Magic Square

Magic square, a square matrix that is frequently divided into cells and filled with numbers or letters in specific arrangements that were once thought to have special, magical feature. Originally used as religious symbols, they later became protective charms or divination tools; and finally, when the original meanings were lost, they were considered mere curiosities or puzzles, except for some Western mathematicians who continue to study them as number theory problems.

A square sequence of numbers, usually positive integers, is referred to as a magic square if the sums of the numbers in each row, column, and both main diagonals are the same. The number of integers along one side (n) determines the order of the magic square, and the constant sum is known as the magic constant. If the array only includes positive integers,

Magic square

“Magic squares are named because each row, column, and diagonal in the square has the same sum, which is known as the magic constant. The term sum refers to the solution to an additional problem.”

Rule for making a magic square:

• Insert the next number in the middle column of the first row of the matrix and work our way up to the top left corner.

• If the row exceeds or is not in the matrix, change the column to the left column, place the number at the last row of the matrix, and try again for the top left corner.

• If the column exceeds or is not in the matrix, change the row to the top row and place the number in the last column of that matrix, then return to the top left corner.

• If the top left corner is not empty, or if both row and column exceed the range, place the number at the bottom of the previous number.

Magic squares formula

The standard or normal magic square is defined as a square matrix arrangement of the first n2 natural numbers (or positive integers) such that the sum of the numbers in each column, row, and diagonal is the same magic number. 

n Determines this magical number, which equals 

n(n2+1)2

How to Solve a Magic Square

Magic squares have grown in popularity since the introduction of mathematics-based games such as Sudoku. A magic square is a number arrangement in a square such that the sum of each row, column, and diagonal is one constant number, the so-called “magic constant 

Step for solve a magic square given below:

1. On a piece of paper, arrange the numbers in ascending order from least to higher.

2. To get the total, add all nine of the numbers on your list.

3. Multiply the total from Step 2 by 3.

4. Return to your number list, and the number in the very centre of that list will be placed in the center of the magic square.

How to solve magic square 6×6

For a magic square of order 6, we need to substitute n=6 to find the magic sum, which allows us to easily form the magic square 6×6.

When n=6, the total value =6(62+1)2=6(36+1)2=6(37)2=2222=111

As a result, the magic square 6×6 sum 111 is as follows:

Magic square 7×7 total 

For a magic square of order 7, we need to substitute n=7 to find the magic sum, which allows us to easily form the magic square 7×7.

When n=7, the total value =7(72+1)2=7(49+1)2=7(50)2=3502=175

As a result, the magic square 7×7 sum 175 is as follows:

Conclusion

In this article, we discussed that, a magic square is a square with several distinct integers arranged in such a way that the total or sum of the numbers is the same in every row, column, and main diagonal, as well as in some or all of the other diagonals. A magic square is a number grid in which every line, column, and diagonal adds up to the same total. In some factorial experiments, as well the use of magic squares is demonstrated for balancing out linear trend from main variable effects and lower order interactions. Some tools for determining the size of the trend are also mentioned.