A*magic square*is a square matrix drawn as a checkerboard filled with numbers or letters in particular arrangements. Mathematicians are most interested in*arithmetic*squares consisting of*N*² boxes, called*cells*, filled with integers that are all different. Such an array of numbers is called a magic square if the sums of the numbers in the horizontal rows, vertical columns, and main diagonals are all equal. If the integers in a magic square are the consecutive numbers from 1 to*N*², the square is said to be of the*N*th order, and the*magic number*, or sum of each