This mystery quickly spread all over the Internet. Thousands of people began to wonder how the magic square works. Today you finally find the answer!

The Secret of the Magic Square

In fact, this riddle is quite simple and made with the expectation of human inattention. Let's understand how the magic black square works with a real example:

1. Let's think of any number from 10 to 19. Now let's subtract its constituent digits from this number. For example, let's take 11. Let's subtract one unit from 11 and after - one more unit. It will come out 9. In fact, it does not matter which number from 10 to 19 you take. The result of the calculations will always be 9. The number 9 in the "Magic Square" corresponds to the first digit with pictures. If you look closely, you can see that the same figures are assigned to a very large number of numbers.
2. What happens if you take a number between 20 and 29? Maybe you already guessed it? Correctly! The result of calculations will always be 18. The number 18 corresponds to the second position on the diagonal with pictures.
3. If you take a number from 30 to 39, then, as you can already guess, the number 27 will come out. The number 27 also corresponds to the number on the diagonal of such an inexplicable “Magic Square”.
4. A similar algorithm remains true for any numbers from 40 to 49, from 50 to 59, and so on.

That is, it turns out that it doesn’t matter what number you guessed - the “Magic Square” will guess the result, because in cells numbered 9, 18, 27, 36, 45, 54, 63, 72 and 81, in fact, there is the same symbol .

In fact this riddle can be easily explained with a simple equation:

1. Imagine any two-digit number. Regardless of the number, it can be represented as x*10+y. Tens act as "x" and ones as "y".
2. Subtract from the hidden number the numbers that make it up. Add the equation: (x*10+y)-(x+y)=9*x.
3. The number that came out as a result of the calculations must point to a specific symbol in the table.

It doesn't matter which digit will be in the role of "x", one way or another you will get a character whose number will be a multiple of nine. In order to make sure that there is one character under different numbers, just look at the table and at the numbers 0,9,18,27,45,54,63,72,81 and the next.

In ancient times, great scientists considered numbers to be the basis of the essence of the world. The magic square, the secret of which is that the sum of the numbers in the resulting square in each horizontal, in each vertical, and in each diagonal is the same, carries this essence.

But complete description Magic squares do not exist to date.

The magic square of Pythagoras, "attracting" the energy of wealth, was compiled by the founder
The great scientist who founded the religious and philosophical doctrine and proclaimed quantitative relations the basis of things, believed that the date of birth of a person is his essence.

Knowing how the magic square works, one can not only find out the character traits of a person, his state of health, his intellectual and creative abilities, but also draw up a program for his improvement and development. The numbers, which are written in a square in a special way, attract not only wealth, but also the necessary energy flows for a person. For example, Paracelsus depicted his square as a talisman of health. The numbers form three rows, that is, there are nine numbers in a square. To determine your numerological code, you need to calculate these nine numbers.

How does the magic square work?

The first horizontal row of the square is formed by numbers: the day, month and year of a person's birth. For example, the date of birth of a person corresponds to 08/09/1971. Then the first number in the square will be 9, which is written in the first cell. The second number is the number of the month, i.e. 8.

At the same time, it is worth paying attention, if the month of a person’s birth corresponds to December, that is, the number 12, then it must therefore be converted by addition to a simple number 3. The third digit corresponds to the number of the year. To do this, it is necessary to decompose 1971 into composite numbers and calculate their total amount equal to 18 and further simplify 1 + 8 = 9. We fill in the upper horizontal field of the square with the resulting numbers: 9,8,9.

In the second row of the square, numbers are written corresponding to the name, patronymic and surname of a person according to numerology. Each letter has its own numerical value. Numbers can be obtained from the correspondence table of letters and numbers by numerology. Next, you need to sum the numbers of the first name, patronymic and last name and bring them to simple values.

The second row of the square is filled with the resulting numbers. The fourth number corresponds to the number of the name, the fifth - to the patronymic, and the sixth - to the surname. Now we have the second line of the energy square.

A further principle of how the magic square works is based on astrology.

The seventh digit corresponds to the number of the person's zodiac sign. Aries is the first sign under the number 1, and then in order to the sign of Pisces - 12. When filling out the third row of the square, two-digit numbers should not be reduced to primes, they all have their own meaning.

The eighth digit is the number of the sign according to That is, in our version, 1971 is the year of the Boar.

