Sudoku method (3)

How to construct a most perfect (Franklin pan)magic 1024x1024 square in 9 steps by using only one 4x4 Sudoku

4x4 Sudoku

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

Step 1

Use the 4x4 Sudoku and a shifted version of the 4x4 Sudoku on a 2x2 carpet to construct a 4x4 panmagic square.

4x4 Sudoku shifted on 2x2 carpet

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

4x number            +   1x number          +1                          = 4x4 panmagic square

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

Step 2

Use a grid with 2x2 the 4x4 panmagic square and a grid with 2x2 the shifted versions of the 4x4 Sudoku to construct an 8x8 most perfect (Franklin pan)magic square.

Construct the grid with 2x2 the shifted versions of the 4x4 Sudoku as follows:

 + + + +

1x number                                 +    16x number                   = 8x8 Franklin panmagic square

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

Step 3

Use a grid with 2x2 the 8x8 most perfect (Franklin pan)magic square and a grid with 2x2 the shifted versions of 8x8 Sudoku grid to construct an 16x16 most perfect (Franklin pan)magic square. See step 2 to construct the Sudoku grid

1x number

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

+

64x number

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

=

Most perfect 16x16 (Franklin pan)magic square

 171 85 256 2 251 5 176 82 235 21 192 66 187 69 240 18 88 170 3 253 8 250 83 173 24 234 67 189 72 186 19 237 1 255 86 172 81 175 6 252 65 191 22 236 17 239 70 188 254 4 169 87 174 84