What is a Magic Square? A magic square is an arrangement of the numbers from 1 to nA2 (n-squared) in an nxn matrix, with each number occurring exactly once, and such that the sum of the entries of any row, any column, or any main diagonal is the same. It is not hard to show that this sum must be n(nA2+1)/2. The simplest magic square is the 1x1 magic square whose only entry is the number 1. The next simplest is the 3x3 magic square 1 3 5 7 4 9 2 and those derived from it by symmetries of the square. This 3x3 square is definitely magic and satisfies the definition given above