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Pan Magic Squares 7 x 7, Interactive Solution, Sudoku Method

Introduction

Pan Magic Squares of the 7th order can be constructed by means of following Sudoku Comparable Method:

1. 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.

2. 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:

1. A: shift 2 columns to the left / B: shift 2 columns to the right
2. A: shift 2 columns to the left / B: shift 3 columns to the right
3. A: shift 2 columns to the left / B: shift 3 columns to the left
4. A: shift 3 columns to the left / B: shift 2 columns to the right
5. A: shift 3 columns to the left / B: shift 3 columns to the right
6. A: shift 3 columns to the left / B: shift 2 columns to the left

3. 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 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 7 8 First Row B 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 Completion Scheme: 1 2 3 4 5 6

Procedure:

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

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

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

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

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

1. for square C   (default);
2. for Horizontal Reflection of square C;
3. for Vertical   Reflection of square C;
4. for  90 degr   Rotation   of square C;
5. for Horizontal Reflection of 90 degr Rotated Square C;
6. for Vertical   Reflection of 90 degr Rotated Square C;
7. for 180 degr   Rotation of C;
8. for 270 degr   Rotation of C.

6. 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 Cn and finally in 777.600 * 49 * 8 = 304.819.200 possible Pan Magic Squares of the 7th order.

Have Fun!