Magic Squares and How to Construct them

How to find the position of all numbers in a magic square of order three. Also, how to create magic squares of odd order with the method of de la Loubère and magic squares of even order with the method of Devedec

Known since ancient times, magic squares are arrays filled with numbers, made up of an equal number of rows and columns. Numbers are usually positive integers and must all be distinct from each other. What makes these squares “magical” is that the sum of the numbers in each row, column, and main diagonal is always the same.

Some definitions

Magic squares are called normal if they are filled with a progressive series of natural numbers starting from 1 up to n², where n is the number of rows or columns that make up the square. The constant sum of the horizontal, vertical, and diagonal lines is called the magic constant and equals

For example, if the number of vertical lines is 4, the magic constant is

The number of rows and columns defines the order of the magic square. Therefore, a magic square with 5 rows and 5 columns will be of order 5, one with 6 rows and 6 columns of order 6, etc. Since the construction rules are different, it is also important to distinguish whether the number of rows and columns is odd or even. A magic square with an odd number of rows and columns is said to be…