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Magic square: how it works

The magic number for the square on the engraving by Durer - 34

Magic Squares are used in recreational mathematics from antiquity.

In modern culture, these tables have gained popularity due to the Japanese Sudoku.


The magic square integers are distributed so that their sum is horizontal, vertical, and diagonal equal the same number, the so-called magic constant.

Magic Quadrant in the cultures of the world

An example of the magic square is the Luo Shu, which is a table of 3 to 3. It entered the numbers from 1 to 9 so that the sum of each row and diagonal gives the number 15.
One Chinese legend tells how one day inthe flood King tried to build a canal that would have led the water into the sea. Suddenly, from the river Luo turtle appeared a strange pattern on the shell. It was inscribed in a grid with squares with numbers from 1 to 9. The sum of the numbers on each side of the square, as well as on the diagonal was 15. This number corresponds to the number of days in each of the 24 Chinese solar year cycles.

Square Lo Shu magic square is also called Saturn. The bottom line in the middle of the square is the number 1, and in the upper right cell number 2.

Magic Quadrant is present in other cultures: Persian, Arabic, Indian and European. It captures in his engraving "Melancholia" in 1514 by the German artist Albrecht Dürer.

Magic square on Durer's engraving is considered the first of those that have ever appeared in European art culture.

How to solve the magic square

should solve the magic square, fillingcell numbers so that each line in the amount turned magic constant. magic square Party may consist of even if an odd number of cells. Most popular magic squares consist of nine (3x3) or sixteen (4x4) cells. There is a wide variety of magic squares and their possible solutions.

How to solve the square with an even number of cells

You will need a piece of paper with a painted on them 4x4 square, a pencil and an eraser.
Fill in the cells of the square numbers from 1 to 16 starting from the top left cell.
1; 2; 3; 4
5; 6; 7; 8
9; 10; 11; 12
13; 14; 15; 16
The magic constant of the square - 34. Swap the numbers on the diagonal line from 1 to 16. For simplicity interchange 16 and 1, and then 6, and 11. The result will be the diagonal numerals 16, 11, 6, 1.
16; 2; 3; 4
5, 11; 7; 8
9, 10; 6; 12
13; 14; 15; 1
Swap of the second diagonalline. This line begins with the digits 4 and ends with the numeral 13. The swap them. Now reverse the two other numbers - 7 and 10. From top to bottom on the line number will be placed in the following order: 13, 10, 7, 4.
16; 2; 3, 13
5; 11; 10; 8
9; 7; 6; 12
4; 14; 15; 1
If you consider the amount per line, you get 34. This method works with other squares with an even number of cells.

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