Project work in mathematics "mathematical tricks". Mathematical tricks: trick to guess the intended number - nothing

INTRODUCTION

Like many other cross-discipline subjects, mathematical tricks receive little attention from either mathematicians or magicians. The former are inclined to regard them as empty fun, the latter neglect them as too boring. Mathematical tricks, let's face it, do not belong to the category of magic tricks that can keep an audience of spectators unsophisticated in mathematics spellbound; such tricks usually take a lot of time and are not very effective; on the other hand, there is hardly a person who intends to draw deep mathematical truths from their contemplation.

And yet, mathematical tricks, like chess, have their own special charm. Chess combines the elegance of mathematics with the pleasure that the game can bring. In mathematical tricks, the elegance of mathematical constructions is combined with entertainment. It is not surprising, therefore, that they bring the greatest pleasure to those who are simultaneously familiar with both of these areas.

Goal of the work: study 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. Perform selected math tricks in class.

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 acquired knowledge.

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

Hypothesis: It can be assumed that if you attract the attention of students to mathematical tricks, then it will be possible to interest them in studying the subject of mathematics and contribute to the development of mental calculation skills for demonstrating mathematical tricks.

Chapter 1. Theoretical part.

1.1. Illusionists and magicians of the world.

The history of Hocus Pocus.

The art of illusion has its roots in ancient times, when techniques and techniques for manipulating people’s consciousness began to be used not only to control them (as shamans and priests did), but also for entertainment (fakir performances). In the Middle Ages, more professional artists appeared: puppeteers, magicians using various mechanisms, as well as card players and sharpers.

In the 15th century the girl was executed for witchcraft. This was in Germany. Her only fault was that she performed a trick with a handkerchief: she tore it into pieces, 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 and meant ruin for another.

Simultaneously with the development of magic tricks, there was an active development of deceptive tricks, which does not entirely decorate the magic business. However, the true talent and skill of the “right” magicians can reduce all dishonest tricks to nothing. The first mentions of magicians came to us from the distant 17th century. The residents of Germany and Holland were indelibly impressed by the “magician” Ojes Vohes (the magician borrowed this name from the mysterious demon magician from Norwegian legends).

During his magical sessions, the wizard said: “Hocus pocus tonus talonus, vade celeriter jubeo. The spectators could only make out 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 illusionists and tricksters began to call their performances tricks.

At the end of the 18th - beginning of the 19th centuries. With the development of mechanical engineering, mechanical illusionary automatic toys 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 Claus. His figures could write on paper.

Designer Jacques de Vaux-Kanyun made working mechanical figures of a flutist and a drummer in full human height and a duck that could quack, peck food and flap its wings. Hungarian Wolfgang von Kempelen invented the figure of the “chess player”, with whom you could play a game of chess. But in fact, only the hand of the doll was mechanical, moving the chess pieces on the board, and it was controlled by the chess player - the person sitting inside.

In the 18th century The performances of magicians were improved by the Italian Giuseppe Pinetti. It was he who was the first to perform magic tricks not in market squares, but on a real theater stage. He made it an art for a sophisticated audience, furnishing the tricks with lush decorations and intricate plots. English newspapers of that time preserved notes about his performances in London in 1784. Pinetti surprised viewers with his capabilities: he read texts with his eyes closed, 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, and large mirrors.

After such a performance, Pinetti went on an international tour of European countries, including Portugal, France, Germany and even Russia. In St. Petersburg, he gave 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 was brought 15 reports from 15 outposts that Pinetti left through each outpost. In 1800, Giuseppe died at the age of 50.

Giuseppe loved his tricks, he lived the illusion and created it in his daily life. They said that while walking down the street, a magician could buy a hot bun from a tray and, in front of a crowd of onlookers, break it in half and pull out a gold coin. After 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, in front of the gathered people, broke them in half, 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, contained nothing. The audience laughed. When food was brought to Ben Ali 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 easily be considered among the famous illusionists of that time: Giacomo Casanova (1725-1798) and Count Alessandro Cagliostro (1743-1795). Numerous legends have circulated and continue to circulate about their magic tricks; it is difficult to distinguish what is true in them and what is the fabrication of an enthusiastic crowd.

At the end of the 18th - beginning of the 19th centuries. The industrial revolution begins in Europe, steam engines, steamships, spinning machines and many technical innovations appear. Tricks are becoming more technical and complex, magicians are becoming professionals - inventors of complex mechanical tricks.

The place of “wizards”, “magicians” and “sorcerers” is taken by “doctors” and “professors”, giving the tricks “scientific” and “seriousness”. These are “scientific magicians” such as Jean-Eugene-Robert Houdin, who is called the “father of modern magic.” 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 throughout the history of mankind, many tricks have been invented with them, which later began to turn into tricks. Tricks with numbers can be demonstrated anywhere, in front of any audience; there is no need for sleight of hand, but only a good memory and knowledge of the system of actions.

1. 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.

2. 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.

3. Focus “Magic table”.

There is a table on the board or screen in which numbers from 1 to 31 are written in a well-known manner 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 in mind.

