home > Pumps > The trick is to guess the conceived number is nothing. Start in science. Focus "Phenomenal memory"

The trick is to guess the conceived number is nothing. Start in science. Focus "Phenomenal memory"

Focus "Phenomenal memory"

Trick “Guess the planned number”.

The magician invites a student to write any three-digit number on a piece of paper. Then add the same number to it again. The result is a six-digit number. Pass the sheet to a neighbor, let him divide this number by 7. Pass the sheet on, let the next student divide the received number by 11. Pass the result again, let the next student divide the received number by 13. Then pass the sheet to the “magician”. He can name the planned number.

This is done very simply: you are looking for a figure that, together with the sum of the figures reported to you, would make 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, adding 2 + 8, you realize that there is not enough to the nearest number divisible by 9, that is, up to 18 8. This is the crossed out number.

Focus “Guess the crossed out number”.

Let someone think of a multi-digit number, for example, the number 847. Ask him to find the sum of the digits of this number (8 + 4 + 7 = 19) and subtract it from the planned number. It turns out: 847-19 = 828. including what happens, let him cross out the number - no matter which one, and tell you all 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 being done with it.

Focus "Who has which card?"

An assistant is required to perform the focus. There are three cards with marks on the table: “3”, “4”, “5”. Three people come to the table and each takes one of the cards and shows it to the assistant "magician". The "magician", without looking, must guess who took what. The assistant tells him: “Guess” and the “magician” tells who has which card.

Trick "Guess the planned number without asking anything."

The magician offers students the following actions:

The first student thinks of a two-digit number, the second one assigns to
to him on the right and left the same number, the third divides the resulting six-digit number by 7, the fourth - by 3, the fifth - by 13, the sixth - by 37 and gives his answer to the one who thinks, who sees that his number has returned to him.

MAGIC MATRIX.

Number the cells of the 4x4 matrix with numbers from 1 to 16.

Circle any number you like. Cross out all the numbers that are in the same column and on the same line with the circled number. Circle any of the uncrossed numbers and cross out the numbers that are on the same line and in the same column with it. Circle any of the remaining numbers and cross out those numbers that are on the same line and in the same column with them. Finally, circle the only remaining number. Add up the numbers in circles. Nowyou can call them the amount. You get 34.

Secret focus.

Why does the drawn matrix "make" always choose four numbers that add up to 34? The secret is simple and elegant. Above each column we write the numbers 1, 2, 3, 4, and to the left of each row - the numbers 0, 4, 8, 12:

1 2 3 4

These eight numbers are calledgenerators matrices. In each cell we write a number equal to the sum of the two generators located at the row and the column at the intersection of which the cell is located. As a result, we get a matrix, the cells of which are numbered in order from 1 to 16, and their sum is equal to the sum of the generators.

For lovers of mathematical tricks, I'm posting a new selection!

There are some pretty interesting options. Enjoy! :)

Focus "Phenomenal memory".

To carry out this trick, it is necessary to prepare many cards, on each of which put its number (two-digit number) and write down a seven-digit number according to a special algorithm. The "magician" hands out the cards to the participants and announces that he has memorized the numbers written on each card. Any participant calls the number of the box, and the magician, after thinking a little, says which number is written on this card. The solution to this trick is simple: to name the number, the “magician” does the following: adds 5 to the card number, turns 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 number of units is taken. For example: card number - 46. Add 5, get 51, rearrange the numbers - get 15, add the numbers, the next one - 6, then 5 + 6 = 11, that is, take 1, then 6 + 1 = 7, then the numbers 8, 5. Number on the card: 1561785.

Trick “Guess the planned number”.

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

Focus "Magic table".

On the board or screen there is a table in which, in a known way, numbers from 1 to 31 are written in five columns. The magician invites those present to think of any number from this table and indicate in which columns of the table this number is located. After that, he calls the number you have conceived.

Focus Key:

For example, you think 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 last row of the table in the corresponding columns, and we get the planned number. (1 + 2 + 8 + 16 = 27).

Focus "Guess the crossed out number"

Why does this happen?

Because if you subtract the sum of its digits from any number, then there will be 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 - a digit of hundreds, in - a digit tens, s - number of units. This means that there are only 100a + 10b + s units in this number. Subtracting from this number the sum of digits (a + b + c), we get: 100a + 10b + c- (a + b + c) = 99a + 9b = 9 (11a + b), i.e. a number divisible by 9. When performing a trick, it may happen that the sum of the digits given to you is itself divisible by 9, for example 4 and 5. This shows that the strikethrough digit is either 0 or 9. Then you must answer: 0 or 9.

Focus "Who has which card?"

An assistant is required to perform the focus.

There are three cards with marks on the table: “3”, “4”, “5”. Three people come to the table and each takes one of the cards and shows it to the assistant "magician". The "magician", without looking, must guess who took what. The assistant tells him: “Guess” and the “magician” tells who has which card.

