A magic square is an n x n grid in which numbers have been written in such a way that the sum of the numbers along any row, column, or main diagonal is always the same magic constant. In a pure magic square, the numbers in the grid must be the consecutive integers from one to n² with each number used exactly once. The number n is called the order of the square. The unique order 3 magic square was known in China at least by 500 BC where it is called the lo shu.

Most literature on magic squares is about how to construct magic squares in general and those with special properties. A magic square in which all broken diagonals add up to the magic constant is called pandiagonal. A magic square in which cells that are situated directly opposite from the center is called associative...