In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the sum of n numbers in all rows, all columns and both diagonals is the same constant called the magic number. The magic square in normal is represented using n x n matrix. A normal magic square contains the integers from 1 to n2. Normal magic squares exist for all orders , except n = 2. The magic constant for normal magic squares of order n is given by n(n2 + 1)/2. There are several methods for constructing the magic square of any given order. This paper proposes algorithms to obtain the magic square of any given order n. Some of the algorithms are straight forward and others are designed using the divide and conquer technique.

The magic square is represented by n x n matrix. The normal magic square contains numbers from 1 to n2 (Ellis et al., 2002). There exists a magic square for all orders , except n = 2. Several methods exist for construction of magic square of any given order (www.wikipedia.org).

The magic squares have several applications in fields of discrete and combinatorial mathematics, and also in the area of graph theory. One such application of magic square is in graph labeling. It has been proved using the magic square of order n that, “There exists a vertex magic total labeling for all complete graph K_n” (Krishnappa et al., 2009 and 2010).

Our process of constructing a magic square of order n is divided into the following categories and subcategories:

Magic square of order n, where n is odd.

Magic square of order N, where N is even.

Magic square of order 4.

Magic square of order N, for all mod 4.

Magic square of order N, for all mod 4.

Computational Mathematics Journal, Magic Square Construction Algorithms, Magic Square Construction Applications, Graph Labeling, Magic Square Problem, Single Matrix, Combinatorial Mathematics, Discrete Mathematics, Recreational Mathematics.