The ninth digit represents the numerological code of a person's desire. For example, a person strives to have excellent health, therefore, you need to find the numbers corresponding to the letters in this word. The result is 49, which is then simplified by addition to 4. Numbers from 10 to 12, as in the case of a person's zodiac sign, do not need to be reduced. Now, knowing how the magic square works, you can easily compose it and carry it with you like a talisman or decorate it like a picture and hang it at home.

Brings good luck to People whom He correctly guessed the Symbol, try it yourself!

Tell relatives, friends and acquaintances about the Magical Black Square so that happiness and good luck come to you and to Them! It works, the main thing is to believe in it!

1. Think of any two digit number
2. Subtract the constituent numbers from it (for example, from the number 54 you need to subtract 5 and 4, you get 45)
3. Find this number in the table and magic symbol to which it corresponds
4. Mentally imagine this symbol
5. Focus on this symbol for at least 3 seconds
6. Click on big black square ↓

How to use the Magical Black Square and its Luck for Yourself?

If the Magical Black Square correctly guessed your thoughts once, then He always maintains a mental connection with you and helps you in different situations Life and you will immediately feel it.

People who learn from you about the Magical Black Square will also share their Luck with you on a mental level and you will have more and more Luck.

How more people learn from you about the Magical Black Square and use it, the more Happiness and Good Luck will come to you!

To begin with, tell all relatives, friends, acquaintances and close people about the Magical Black Square and how He guessed your Symbol.

It is very important! The more such people there are, the more Happiness and Good Luck will come to you because of your mental connection with the Magical Black Square! Leave it to people everywhere, in all forums, in comments, on walls, on boards and in chats...

The best way to do this is by mail - send your story and the link to the Magic Black Square page to your friends!

The more - the better and more people! It's so simple! And you will immediately feel the result!

Opinions of scientists about the Magic Black Square.

By Gary Wambwell
Professor of the Department of Sensory Energy and Renewable Flows
Mossachusetts, West Virginia, USA

The phenomenon of the Magic Black Square effect is known modern science long ago. Although, unfortunately, it has not yet been fully studied. Our department and I personally have been studying the influence of the Magic Black Square on the energy aspect of the fate of an individual person in various socio-cultural situations since April 1998. At first, these were separate experiments with the participation of random volunteers, without the proper material and technical base. In the process of working on the phenomenon of the Magical Black Square, our group was able to identify amazing patterns in the change in the fate of our subjects after the Magical Black Square correctly guessed their thoughts. Well-being improved, illnesses receded and immunity was strengthened, significant changes for the better were observed in personal life, stable and favorable confident growth immediately set in business, leading to a progressive increase in the income of volunteers.

Naturally, having received such sensational results, we decided not to stop there and continued our research with the involvement of third-party investors. Our investor set us a difficult task: to reveal the so-called "limit of possibilities" of the Magical Black Square! That is, to document the onset of the moment when the amazing impact of the Magic Black Square on the fate of a person ends and what will happen to this person then. As a test subject, he offered himself, as he had already made sure of the positive impact of the Magic Black Square on his fate.

I have no right to disclose the names and some details of this experiment, this is the requirement of our investor. I can only say that the experiment is still going on and so far there are no objective prerequisites for its completion!

At the time of the beginning of our experiment with the Magical Black Square, the subject was an aspiring entrepreneur, had a small food manufacturing company software for computers. Within one year after the start active interaction with the Magic Black Square, his business increased seventeen times and continued to grow. We could not predict the possible consequences of such an unexpected success and came out with a collegial proposal to complete the experiment, but our investor and part-time test subject flatly refused at his own peril and risk.

Today, his fortune is measured in billions of dollars and he is in the top thirty the richest people planets. And all this, in his opinion, happened to him solely thanks to the Magic Black Square.

Therefore, in answer to your question, I can only say that if the Magic Black Square correctly guessed your symbol, then in order to achieve the maximum positive effect, you urgently need to tell as many people as possible about this and continue to do this by posting a link everywhere. Given the positive dynamics of our long-term successful experiment, I can unequivocally state that you will be able to feel the beneficial influence of the Magical Black Square on your Destiny in a few days after the first interaction with It.

I would also like to add that at the moment there are simply no analogues to the Magic Black Square in terms of its beneficial effect on the fate of a person. Thank you.

Real facts of different people about the Magical Black Square in their Life.

Alexandra M. (Nikopol)

The first time the Magical Black Square appeared in my life was two years ago. I then broke my leg and was in the hospital, waiting for a difficult, dangerous operation. My husband Arseniy brought a laptop to the ward and I accidentally landed on the page of this site. I guessed the number and did everything right. And the Magic Black Square guessed my thoughts correctly!!! My husband said it was good luck. And the next day the doctor told me that I did not need surgery and that my leg suddenly began to heal very quickly! I told my neighbors in the ward about this and they also read fortunes on the Magic Black Square and soon everyone was discharged.

Vladimir Vasilyevich (Stavropol Territory)

My business partner Alexey told me about the Magic Black Square. He had family problems. The magical Black Square correctly guessed his symbol and very soon his problems disappeared by themselves. In addition, he began to notice that he began to get a lot of luck in life. He suddenly received an unexpected inheritance from distant relative in Canada, and invested money profitably in business and earned even more. And all this thanks to the Magic Black Square! And I just had a nuisance in my life - my car was stolen. The police could not do anything and I was already thinking of selling something, because the car is very necessary for me at work, without it it’s like without hands. Alexey advised me to tell fortunes on the Magic Black Square and, lo and behold, He correctly guessed my symbol! You will not believe it, but after 2 (!) hours they called from the police and said that my car was found!!! Thanks to Magic Black Square for help and good luck!

Ostronosov M.Yu. (Customs Broker)

Last fall, my girlfriend left me for my former classmate Kirill. It was very painful and insulting to watch how my friend and my ex girlfriend walk together and kiss in front of everyone. I couldn't sleep or eat and didn't know what to do. My elder sister I received a letter in the mail from my good friend, in which there was a link to this page. She showed it to me and demanded that I think of a number. I did as she asked and Magic Black Square guessed my symbol correctly!!! I did not attach any importance to this, but the next week I met an amazing girl in the supermarket and she immediately liked me too! Now we meet and we have very serious plans for the future. Maybe even get married! This is how the Magical Black Square helped me in Hard time! I sent a link to the square to all my friends and acquaintances, and even Kirill too. May they all be happy!!! I do not mind )

Julia (Cambridge UK)

We lived in a small town in the north of the Arkhangelsk region in Russia. My father worked in a company selling refrigeration equipment, and my mother could not find a job and was engaged in housework. I went to school in eighth grade. One evening on a forum about flower breeding, I saw this link to a magic square and at first I did not believe that he could guess a person’s thoughts! I thought of a number and wrote down the symbol on a piece of paper so as not to forget. How surprised I was when the Magical Black Square correctly guessed my thoughts! I showed it to my dad and he said that he had never seen anything like this before and that it was probably some kind of trick. I already forgot about this adventure of mine, as one day at the end of the working week, dad came home from work and told my mom and me that his company was sending us to England for an internship for six months!!! For some reason, I immediately remembered the Magic Black Square and how He then guessed my thoughts. I told my dad about it and he told me that this is how it is! We moved to the UK with the whole family and now we live in the city of Cambridge and I study at a very good lyceum, I learned English without any problems and my dad was offered a permanent job here and English citizenship for our whole family!!! Dad is still thinking, but I'm sure that thanks to the Magic Black Square, everything will be fine with us! Now I leave a link in all forums and chats so that Luck does not leave our family!

Many at least half of their ears heard about the magic square (VK). However, not everyone knows what it is, how to solve it and how it works. Do you want answers to these questions? Read this article!

A magic square is a special square table in which an integer is entered in each cell. The sum of the numbers in such a table along any of the rows, columns and diagonals will be equal to a certain column. Let's say we have a square:

To verify its "magic" properties, you need to find the sums of 3 numbers vertically, horizontally and diagonally:

You can see that no matter how we add, the number “15” will still turn out. This means that this square is magical. Surely many of you have the thought in your head: “What is the secret? How does the magic square work? I will try to answer this question.

Many believe that the properties of VC are due to some kind of magic, miracles, mystical powers. But I have to immediately disappoint such people. There is no magic in this phenomenon. Everything is based on a special equation.