Focus Key:

Let's consider the possible options. Cards can be positioned as follows: 3, 4, 5 4, 3, 5 5, 3, 4

3, 5, 4 4, 5, 3 5, 4, 3

Since the assistant sees which card each person took, he will help the “magician”. To do this, you need to memorize 6 signals. Let's number six cases:

First - 3, 4, 5

Second - 3, 5, 4

Third - 4, 3, 5

Fourth - 4, 5, 3

Fifth - 5, 3, 4

Sixth - 5, 4, 3

If the first case, then the assistant says: "Done!"

If case is the second - then: "So, done!"

If the third case - then: "Guess!"

If the fourth - then: "So, guess!"

If the fifth - then: "Guess!"

If the sixth - then: "So, guess!".

Thus, if the variant starts with the number 3, then “Done!”, If from the number 4, then “Guess!”, If from the number 5, then “Guess!”, And the students take the cards one by one.

Trick "Who took what?"

To accomplish this ingenious trick, you need to prepare three little things that fit in your pocket, for example - a pencil, a key and an eraser and a plate of 24 nuts. The magician invites three students to put a pencil, key or eraser in their pocket during their absence, and he will guess who took what. The guessing procedure is carried out as follows. Returning to the room after the things are hidden in the pockets, the magician hands them nuts from a plate to save. The first gets one nut, the second two, the third three. Then he leaves the room again, leaving the following instruction: each must take more nuts from the plate, namely: the holder of the pencil takes as many nuts as he was given; the holder of the key takes twice the number of nuts that was handed to him; the holder of the eraser takes four times the number of nuts given to him. Other nuts remain on the plate. When all this is done, the "magician" enters the room, glances at the plate and announces who has what item in his pocket. The answer to the trick is as follows: each method of distributing things in pockets corresponds to a certain number of remaining nuts. Let's designate the names of the focus participants - Vladimir, Alexander and Svyatoslav. We will also designate things with letters: pencil - K, key - KL, eraser - L. How can three things be located between three participants? In six ways:

There can be no other cases. Now let's see what residuals correspond to each of these cases:

Vl Al Sv

Number of nuts taken

Total

Remainder

K, KL, L

K, L, KL

KL, K, L

CL, L, K

L, K, KL

L, KL, K

1+1=2;

1+1=2

1+2=3

1+4=5

2+4=6;

2+8=10

2+2=4

2+8=10

2+2=4

2+4=6

3+12=15

3+6=9

3+12=15

3+3=6

3+6=9

3+3=6

You see that the remainder of the nuts is different in all cases, therefore, knowing the remainder, it is easy to establish what is the distribution of things between the participants. The magician again - for the third time - leaves the room and looks there in his notebook with the last tablet (there is no need to memorize it). On the plate, he determines who has which thing. For example, if there are 5 nuts left on the plate, then this means a case (KL, L, K), that is: Vladimir has the key, Alexander has an eraser, Svyatoslav has a pencil.

4th magician (I team)

Focus "Favorite number".

Anyone 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 is a work written only with his favorite number. The second option is also possible: multiply the number 12345679 by your favorite digit 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 planned number without asking anything."

The magician offers students the following actions:

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

Fan Contest - “Happy Score”. A representative is invited from each team. There are two tables on the blackboard, on which numbers from 1 to 25 are marked in random order. At the signal from the leader, students must find all the numbers on the table in order, whoever does it faster won.

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. He invites someone, giving 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 between 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 he got.

Trick "Guessing the day, month and year of birth"

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

Trick "Guess the planned 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, and inform the magician of the result. From this number he subtracts 250 and the number of hundreds will be the number of the planned day. Clue to the trick: let's say Thursday is conceived, that is, day 4. Let's do the following: ((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 number of units to the number of tens - the number of years will be obtained.

INTRODUCTION

Like many other subjects at the intersection of two disciplines, mathematical magic tricks do not receive much attention from either mathematicians or magicians. The former tend to view them as empty fun, while the latter neglect them as too boring. Mathematical magic tricks, frankly, do not belong to the category of magic tricks that can keep an audience of non-mathematically sophisticated audiences enchanted; such tricks are usually time-consuming and not very effective; on the other hand, there is hardly a person who is going to draw deep mathematical truths from their contemplation.

And yet, mathematical tricks, like chess, have their own special charm. Chess combines the grace of mathematical construction with the pleasure that the game can bring. In mathematical tricks, the elegance of mathematical constructions is combined with amusement. It is not surprising, therefore, that they bring the greatest pleasure to the one who is familiar with both of these areas at the same time.

Purpose of work: research of mathematical tricks.

Tasks:

1. Study the literature on this issue and Internet resources.

2. Select and summarize the most interesting, fascinating mathematical tricks.

3. Conduct selected math tricks in the classroom.

4. Find out the secret of mathematical tricks.

Object of study:mathematical tricks based on the properties of numbers, actions, mathematical laws, equations.

Research methods

Study, analysis, practical application of the knowledge gained.

Relevance of the topic:is this: mathematical tricks are rarely considered and applied in teaching mathematics.

Hypothesis: It can be assumed that if you draw the attention of students to mathematical tricks, then it will be possible to interest them in studying the subject of mathematics, to promote the development of oral numeracy skills to demonstrate mathematical tricks.

Chapter 1. Theoretical part.

1.1. Illusionists and magicians of the world.

The history of the hocus-pocus appearance.

The art of illusion has its roots in antiquity, when the methods and techniques of manipulating people's minds began to be used not only to control them (as did shamans, priests), but also for entertainment (representations of fakirs). In the Middle Ages, more professional artists appeared: puppeteers, magicians using various mechanisms, as well as card players and cheats.

In the XV century. the girl was executed for witchcraft. It was in Germany. Her only fault was that she performed a trick with a handkerchief: tore it apart, and then put them together, turning them into a whole handkerchief. Tricks passed down from generation to generation for several hundred years served not only for entertainment, but also made the poor rich, the rich poor, and also brought joy to one person and meant ruin for another.

Simultaneously with the development of focal creativity, there was an active development of deceptive tricks, which does not quite decorate the focal case. However, the true talent and skill of the "correct" magicians can nullify all the dishonest tricks. The first mentions of magicians have come down to us from the distant 17th century. The inhabitants of Germany and Holland were impressed by the "magician" Ohes Voches (the magician borrowed this name from the mysterious demon magician from Norse legends).

During his magical sessions, the magician used to say: “Hocus pocus tonus talonus, wade celeriter yubeo. The audience, on the other hand, made out only the mysterious "hocus pocus" from all this muttering. Therefore, the wizard received the nickname of the same name. These magic words seemed funny to other representatives of the profession, they picked them up, and soon all the illusionists and tricksters began to call their performances tricks.

At the end of the 18th - beginning of the 19th century. with the development of mechanical engineering, mechanical illusion toys-automatic machines appear. Three such mechanical dolls, which depicted human figures, were invented by the director of the Physics and Mathematics Office of the Vienna Imperial Palace, Friedrich von Klaus. His figures could write on paper.

The designer Jacques de Vaux-Canyon made the acting mechanical figures of a flutist and drummer in full human height and a duck that could quack, peck food and flap its wings. The Hungarian Wolfgang von Kempelen invented the "chess player" piece with whom one could play a game of chess. But in reality, only the hand of the doll was mechanical, moving the chess pieces on the board, while it was controlled by the chess player - the person sitting inside.

In the XVIII century. the performances of the magicians were improved by the Italian Giuseppe Pinetti. It was he who first began to show magic tricks not in market squares, but on a real theatrical stage. He made it art for a sophisticated audience, furnished the tricks with magnificent decorations, intricate plots. English newspapers of that time preserved notes about his performances in London in 1784. Pinetti amazed the audience with his abilities: he read texts with closed eyes, distinguished objects in closed boxes.

The magician even attracted the attention of the monarch of England, George III, who invited Pinetti to perform for members of the royal family at Windsor Castle. The magician did not lose face, he brought with him a huge number of assistants, exotic animals, complex mechanisms, large mirrors.

After such a performance, Pinetti went on an international tour of European countries, on his way were Portugal, France, Germany and even Russia. In St. Petersburg, he held several performances and was even invited to the palace of Emperor Paul I. When Pinetti was leaving Russia, Tsar Paul I asked him to surprise everyone with some kind of magic. At that time, it was possible to leave St. Petersburg through 15 outposts. Pinetti promised the king that he would pass through all 15 outposts at the same time, and he kept his word. The tsar received 15 reports from 15 outposts that Pinetti had set out through each outpost. In 1800, Giuseppe died at the age of 50.

Giuseppe loved his magic tricks, he lived an illusion and created it in his daily life. It was said that, walking down the street, a magician could buy a hot bun from a stall and in front of a crowd of onlookers, breaking it in half, pulled out a gold coin. In a second, this coin turned into a medallion with the magician's initials.

The famous magician Ben Ali often showed such a trick at the fair. He approached any merchant, bought pies from him, broke them in half in front of the assembled people, and a coin was found in each pie. The surprised merchant could not believe this miracle and began to "check" all his other pies, which, of course, had nothing. The audience laughed. When Ben Ali was brought food in a restaurant, he covered the entire table with a blanket, and when he took it off, instead of food, there was a shoe on the table. The boot was covered again and the food returned.

Two other famous Italians can be safely ranked among the famous illusionists of that time: Giacomo Casanova (1725-1798) and Count Alessandro Cagliostro (1743-1795). Numerous legends have been circulating about their magic tricks, it is difficult to distinguish what is true in them and what is the invention of an enthusiastic crowd.

At the end of the 18th - beginning of the 19th century. in Europe, the industrial revolution begins, steam engines, a steamer, spinning machines and many technical innovations appear. Tricks become more technical and complex, magicians become professionals - inventors of complex mechanical tricks.

The place of "wizards", "magicians" and "sorcerers" is taken by "doctors" and "professors", who give the tricks "scientific" and "seriousness". These are such "scientists-magicians" as Jean-Eugene-Robert Houdin, who is called "the father of the modern focus". Modern magicians still use the mechanisms of Jean-Eugene-Robert Houdin.

