### Basic pattern method (2)

Use a 4x4 panmagic square to construct a 8x8 Franklin panmagic square.

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

Choose a 4x4 panmagic square and split it as follows:

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

Fill in the empty cells crosswise with the same numbers in the 4x4 sub-square:

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

Combine the 2 squares and put the same 2 squares below to complete the first grid of the 8x8 magic square:

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

Replace the numbers using the table above:

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

In total there are 6 ways to split the panmagic 4x4 square to construct the basic grid:

1 split the panmagic 4x4       Complete grid and replace numbers  =  8x8 Franklin panmagic square

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

2 split the panmagic 4x4       Complete grid and replace numbers  = 8x8 Franklin panmagic square

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

3 split the panmagic 4x4           Complete grid and replace numbers 8x8 Franklin panmagic square

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

4 split panmagic 4x4                 Complete grid and replace numbers = 8x8 Franklin panmagic square

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

5 split panmagic 4x4         Complete grid and replace numbers = 8x8 Franklin panmagic square

 16 10 3 5 16 7 10 1 12 3 14 5 48 23 58 1 60 3 46 21 2 8 13 11 2 9 8 15 6 13 4 11 18 41 8 63 6 61 20 43 7 1 12 14 7 16 1 10 3 12 5 14 7 64 17 42 19 44 5 62 9 15 6 4 9 2 15 8 13 6 11 4 57 2 47 24 45 22 59 4