This is a method reminiscent of the Kronecker product of two matrices, that builds an nm × nm magic square from an n × n magic square and an m × m magic square.Hartley, M. "Making Big Magic Squares". The "product" of two magic squares creates a magic square of higher order than the two multiplicands. Let the two magic squares be of orders m and n. The final square will be of order m × n. Divide the square of order m × n into m × m sub-squares, such that there are a total of n2 such sub-squares. In the square of order n, reduce by 1 the value of all the numbers. Multiply these reduced values by m2, and place the results in the corresponding sub-squares of the m × n whole square. The squares of order m are added n2 times to the sub-squares of the final square. The peculiarity of this construction method is that each magic subsquare will have different magic sums. The square made of such magic sums from each magic subsquare will again be a magic square. The smallest composite magic square of order 9, composed of two order 3 squares is given below.