1.2. Mathematical tricks.

Numbers surround us everywhere: in stores, on the street, at work, at home. It is not surprising that in the entire history of mankind, many tricks were invented with them, which later began to turn into tricks. Tricks with numbers can be demonstrated anywhere, in front of any audience, no manual dexterity is needed, but only a good memory and knowledge of the system of actions is required.

1. Focus "Phenomenal memory".

2. Focus “Guess the planned number”.

3. Focus "Magic table".

Focus Key:

4. Focus “Guess the crossed out number”.

Why does this happen?

5. Focus “Who has which card?”.

An assistant is required to perform the focus.

Focus Key:

Let's consider the possible options. Cards can be positioned as follows: 3, 4, 5 4, 3, 5 5, 3, 4

3, 5, 4 4, 5, 3 5, 4, 3

Since the assistant sees which card each person took, he will help the “magician”. To do this, you need to memorize 6 signals. Let's number six cases:

First - 3, 4, 5

Second - 3, 5, 4

Third - 4, 3, 5

Fourth - 4, 5, 3

Fifth - 5, 3, 4

Sixth - 5, 4, 3

If the first case, then the assistant says: "Done!"

If case is the second - then: "So, done!"

If the third case - then: "Guess!"

If the fourth - then: "So, guess!"

If the fifth - then: "Guess!"

If the sixth - then: "So, guess!".

Thus, if the variant starts with the number 3, then “Done!”, If from the number 4, then “Guess!”, If from the number 5, then “Guess!”, And the students take the cards one by one.

6. Focus "Who took what?"

Vladimir

Alexander

Svyatoslav

There can be no other cases. Now let's see what residuals correspond to each of these cases:

Vl Al Sv

Number of nuts taken

Total

Remainder

K, KL, L

K, L, KL

KL, K, L

CL, L, K

L, K, KL

L, KL, K

1+1=2;

1+1=2

1+2=3

1+4=5

2+4=6;

2+8=10

2+2=4

2+8=10

2+2=4

2+4=6

3+12=15

3+6=9

3+12=15

3+3=6

3+6=9

3+3=6

7. Focus "Favorite number".

8. Trick "Guess the number you have conceived without asking anything."

The magician offers students the following actions:

9. Focus “Number in an envelope”.

10. Focus "Guessing the day, month and year of birth."

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

11. Focus "Guess the planned day of the week."

12. Focus “Guess the age”.

13. Focus "By division remainders".

Ask the viewer to think of any number between 0 and 60. Ask them to divide that number by 3, then 4, and finally 5, and then name the remainders of the division in order. This is quite enough to guess the intended number.
The secret of focus: To guess the number, the first remainder must be multiplied by 40, the second by 45, and the third by 36. If you add up all the pieces and divide the sum by 60, then the remainder will be the intended number.
For example: the conceived number 10. After dividing, you get the remainders 1, 2, 0. With them you perform the indicated actions: 1 × 40 = 40,

2 × 45 = 90, 0 × 36 = 0.40 + 90 + 0 = 130, 130: 60 = 2. Here, after dividing 130 by 60, the remainder is the intended number 10.

14. Focus "Who is older?"

Tell two viewers that you can, without knowing their age, determine how much older one is than the other. Ask the younger to subtract the number of his years from 99. And then have the older add the number of his years to this difference and announce the result.
To determine the difference in age, you need to subtract 100 from the resulting number and add one to the result.
For example, the youngest viewer is 9 years old and the older one is 14. Subtract 9 from 99 to get 90; 90 plus 14 equals 104. Subtract 100 from 104 and add one. We get 5 - this will be the age difference.

15. Focus "Six Suitable Numbers".
On six pieces of paper out of the way, write six different numbers. Tell the audience that no matter which number from 1 to 60 they name now, you will add it from the numbers written on the sheets.
Whatever number the audience calls after that, lay out these or those sheets, and their sum will correspond to the named number, although adding sixty whole numbers of six numbers seems to be an impossible task.
Secret of Focus: In fact, the task is quite doable. On six sheets of paper you wrote the numbers: 1, 32, 4, 8, 16, 2. Whatever number the audience calls from 1 to 60 now, it will be easy for you to lay out the required number. Called, for example, 51. Lay out sheets 32, 16, 1, 2, you get 51. Or, for example, they will call 27: 1 + 8 + 16 + 2 = 27, etc.

16. Focus "Transferring cards".

Write on 16 identical cards the numbers from 1 to 16. Invite one of the viewers to guess any of the written numbers. Collect the cards in a pile, numbers down, and then, opening the cards one by one, fold them, numbers up, alternately in two piles. Ask the viewer who is thinking of the number what stack it is in.
Then put the pile, in which there is no intended number, on the pile indicated by the viewer, and, turning the resulting pile of 16 cards with the numbers down, put the cards again into two piles, as indicated above. This procedure with the expansion of cards should be done a total of four times. After the fourth answer, you can easily find a card with a conceived number.
Secret of Focus: The Designed Number card will be the bottom of the last 8 cards listed. This is easy to understand if you imagine where the card with the intended number will fall every time the cards are laid out.
After the cards have been placed on two piles for the first time, then folded back into one pile, as indicated in the focus condition, the card with the intended number is among the bottom eight cards. The eight cards are divided equally between the two piles the next time they are unfolded.
This means that after the cards are collected in one pile for the second time, the card with the intended number will be among the four lower cards. The third time it will be among the two bottom cards, and, finally, after the fourth unfolding of the cards, the hidden card will be the bottom one in one of the piles.