Magic constant

As a rule, before creating a VC, it is necessary to calculate the so-called "magic constant" (MC). The magic constant is the number that we will get when summing up the numbers of the square. You can calculate MC using a fairly simple equation:
MK \u003d (n * (n 2 + 1)): 2

In accordance with the conditions of the equation, n is a number indicating the number of rows or columns in a square table. For clarity, using this equation, we calculate the MC for a 3x3 square table (you could observe this square above).

• MK \u003d (3 * (3 2 + 1)): 2
• MK = (3*(9 + 1)): 2
• MK \u003d (3 * 10): 2
• MK = 30:2
• MK = 15

It is worth noting that there are incomplete magic squares (semi-magic squares). This is the name of VC, which have lost some of the "magic" properties. For example, if the sums of numbers along the diagonal are not equal to a constant, then such a square will be called semi-magic.

After calculating the constant using the equation, you can start building a square. To make a VC, you must be guided by a clear sequence of actions.

If a number has crawled out of the right side of the square table, write this number in the farthest cell of the corresponding row.

• Second exception

If a number is outside the top line of a square table, write that number in the lowest cell of the corresponding column.

• Third exception

If the number falls on a occupied cell, write it under the previous recorded number.

Looking at the figure, you can see that in the "one line up, one column to the right" principle, we should put the number "4" in the center of the top column. But we cannot do this, because the cell is already occupied by the number "1". Therefore, using the "third exception", we put "4" under the previous recorded number ("3").

Outcome.

We examined the basics and basics of creating a VC and analyzed the construction process using the simplest 3x3 square as an example. You can create squares more complex and larger. The main thing to remember is that all VKs are created according to similar principles.

There are a huge number of VKs in the world. For thousands of years, ancient sages, philosophers and mathematicians have created new types of squares (the square of Yang Hui, Khajuraho, Albrecht Dürer, Henry Dudeney and Allan Johnson Jr., etc.). It is noteworthy that they are all developed using the same equation, which was described in this article.

Varieties of VC include incomplete magic squares.

The first VC (called the Lo Shu square) was seen in 2200 BC. e. in Ancient China. The square was drawn on a turtle shell. The ancient sages considered the VC a model of space and expected that with the help of a magic square, problems of a universal scale could be solved. But as far as we know, in fact, there is no miracle in this, everything is done using a special equation.

However, despite this, Lo Shu is used in numerology to this day. The numbers indicating the date of birth of a person are located in the cells of a square table. The numbers are then deciphered based on location and meaning.

Lo Shu is actively used in the practice of Feng Shui. With its help, the most favorable zones are determined depending on a specific period of time.

Also, VC is used as a puzzle. Surely you often met such a puzzle while reading the newspaper, but simply did not focus on it. The Magic Square is somewhat reminiscent of the popular Japanese game Sudoku. VK is one of the most antique, old puzzles in the world. Sometimes scientists argue about what came first - Sudoku or VK. Solving magic squares, like other puzzles, is good for stimulating brain activity. With the above equation, you can create your own puzzle.

Video about how the magic square works

There are several different classifications of magic squares.

fifth order, designed to somehow systematize them. In the book

Martin Gardner [GM90, pp. 244-345] describes one of these methods -

according to the number in the central square. The method is curious, but nothing more.

How many squares of the sixth order exist is still unknown, but there are approximately 1.77 x 1019. The number is huge, so there is no hope of counting them using exhaustive search, but no one could come up with a formula for calculating magic squares.

How to make a magic square?

There are many ways to construct magic squares. The easiest way to make magic squares odd order. We will use the method proposed by the French scientist of the 17th century A. de la Louber (De La Loubère). It is based on five rules, the operation of which we will consider on the simplest magic square 3 x 3 cells.

Rule 1. Put 1 in the middle column of the first row (Fig. 5.7).

Rice. 5.7. First number

Rule 2. Put the next number, if possible, in the cell adjacent to the current one diagonally to the right and above (Fig. 5.8).

Rice. 5.8. Trying to put the second number

Rule 3. If the new cell goes beyond the square above, then write the number in the very bottom line and in the next column (Fig. 5.9).

Rice. 5.9. We put the second number

Rule 4. If the cell goes beyond the square on the right, then write the number in the very first column and in the previous line (Fig. 5.10).

