ABSTRACT
A magic square is a square of numbers using the integers 1, 2, .. n2 , such that the sums of the numbers in each row, each column and each diagonal are the same. The value of these sums can be shown to be 1 2 n n 2 + 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315069555/5d5201a7-70ac-4d14-a96d-80b2cf916e2e/content/ieq0117.tif"/> . For example, the square above can be written 8 1 6 3 5 7 4 9 2 and every row, column and diagonal adds up to 15; for example 8 + 3 + 4 = 15, 4 + 5 + 6 =15 and 1 + 5 + 9 = 15. This particular magic square is also said to be a perfect magic square. The sum of any two numbers in symmetric positions with respect to the middle number are equal to twice the middle number; for example, 6 + 4 = 2 × 5 and 3 + 7 = 2 × 5.