17. Focus "Exact date".

Ask someone to think about an important date in their life, be it a birthday, a public holiday, or even a completely fictional day. Let's take March 25 as an example.
Without looking at the date, ask him to do the following operations on the calculator:
month number (January - 1st, December - 12th) = 3;
multiply by 5 = 15;
add 6 = 21;
multiply by 4 = 84;
add 9 = 93;
multiply by 5 = 465;
add day number = 490;
add 700 = 1190.
Ask what the calculator shows, then quickly subtract 865. The resulting number is the exact date: the last two digits are the day of the month, and the first day (or dates) is the number of the month. In this case, 1190 - 865 = 325, that is, March (3rd month), the 25th.

18. Focus "All roads lead to zero."

The viewer guesses a two-digit number, performs certain actions and, as a result, he gets zero.
Focus secret:
The viewer guesses any two-digit number. For example, 45. Then he has to swap the numbers, it turns out 54. The result is written 4 times in a row. 54545454. The viewer removes the 1st and last digits of this number 454545. The resulting number is multiplied by 3. In this case, the answer is 1363635. The resulting number is divided by 7 (we get 194805). We divide this number by 9 (it turns out 21645). Divide the number by 13 (it turns out 1665). Divide the resulting number by the originally conceived (45) answer 37. Please note that 37 is always obtained for any originally conceived numbers. So, to get it, it remains to read out any options 37.
This trick may surprise even strong mathematicians.

2. Conclusion.

Mathematical tricks are varied. In many mathematical tricks, numbers are veiled by objects related to numbers. They develop skills in rapid oral counting, computational skills. viewers can guess both small and large numbers. Mathematical tricks with numbers are based on the ability to handle numbers and the laws of exact science, while such tricks in no way detract from its importance.

Tricks with the use of mathematics can not only entertain a person who is experienced in the exact sciences, but also attract attention and develop interest in the "queen of sciences" among those who are just getting to know her.

With our research work, we tried to prove to our viewers that mathematics is a very interesting and informative subject, and not dry and boring as it might seem at first glance.

Having worked with theoretical material and applied it in practice, we made the following conclusions:

1. Learning to unravel the secrets of mathematical tricks is quite simple, the main thing is to grasp the essence of the ongoing mathematical transformations, and you can easily surprise others.

2. In order to effectively speak in front of the audience, you need to train attention, memory, as well as the ability to quickly and correctly count in the mind.

By studying tricks, you can learn to think rationally and look at the root. Arrange small performances at home, at school and with friends, and your life will become more interesting and brighter! A five-minute intellectual exercise in a lesson in the form of a math trick can make math a favorite subject!

3. List of used literature.

A.A. Akopyan A large book of tricks and tricks from the repertoire of Harutyun and Hmayak Akopyanov. –M.: Eksmo, 2008. -400s.
Vadimov A.A. The art of focus, M., 1959.
Gardner M. Mathematical miracles and secrets: mathematical tricks and puzzles / per. from English V.S.Berman. - M .: Nauka, 1978.-128p.
Colan A. Focuses. Become a real wizard! / Translated from English. M. Polyakova. - M.: Egmont Russia Ltd., - 2007.-64p.
The best magic tricks and experiments. –M .:
Nagibin F.F., Kanin E.S. Math Box: A Student Manual. - M .: Education, 1984.160s.
Ozhegov S.I. Dictionary of the Russian language. - M.: Russian language, 1983 .-- 816s.
Samoylenko I. Amazing tricks and tricks. Secrets of craftsmanship. Tricks and tricks for beginners. Handbook of the wizard. - Rostov on Don: Vladis: M.: RIPOL classic, 2008. -416p.
Peter Eldin. Children's encyclopedia. Magic tricks. M.: Astrel, 2001 .-- 64p.
Chkanikov I. Games and entertainment. - M .: State. publishing house of children's literature, -1957. -512s.

Mathematical tricks (1-3)

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

The main topic of mathematical tricks is guessing the conceived numbers or the results of actions on them. The whole “secret” of these tricks is that the “guesser” knows and knows how to use the special properties of numbers, but the “inventor” does not know these properties).

Mathematical tricks are interesting in that each trick has its own mathematical interest and consists in "exposing" its theoretical foundations, which in most cases are quite simple, but sometimes they are cleverly disguised.

You can check the feasibility of each trick using any example, but to substantiate most arithmetic tricks, it is most convenient to resort to algebra. At first, you can omit the "proofs" of tricks and limit yourself only to assimilating their content in order to show your friends. But proofs will not complicate 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 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 conceived number. Tell me the result. I will guess the planned number.

Guessing method.
Add 2 to the result, and divide the sum by 3. The quotient is the planned number.
Example.
Conceived 18; 18 - 1 = 17; 17x2 = 34; 34 + 18 = 52. Guessing: 52 + 2 = 54; 54: 3 = 18.
Proof. The intended number will be denoted 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 in the series "mathematical tricks".
Invite your friend to think of a number. Then make him several times in succession to multiply and divide the number he conceived by various, arbitrarily assigned numbers. Let him not tell you the result of the actions.

After several multiplications and divisions, stop and ask the person who is thinking of the number to divide the result he received by the number that he intended, then add the number that was planned to the last quotient and tell you the result. From this result, you immediately guess the number conceived by your friend.

The secret is very simple. The guessing person himself also needs to conceive an arbitrary number (for example, 1) and perform all the multiplications and divisions assigned to him on it, up to division by the originally conceived number. Then, in the quotient, he will get the same number as the other who conceived, even if the originally conceived numbers were different for them. After that, the guesser must subtract his result from the result reported to him. The difference will be the required number.

Example. The number 7 is conceived. 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. It turns out 70, and after dividing by the conceived number and adding the conceived number -17.

At the same time, you "mentally" conceived the number 1. Multiply by 12, it turns out 12. Divide by 2, it turns out 6. Multiply by 5, it turns out 30. Divide by 3, it turns out 10. Subtracting 10 from 17, you get the required number 7.

Remark 1. To enhance the effect, you can provide an opportunity for the person who has conceived a number to assign the numbers by which he would like to multiply and divide the resulting results, if only he would tell you these numbers every time.

Remark 2. It is not necessary to alternate multiplication and division. You can first assign several multiplications, and then several divisions, or vice versa.

Prove this arithmetic trick, that is, show "in letters" that the trick works for any conceived number.

Focus 3.

Let's continue the free trick training and show an interesting mathematical trick with numbers.
To teach this trick, let us accept or agree to call the most part of an odd number that part of it that is 1 more than the other. So, for the number 13, the greater part is 7, for the number 21, the greater part is 11.

Think of a number. Add half of it to it, or if it's odd, then most of it. Add half of it to this amount, 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 received answer to the question, the conceived number is:

Quadruple 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. Performing the required actions, we have:

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

Guessing: 3 4 + 3 = 15. Conceived 15.

Prove this mathematical trick too. When considering the proof, I advise you to take into account that any integer (which means, to the conceived) can be represented in the form of one of the following forms:

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

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

Continuation Free training in magic tricks:

Number in an 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 for which you want to make love. The last two are your age.

Guess the crossed out number

You have 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 is subtracted from the larger number. The resulting difference is multiplied by any number. In the resulting work, one non-zero digit is randomly crossed out. Then the participant must tell you in no particular order all the uncrossed numbers. You guess the crossed out.

The secret of focus ... If the numbers are rearranged and the smaller is subtracted from the larger, then the resulting difference is divided by 9. It is clear that the product must also be divisible by 9. The sum of the numbers of this product must also be divisible by 9. When you are told the numbers, you add them mentally. After you have been given all the numbers, you must figure out which figure to add to your total so that the resulting number is divisible by 9. In the course of action, you can always add the numbers of the received subtotal to make the calculation easier. For example, if you have a total of 25 and must 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 demonstrator stands with his back to the audience, and one of them selects any month on the monthly report card and marks on it a square containing 9 numbers. Now it is enough for the viewer to name the smallest of them, so that the showing immediately, after a quick calculation, will announce the sum of these nine numbers.

Explanation. The indicator 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 calculate it silently:
1. Your birthday (to yourself) multiplied by two.
2. Add 5 to the result.
3. The result is multiplied by 50.
4. Add the number of the month in which you were born.

Ask the person for a number. Then just subtract 250 from the result, and you're done. It will turn out to be 4 or 3 digits. The first 2 (maybe one digit) are the day, and the last two are the month .

Sly leaf

You choose 5 participants from the audience and give them identical sheets of paper. Let the first of them write on a piece of paper any two-digit number and show this number to the second. The second participant must add the same number to this number on the right and left 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 sees by 7, writes down 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 viewer divides the number by 37, writes the result on a piece of paper, adds it and gives it to you. You take the same piece of paper, without looking at the resulting pieces of paper, write the original number, fold your piece of paper, go to the first viewer and show his piece of paper to the rest of the audience. Then take out your piece of paper, unfold it and, having named the number to the audience, show it.

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

Number in an envelope

Then let him 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 between 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 he got.

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

Focus 1: "Familiar Numbers"

Write down the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 on a piece of paper in sequence. Ask a student to put in their mind any three numbers that follow one after the other. And the result is to name it. For example, he will choose 5, 6 and 7. In this case, the amount will be 18. After that, the teacher immediately calls the numbers conceived.

Focus secret:

Introduction

Learning tricks, a person develops artistry, creativity. Math tricks focus children's attention on the math lesson, thanks to the entertaining essence of the trick combined with the mathematical nature of the secret (once the trick is shown, the child can be stimulated to take action in the lesson under the pretext of revealing the secret). The whole point when looking at the focus is to find a clue and enjoy the "magical actions".

