### Sudoku method 1

How to use a (4x4) Sudoku to construct a (4x4 pan)magic square?

A sudoku mostly consists of 9 rows and 9 columns. In each row and in each column (and in each 3x3 section) you find all the numbers from 1 up to 9. Take a 4x4 Sudoku and construct a 4x4 (pan)magic square in 4 steps.

(1st) Fill in the numbers 0 up to 3 instead of 1 up to 4. Take care that you find all the numbers from 0 up to 3 in each row, column and diagonal.

(2nd) Construct the second grid by rotating the first grid a quarter to the right.

(3rd) Take 4x number from first grid and add 1x number from the same cell of the second grid.

(4th) Add 1 to each cell.

4x number           +   1x number           =   +1                              magic square

 0 1 2 3 2 1 3 0 2 5 11 12 3 6 12 13 3 2 1 0 3 0 2 1 15 8 6 1 16 9 7 2 1 0 3 2 0 3 1 2 4 3 13 10 5 4 14 11 2 3 0 1 1 2 0 3 9 14 0 7 10 15 1 8

This magic square happens to be panmagic!

Franklin panmagic 8x8 square

It is also possible to use the Sudoku grids of a panmagic 4x4 square to construct a Franklin panmagic 8x8 square.  Construct three 8x8 grids.

● The first 8x8 grid is 2x2 the first 4x4 Sudoku grid.

● Split the second 4x4 Sudoku grid to construct the second 8x8 grid:

Split the second 4x4 Sudoku grid:                 Complete the grids by filling in crosswise:

 1 3 2 0 0 1 3 2 2 3 1 0 3 1 0 2 3 2 0 1 1 0 2 3 0 2 3 1 0 1 3 2 2 3 1 0 2 0 1 3 3 2 0 1 1 0 2 3

Combine the two 4x4 Sudoku grids and copy the two grids to complete the 8x8 grid.

● The third (fixed) 8x8 grid is the same as the second grid of basis pattern method 1.

Take 4x number from 1st grid  +1x number from 2nd grid     +    16x number from 3rd grid

 0 1 2 3 0 1 2 3 0 1 3 2 2 3 1 0 0 3 0 3 0 3 0 3 3 2 1 0 3 2 1 0 3 2 0 1 1 0 2 3 0 3 0 3 0 3 0 3 1 0 3 2 1 0 3 2 0 1 3 2 2 3 1 0 3 0 3 0 3 0 3 0 2 3 0 1 2 3 0 1 3 2 0 1 1 0 2 3 3 0 3 0 3 0 3 0 0 1 2 3 0 1 2 3 0 1 3 2 2 3 1 0 1 2 1 2 1 2 1 2 3 2 1 0 3 2 1 0 3 2 0 1 1 0 2 3 1 2 1 2 1 2 1 2 1 0 3 2 1 0 3 2 0 1 3 2 2 3 1 0 2 1 2 1 2 1 2 1 2 3 0 1 2 3 0 1 3 2 0 1 1 0 2 3 2 1 2 1 2 1 2 1

+1                                                        =     Franklin panmagic 8x8 square

 0 53 11 62 2 55 9 60 1 54 12 63 3 56 10 61 15 58 4 49 13 56 6 51 16 59 5 50 14 57 7 52 52 1 63 10 54 3 61 8 53 2 64 11 55 4 62 9 59 14 48 5 57 12 50 7 60 15 49 6 58 13 51 8 16 37 27 46 18 39 25 44 17 38 28 47 19 40 26 45 31 42 20 33 29 40 22 35 32 43 21 34 30 41 23 36 36 17 47 26 38 19 45 24 37 18 48 27 39 20 46 25 43 30 32 21 41 28 34 23 44 31 33 22 42 29 35 24

Use this method [Sudoku method (1)] to construct magic squares of order is 2^n (= 2x2, 2x2x2, 2x2x2x2, ...) from 4x4 to infinity. See 4x48x816x1632x32

8x8, Sudoku method (1).xls