The solution to the trick:

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 last row of the table in the corresponding columns, and we will get the intended number. (1+2+8+16=27).

4. 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, 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, s – 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+9c=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.

5. Focus “Who has what card?”

An assistant is needed to perform the trick.

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

The solution to the trick:

Let's consider the possible options. Cards can be arranged 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 remember 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 the case is the second, then: “Okay, done!”

If it’s the third case, then: “Guess!”

If it’s the fourth, then: “So, guess!”

If it’s the fifth, then: “Guess!”

If it’s the sixth, then: “So, guess!”

Thus, if the option starts with the number 3, then “Ready!”, if with the number 4, then “Guess!”, if with the number 5, then “Guess!”, and students take the cards in turn.

6. Focus “Who took what?”

To perform this ingenious trick, you need to prepare three small things that fit in your pocket, for example, a pencil, a key and an eraser, and a plate with 24 nuts. The magician invites three students to hide a pencil, key or eraser in their pocket during his absence, and he will guess who took what. The guessing procedure is carried out as follows. Returning to the room after the things have been hidden in their pockets, the magician hands them nuts from a plate to keep. The first one is given one nut, the second one two, the third three. Then he leaves the room again, leaving the following instructions: everyone must take more nuts from the plate, namely: the owner of the pencil takes as many nuts as were handed to him; the owner of the key takes twice the number of nuts that were given to him; the owner of the eraser takes four times the number of nuts that were given to him. The remaining 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 their pocket. The solution to the trick is as follows: each way of distributing things in the pockets corresponds to a certain number of remaining nuts. Let's designate the names of the participants in the focus - Vladimir, Alexander and Svyatoslav. Let's also denote things by letters: pencil - K, key - KL, eraser - L. How can three things be located between three participants? Six ways:

Vladimir

Alexander

Svyatoslav

There can be no other cases. Let's now see which remainders correspond to each of these cases:

Vl Al St

Number of nuts taken

Total

Remainder

K, KL, L

K, L, KL

KL, K, L

KL, L, K

L, K, KL

L, CL, 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 determine what the distribution of things is between the participants. The magician again - for the third time - leaves the room and looks into his notebook with the last sign (there is no need to remember it). Using the sign, he determines who has what item. For example, if there are 5 nuts left on the plate, then this means the case (KL, L, K), that is: Vladimir has the key, Alexander has the eraser, Svyatoslav has the pencil.

7. 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.

8. Focus “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 adds 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.

9. 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.

10. 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 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 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.

12. “Guess the age” trick.

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.

13. Focus “By division remainders.”

Invite the viewer to think of any number from 0 to 60. Ask them to divide this number by 3, then by 4 and finally by 5, and then name the remainders of the division in order. This is quite enough to guess the intended number.
The secret of the trick: To guess the number, you need to multiply the first remainder by 40, the second by 45 and the third by 36. If you add up all the products and divide the sum by 60, the remainder will be the intended number.
For example: the intended number is 10. After division, the remainders are 1, 2, 0. With them you perform the following 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 spectators that you can tell how much older one is than the other without knowing their ages. Invite the younger one to subtract the number of his years from 99. And then let the older one add the number of his years to this difference and announce the result.
To determine the age difference, you need to subtract 100 from the resulting number and add one to the result.
For example, the age of the youngest viewer is 9 years old, and the older one is 14. Subtract 9 from 99 and get 90; 90 plus 14 equals 104. Subtract 100 from 104 and add one. We get 5 - this will be the age difference.

15. “Six suitable numbers” trick.
On six pieces of paper, out of sight of the audience, write six different numbers. Tell the audience that whatever number from 1 to 60 they name now, you will add it up from the numbers written on the pieces of paper.
Whatever number the audience names after this, lay out certain sheets of paper, and their sum will correspond to the named number, although adding as many as sixty from six numbers seems an impossible task.
The secret of the trick: In fact, the task is quite doable. On six pieces of paper you wrote the numbers: 1, 32, 4, 8, 16, 2. Whatever number from 1 to 60 the audience names now, it will be easy for you to lay out the required number. They named, for example, 51. Lay out sheets of paper 32, 16, 1, 2, you get 51. Or, for example, they call 27: 1 + 8 + 16 + 2 = 27, etc.

16. Focus “Shifting cards.”

Write numbers from 1 to 16 on 16 identical cards. Invite one of the spectators to wish for one of the written numbers. Collect the cards in a pile with the numbers down, and then, revealing the cards one at a time, stack them with the numbers up alternately in two piles. Ask the spectator who thought of the number which pile it is in.
Then place the pile that does not contain the intended number on the pile indicated by the spectator, and, turning the resulting pile of 16 cards over with the numbers facing down, again arrange the cards into two piles, as indicated above. This procedure for arranging the cards should be done only four times. After the fourth answer, you will easily find a card with the intended number.
The secret of the trick: The card with the intended number will be the bottom in the stack of 8 cards indicated last time. This is easy to understand if you imagine where the card with the intended number will fall each time the cards are laid out.
After the cards have been arranged into two piles the first time, then again placed into one pile as specified in the trick condition, the card with the intended number is among the bottom eight cards. These eight cards will be distributed equally between the two piles the next time they are dealt.
This means that after the cards are collected into one pile a second time, the card with the intended number will be among the four lower cards. The third time it will be among the bottom two cards, and finally, after the fourth laying out 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 fictitious day. Let's take March 25th as an example.
Without looking at the date, ask him to do the following 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 number (or numbers) is the number of the month. In this case, 1190 – 865 = 325, that is, March (3rd month), 25th.