Objectives of the event

Arouse students' interest in mathematics, instill a love for it. To cheer up students. Explain what mathematical tricks are, why they are needed, teach children a few of them.

Event progress

To begin with, the teacher says a few words about mathematical tricks, asks the children a few questions: "Do you like magic tricks? .. And what tricks do you know, can you show? .. Do you want to learn new tricks?" - etc. After a little discussion, it's worth showing a math presentation on the topic of math tricks.

After being shown , you should proceed to the demonstration of tricks. There are many mathematical tricks of different kinds, we will give just a few examples.

Magic tricks:

Day of the week in the palm of your hand
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 hidden number by 2, then add 5, multiply the sum by 5, and add zero at the end. The class is told the result, from which 250 is subtracted. As a result, the number of hundreds will correspond to the day

Focus secret: Let's substitute "x" instead of 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 number of the day.

Note: Tricks of this kind are the most common of all mathematical tricks, so you should not fill the event with them alone.

Phenomenal memory

The teacher writes on a piece of paper a very long number of numbers (22-26 numbers) and declares that he will be able to list all the numbers in the series from memory in the same order. After completing, you can repeat the trick to prove that the number series is absolutely arbitrary (there really should not be any pattern in it).

Focus secret: All numbers in a row are just well-known phone numbers (you can take the last 4-7 numbers from each number).

Note: As you can see from the example, some mathematical tricks use a common trick.

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 there is nine in the middle of the answer received (if the answer is a two-digit number, then write it down as 0 ...). Indeed, the nine stands where it was predicted by the teacher.

Focus secret: Since only 1 and 3 digits are swapped, then for a larger number, the digit in the ones category will always be less, which means that you will need to take 1 from the tens category, and when you need to subtract tens - from the hundreds category (to understand, try to solve with 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

Math tricks are a great way to make children love the subject under study, to understand all the magnificence of its properties and rules.

Mathematical tricks 4-7
Guessing the intended number

Focus 4.

Fourth trick of the seriesMathematical trickssection Let's start, as in the previous trick, that is, offer to think of a number and add half or most of it to it, then again add half of the resulting amount or most of it.

But now, instead of the requirement to divide the result by 9, propose to name all the digits of the resulting result, except for one, by category, so long as this unknown figure is not zero.

It is also necessary that the person who conceived the number said the rank of the figure that is hidden from him, and in what cases (in the first, in the second, or in the first and second, or never) he had to add most of the number.

After that, in order to find out the conceived 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 most of the number had to be added;
- 4, if only in the second case most of the number had to be added;
- 1 if in both cases most of the number had to be added.

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

Example 1. The number 28 is conceived. After the required actions have been completed, it turned out 63. We hid the number 3. Then the guesser adds the number of tens 6 to 9 given to him and gets the number of ones 3. The result 63 is found. The required number (63: 9) x4 = 28.

Example 2. The number 125 was conceived. After completing all the required actions, it turned out 282. Hidden, let’s say, the number of hundreds of 2. Reported: the numbers of tens and units, respectively, 8 and 2, and most of the number was added only in the first case.

Guessing: 8 + 2 + 6 = 16. The closest multiple of nine is 18. This means that the hidden number of hundreds is 18-16 = 2.

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

Example 3. Let the one who thinks about the number say that the last result he obtained consists of three digits, with the first digit 1, and the last 7 and most of the number had to be added in two cases.

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

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

Focus 5.

We continuemathematical tricksguessing the planned number. Fifth mathematical trick. Think of a number (less than a hundred, so as not to complicate the calculations) and square it. Add any number to the intended number (just tell me which one) and square the resulting sum too. 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. Added 6 to the intended number:

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

This result has been reported.
We 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 and 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 tell the remainders of the divisions. From these residuals, using the key formula, you will find the conceived number.

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

S = 40R1 + 45R2 +36 R3 .

If you get S = 0, then the number 60 is conceived; 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 is thinking of a number to come up with the secret of guessing that you own.

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

We guess:

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

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

Do not blindly believe a formula offered without a conclusion. Make sure first that it works flawlessly in all cases allowed by the focus condition, and then demonstrate focus.

Focus 7.

Seventh Mathematical Trick of the Seriesmathematical tricks for guessing the intended number. Having understood the mathematical basis of the tricks outlined here, you can modify them in every possible way, come up with other rules for guessing numbers, and diversify the proposed questions.

For example, such a topic. In the previous trick of guessing the conceived number by its modulo modifiers, 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 expand the limits for the conceived numbers from 7 to 100. Multipliers in the key formula, of course, will also change. Match them for a new key formula that is appropriate for the case.

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

Rhino Trick

(cool trick ... to show tricks to non-believers, but ALL knowledgeable :)))

Guess a number from 1 to 10. Guess it?

You have 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 guess a letter for this number alphabetically. That is, if you get 1, then this is the letter A; 2-letter B; 3-B; 4-D, etc.