Rice. 5.10. We put the third number

Rule 5. If the cell is already occupied, then write down the next number under the current cell (Fig. 5.11).

Rice. 5.11. We put the fourth number

Rice. 5.12. We put the fifth and sixth number

Follow Rules 3, 4, 5 again until you complete the entire square (Fig.

Isn't it true, the rules are very simple and clear, but it's still quite tedious to arrange even 9 numbers. However, knowing the algorithm for constructing magic squares, we can easily entrust the computer with all routine work, leaving ourselves only creative work, that is, writing a program.

Rice. 5.13. Fill in the square with the following numbers

Project Magic squares(Magic)

Field set for the program magic squares quite obvious:

// PROGRAM FOR GENERATION

// ODD MAGIC SQUARE

// BY THE DE LA LOUBERT METHOD

public partial class Form1 : Form

//Max. square dimensions: const int MAX_SIZE = 27; //var

intn=0; // square order int [,] mq; // magic square

int number=0; // current number to square

intcol=0; // current column int row=0; // current line

The de la Louber method is suitable for making odd squares of any size, so we can let the user choose the order of the square, while reasonably limiting the freedom of choice to 27 cells.

After the user presses the coveted button btnGen Generate! , the btnGen_Click method creates an array to store numbers and passes into the generate method:

// PRESS THE "GENERATE" BUTTON

private void btnGen_Click(object sender,EventArgs e)

//order of the square:

n = (int)udNum.Value;

//create an array:

mq = new int ;

//generate magic square: generate();

lstRes.TopIndex = lstRes.Items.Count-27;

Here we begin to act according to the rules of de la Louber and write the first number - one - in the middle cell of the first row of the square (or array, if you like):

//Generate the magic square void generate()(

//first number: number=1;

//column for the first number - middle: col = n / 2 + 1;

//line for the first number - the first one: row=1;

//square it: mq= number;

Now we sequentially add the rest of the cells in cells - from two to n * n:

// move on to the next number:

We remember, just in case, the coordinates of the actual cell

int tc=col;int tr = row;

and move to the next cell diagonally:

We check the implementation of the third rule:

if (row< 1) row= n;

And then the fourth:

if (col > n) ( col=1;

goto rule3;

And fifth:

if (mq != 0) ( col=tc;

row=tr+1; goto rule3;

How do we know that there is already a number in the cell of the square? - Very simple: we prudently wrote zeros in all cells, and the numbers in the finished square are greater than zero. So, by the value of the array element, we will immediately determine whether the cell is empty or already with a number! Please note that here we will need those cell coordinates that we remember before searching for the cell for the next number.

Sooner or later, we will find a suitable cell for the number and write it to the corresponding array cell:

//square it: mq = number;

Try another way to organize the check of the admissibility of the transition to the

wow cell!

If this number was the last, then the program has fulfilled its obligations, otherwise it voluntarily proceeds to provide the cell with the following number:

//if not all numbers are set, then if (number< n*n)

//go to the next number: goto nextNumber;

And now the square is ready! We calculate its magic sum and print it on the screen:

//square completed: writeMQ();

) //generate()

Printing the elements of an array is very simple, but it is important to take into account the alignment of numbers of different "lengths", because a square can contain one-, two-, and three-digit numbers:

//Print the magic square void writeMQ()

lstRes.ForeColor = Color .Black;

string s = "Magic sum = " + (n*n*n+n)/2; lstRes.Items.Add(s);

lstRes.Items.Add("" );

// print the magic square: for (int i= 1; i<= n; ++i){

s="" ;

for (int j= 1; j<= n; ++j){

if (n*n > 10 && mq< 10) s +=" " ;if (n*n >100 && mq< 100) s +=" " ; s= s + mq +" " ;

lstRes.Items.Add(s);

lstRes.Items.Add("" ); )//writeMQ()

We launch the program - the squares are obtained quickly and feast for the eyes (Fig.

Rice. 5.14. Quite a square!

In the book by S. Goodman, S. Hidetniemi Introduction to the development and analysis of algorithms

mov , on pages 297-299 we will find the same algorithm, but in a "reduced" presentation. It is not as "transparent" as our version, but it works correctly.

Add a button btnGen2 Generate 2! and write the algorithm in the language

C-sharp to methodAn old algorithm in a new guise