Pan Magic Squares 7 x 7, Interactive Solution, Sudoku Method
Introduction
Pan Magic Squares of the 7^{th} order can be constructed by means of following Sudoku Comparable Method:

Fill the first row of square A and square B with the numbers 0, 1, 2, 3, 4, 5 and 6.
While starting with 0 there are 6! = 720 possible combinations for each square.

Complete square A and B by copying the first row into the following rows of the applicable square, according to one of the following schemes:

A: shift 2 columns to the left / B: shift 2 columns to the right

A: shift 2 columns to the left / B: shift 3 columns to the right

A: shift 2 columns to the left / B: shift 3 columns to the left

A: shift 3 columns to the left / B: shift 2 columns to the right

A: shift 3 columns to the left / B: shift 3 columns to the right

A: shift 3 columns to the left / B: shift 2 columns to the left

Construct the final square C by means of the matrix operation C = 7 * A + B + [1].


Squares

A

B

C
C = 7 * A + B + [1]


First Row A



First Row B


Completion Scheme:





Procedure:

Select one of the matrix completion schemes, as described in point 2 of the introduction above (default = 1).

Select the first row of matrix A with the left selection buttons, and confirm by pushing button 'Matrix A'.

Select the first row of matrix B with the right selection buttons, and confirm by pushing button 'Matrix B'.

Press the button ‘Square’ to calculate and visualise the resulting Pan Magic Square.

Select a Base Square with the selection button left from the button 'SubCls'. Select:

for square C (default);

for Horizontal Reflection of square C;

for Vertical Reflection of square C;

for 90 degr Rotation of square C;

for Horizontal Reflection of 90 degr Rotated Square C;

for Vertical Reflection of 90 degr Rotated Square C;

for 180 degr Rotation of C;

for 270 degr Rotation of C.

Press the button ‘SubCls’ to visualise the related Sub Class (49 elements) based on row/column shifts of the selected Base Square.
The possible combinations of square A and B described above will result in
6 * 720 * 720 /4 = 777.600 unique solutions.
Each of these 777.600 Pan Magic Squares will result in a unique Class C_{n} and finally in
777.600 * 49 * 8 = 304.819.200
possible Pan Magic Squares of the 7^{th} order.
Have Fun!