Now you have thought and are holding a letter in your head, remember and guess a European country with this letter.

See below for the answer ...

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

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

The rest must be brought up and
play! As if I can read minds, etc.

In order to surprise your friends and family with 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 figure), you need to lay out 12-20 coins. Twelve is the minimum. From those present, a person is selected who will make a guess. In order to avoid mistakes in calculations, you can organize a collegiate guessing from several, or even all of those present. You become your back to the audience.

Rice. 3 Nine

The guessing person 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 you should still proceed from common sense. In order to avoid possible jokes, its value can be limited in advance. After that, the supplicant counts as many coins as he intended as follows: starting from the “leg” from the bottom up, and then further, counterclockwise along the ring. After he has counted the intended number of coins, the count is repeated. You should start with exactly the coin on which the previous account stopped. But now the guessing one counts the coins from one to the intended number along the ring clockwise. Under the coin, on which the account has ended, the guessing person hides, for example, a small inconspicuous piece of paper.

You turn to the audience, make "magic passes" over the table while looking at the audience, and raise the hidden coin.

FOCUS SECRET. Everything is very simple. The fact is that regardless of which number is conceived, the account ends in any case in the same place. To begin with, do this trick in your mind with any number, and you will know which coin it will be. If you are asked to repeat the trick, the nine should be modified by removing or adding a few coins to the stem. 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 little things are laid out on the table. You ask a spectator to turn over coins at random one at a time. Each overturning should be accompanied by the word "is". These actions should be done behind your back. The same coin can be flipped several times. At the end, the supplicant covers one of the coins with his hand. You turn and say exactly how the coin is lying - "heads" or "tails" up.

FOCUS SECRET. All the salt of the trick is in your preparation. After the coins are scattered, it is necessary to count the number of "heads". For each "there is" one must be added to this number. It all depends on the final number. If it turns out to be even, then the number of "heads" in the final combination is even; if the sum is odd, then the number of "heads" is also odd. The position of the hidden coin will be "talked about" by the open ones.

This trick can be done with any of the same objects, which can be placed in one of two possible ways.

As you already understood, the above tricks, like all mathematical tricks, are based on the properties of figures and numbers, and their secrets are 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 mind, making accurate predictions, demonstrating your amazing memory. This book will allow you to acquire "sleight of hand", teach all of the above, and even more. In it you will find tips on how to prepare the audience for a particular focus. And best of all, you will learn the secrets of these amazing magic tricks. Go for it!

Focus with marked dates

The trick starts like this. The viewer is invited 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 arranged in six columns, which is very rare, the sixth column is not taken into account.) In this case, the proponent stands with his back to those present.

Still not turning around, he asks, "How many Mondays have you circled?", Then: "How many Tuesdays?" and so on, going through all the days of the week. After the seventh and last question, the proctor announces the sum of the circled figures.

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

75 + 3 * 2 - 1 * 3 = 78

and declares the received result.

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

1. By the principle of mathematical focus.

(Einstein as a magician mathematician).

Tricks are based on deceiving people in the expectation that this deception will not be immediately noticed. They are harmless in that the magician does not even assume that he will be unconditionally believed. The only calculation is that the essence of his trick will not be immediately revealed. A trick is a kind of entertainment, nothing more.

It is very difficult to know if Einstein considered himself a magician. It is possible that he believed in his genius and absolutely did not possess the gift of self-criticism. After all, even his best friend at that time, he tried himself, without the support of the Academies of Sciences, to put in a psychiatric hospital - for criticizing his article. This is instead of checking for the hundredth time to see if there is a mistake. 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 mistake yourself.

The drawback of Einstein's critics is that they usually refute the conclusions of the "theory of relativity", instead of looking for the error in the work itself, which is much easier. I have already done this work once, but this time I decided to approach Einstein's “work” from a different angle. In this case, you do not need to do mathematics at all. Einstein's errors are, of course, not mathematical, but logical.

What is "math trick"? I will give an example that is familiar to me from school, although the text that I cite may be somewhat different.

Guess the number

Ask someone to guess any number, then subtract 1 from it, multiply the result by 2, subtract the conceived number from the product and tell you the result. By adding the number 2 to it, you will guess your plan.

Guess the date of birth

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

Guess the result of actions on an unknown number

Someone thought of a number. You ask to multiply it by 2, then add 12 to the product, divide the sum in half and subtract the planned number from it. Whatever number is conceived, 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 have their birthday, you can guess their birthday using simple mathcounting. You can, of course, just ask any person when their birthday. But it's much more interesting to surprise a person, to entertain, to amuse or just to impress with the help of mathematics.

Surprise your friend by guessing his birthday without asking her!

What needs to be done?

So:

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

Now ask him to add five to the number that he did.

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

And finally, ask your friend to add the ordinal number of the month in which he was born to the last received result.

Everything!

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

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

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

Shine with this trick with your friends, acquaintances and relatives!

Wish you luck!

This math trick with phone numbera brunette showed me. Her reaction was quite emotional: "Exhausting the brain! 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. I will clarify right away that the focus is designed for a seven-digit city phone number.

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