18. Focus “All roads lead to zero.”

The viewer guesses a two-digit number, performs certain actions and ends up with a zero.
The secret of the trick:
The viewer guesses any two-digit number. For example, 45. Then he must swap the numbers, it will be 54. The resulting result is written down 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. Divide the resulting number by 7 (it turns out 194805). We divide this number by 9 (it turns out 21645). Divide the number by 13 (it turns out 1665). We divide the resulting number by the originally thought (45) answer 37. Please note that 37 is always obtained for any originally thought numbers. So, to get it, all that remains is to subtract 37 in any way.
This trick can 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 quick mental calculation, calculation skills because... spectators 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 do not in any way detract from its importance.

Tricks using 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 educational subject, and not dry and boring as it might seem at first glance.

After working with theoretical material and applying 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 understand the essence of the mathematical transformations taking place, and you can easily surprise others.

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

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

3. List of used literature.

Akopyan A.A. A large book of tricks and tricks from the repertoire of Harutyun and Hmayak Akopyan. – M.: Eksmo, 2008. -400s.
Vadimov A.A. The Art of Focus, M., 1959.
Gardner M. Mathematical miracles and secrets: mathematical tricks and puzzles / trans. from English V.S. Berman. – M.: Nauka, 1978. -128 p.
Koulan A. Focuses. Become a real wizard!/Translated from English. M.Polyakova. – M.: Egmont Russia Ltd., - 2007. -64 p.
The best tricks and experiments. –M.:
Nagibin F.F., Kanin E.S. Math box: A manual for students. – M.: Education, 1984. -160 p.
Ozhegov S.I. Dictionary of the Russian language. – M.: Russian language, 1983. – 816 p.
Samoilenko I. Amazing tricks and tricks. Secrets of mastery. Tricks and tricks for beginners. Wizard's handbook. – Rostov on Don: Vladis: M.: RIPOL classic, 2008. -416 p.
Peter Eldin. Children's encyclopedia. Tricks. M.: Astrel, 2001. - 64 p.
Chkanikov I. Games and entertainment. – M.: State. publishing house for children's literature, -1957. -512s.

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

There are some pretty interesting options. Enjoy! :)

Focus “Phenomenal memory”.

Focus “Guess the intended number.”

Focus “Magic table”.

The solution to the trick:

Trick “Guess the crossed out number”

Why does this happen?

Focus “Who has what card?”

An assistant is needed to perform the trick.

The solution to the trick:

Let's consider the possible options. Cards can be arranged 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 remember 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 the case is the second, then: “Okay, done!”

If it’s the third case, then: “Guess!”

If it’s the fourth, then: “So, guess!”

If it’s the fifth, then: “Guess!”

If it’s the sixth, then: “So, guess!”

Thus, if the option starts with the number 3, then “Ready!”, if with the number 4, then “Guess!”, if with the number 5, then “Guess!”, and students take the cards in turn.

Focus “Who took what?”

There can be no other cases. Let's now see which remainders correspond to each of these cases:

Vl Al St

Number of nuts taken

Total

Remainder

K, KL, L

K, L, KL

KL, K, L

KL, L, K

L, K, KL

L, CL, 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

4th magician (I team)

Focus “Favorite number”.

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

The magician offers students the following actions:

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”

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 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.

Focus “Guess the intended day of the week.”

Focus “Guess the age”.

Focus “Phenomenal Memory”

Focus “Guess the intended number.”

Focus “Guess the crossed out number.”

Focus “Who has what card?”

An assistant is needed to perform the trick. There are three cards with ratings on the table: “3”, “4”, “5”. Three people approach the table and each takes one of the cards and shows it to the “magician’s” assistant. The “magician” must guess who took what without looking. The assistant tells him: “Guess,” and the “magician” names who has which card.

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 it to
he has the same number on his 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 passes on his answer to the person who is thinking, who sees that his number has returned to him.

MAGICAL MATRIX.

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

Circle any number you wish. Cross out all the numbers that are in the same column and on the same row as the circled number. Circle any of the uncrossed numbers and cross out the numbers that are on the same row and in the same column. Circle any of the remaining numbers and cross out those numbers that are on the same row and in the same column. Finally, circle the only remaining number. Add up the numbers circled. Nowyou can call them amount. You got 34.

Secret focus.

Why does the drawn matrix “force” you to 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 line - the numbers 0, 4, 8, 12:

1 2 3 4

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

Focus “Phenomenal memory”.

Focus “Guess the intended 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.

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”.

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”

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.”

Focus “Guess the age”.