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 4x4, 8x8, 16x16, 32x32
