## Magic Square

A magic square of order

*n*is an arrangement of*n*² numbers, usually distinct integers, in a square, such that the*n*numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to*n*².Normal magic squares exist for all orders

*n*≥ 1 except

*n*= 2, although the case

*n*= 1 is trivial as it consists of a single cell containing the number 1. The smallest nontrivial case, shown below, is of order 3:

The constant sum in every row, column and diagonal is called the magic constant or magic
sum,

*M*. The magic constant of a normal magic square depends only on*n*and has the value: