs to be done?

So:

Tell your friend to multiply his birth date by two, but not say the result of his calculations out loud.

Now ask him to add five to the number he got.

Next step: the last result obtained, have your friend multiply by 50. If you have difficulty multiplying, you can take a calculator. So that in no case does an error creep in. It is very important!

And lastly, ask your friend to add the serial number of the month in which he was born to the last result obtained.

All!

Now ask him to voice the result that he got after all the calculations.

Now you subtract 250 from the announced number. You will get a 3-4 digit number as a result.

The first 1-2 digits on the left in this number are the date of birth, and the next two are the month of birth of your friend.

Show off this trick in the circle of your friends, acquaintances and relatives!

Wish you luck!

This math trick with phone numberThe brunette showed me. Her reaction was quite emotional: “Brain blowing! How can this be?!” Indeed, the impression is that shamans with tambourines are dancing around the calculator. Here is a description of this mathematical trick with a phone number. Let me clarify right away that the trick is designed for a city seven-digit phone number.