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Perfect magic squares
Sudoku method (1)
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How to produce a (4x4 pan)magic square from a Sudokuo?
 
 
A Sudoku mostly consists of 9 rows and 9 columns. Each row and each column (and each nonet) must contain
all the digits from 1 to 9. Using a 4x4 Sudoku (which consists of 4 rows and 4 columns) you can produce a magic
square when you follow the next four steps.
 
(1st) Do not fill in the digits 1, 2, 3 and 4, but fill in the digits 0, 1, 2, 3. Ensure that every row, column and dia-
gonal contains all the digits 0, 1, 2 and 3.
 
(2nd) Produce a second 4x4 Sudoku by rotating the first Sudoku (a quarter turn to the right).
 
(3rd) Take a digit from the first Sudoku multiplied by 4 and add (1x) the digit from the same cell of the second Sudoku.
 
(4th) Add 1 to each cell.
 

  4x                                     +     1x                                                             +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 also just happens to be a 4x4 panmagic square!


See more information on page:  4x4 panmagic square



Information for whiz kids:
 

FRANKLIN PANMAGIC 8x8 SQUARE:

It is possible to use the Sudoku patterns of the panmagic 4x4 square to produce a Franklin panmagic
8x8 square. You need three 8x8 Sudoku patterns.
 
● The first 8x8 Sudoku pattern is a 2x2 carpet of the first 4x4 Sudoku pattern.
 
● To produce the second 8x8 Sudoku pattern you need to split up the second 4x4 Sudoku pattern in
two sub-squares and enter digits from the same sub-square in the empty cells crosswise:
 
 
 split up the (2nd ) 4x4 Sudoku pattern:             Enter digits in the empty cells 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 2 sub-squares and add the same 2 sub-squares to the bottom.
 
● The third 8x8 Sudoku pattern is fixed (= column pattern of the basic pattern method).
 
 
 
4x digit from first pattern     +   1x digit from second pattern  +   16x digit from third pattern  =
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
 
 
 
Note that above mentioned method is the ‘Sudoku version’ of the basic pattern method (see also on this
website).



FRANKLIN PANMAGIC 16x16 SQUARE:

It is also possible to use the Sudoku patterns of the panmagic 8x8 square to produce a perfect Franklin
panmagic 16x16 square. You need four 16x16 Sudoku patterns.
 
● The first and second 16x16 Sudoku pattern is a 2x2 carpet of the first respectively second 8x8 Sudoku
pattern.
 
● The third and fourth 16x16 Sudoku pattern are fixed patterns (the third and fourth pattern together =
the column pattern of the basic pattern method).
 
 
 4x digit from first pattern                                            1x digit from second pattern
0
1
2
3
0
1
2
3
0
1
2
3
0
1
2
3
 
 
0
1
3
2
2
3
1
0
0
1
3
2
2
3
1
0
3
2
1
0
3
2
1
0
3
2
1
0
3
2
1
0
 
 
3
2
0
1
1
0
2
3
3
2
0
1
1
0
2
3
1
0
3
2
1
0
3
2
1
0
3
2
1
0
3
2
 
 
0
1
3
2
2
3
1
0
0
1
3
2
2
3
1
0
2
3
0
1
2
3
0
1
2
3
0
1
2
3
0
1
 
 
3
2
0
1
1
0
2
3
3
2
0
1
1
0
2
3
0
1
2
3
0
1
2
3
0
1
2
3
0
1
2
3
 
 
0
1
3
2
2
3
1
0
0
1
3
2
2
3
1
0
3
2
1
0
3
2
1
0
3
2
1
0
3
2
1
0
 
 
3
2
0
1
1
0
2
3
3
2
0
1
1
0
2
3
1
0
3
2
1
0
3
2
1
0
3
2
1
0
3
2
 
 
0
1
3
2
2
3
1
0
0
1
3
2
2
3
1
0
2
3
0
1
2
3
0
1
2
3
0
1
2
3
0
1
 
 
3
2
0
1
1
0
2
3
3
2
0
1
1
0
2
3
0
1
2
3
0
1
2
3
0
1
2
3
0
1
2
3
 
 
0
1
3
2
2
3
1
0
0
1
3
2
2
3
1
0
3
2
1
0
3
2
1
0
3
2
1
0
3
2
1
0
 
 
3
2
0
1
1
0
2
3
3
2
0
1
1
0
2
3
1
0
3
2
1
0
3
2
1
0
3
2
1
0
3
2
 
 
0
1
3
2
2
3
1
0
0
1
3
2
2
3
1
0
2
3
0
1
2
3
0
1
2
3
0
1
2
3
0
1
 
 
3
2
0
1
1
0
2
3
3
2
0
1
1
0
2
3
0
1
2
3
0
1
2
3
0
1
2
3
0
1
2
3
 
 
0
1
3
2
2
3
1
0
0
1
3
2
2
3
1
0
3
2
1
0
3
2
1
0
3
2
1
0
3
2
1
0
 
 
3
2
0
1
1
0
2
3
3
2
0
1
1
0
2
3
1
0
3
2
1
0
3
2
1
0
3
2
1
0
3
2
 
 
0
1
3
2
2
3
1
0
0
1
3
2
2
3
1
0
2
3
0
1
2
3
0
1
2
3
0
1
2
3
0
1
 
 
3
2
0
1
1
0
2
3
3
2
0
1
1
0
2
3
 
 
 16x digit from third (fixed) pattern                             64x digit from fourth (fixed) pattern
2
3
0
1
2
3
0
1
0
1
2
3
0
1
2
3
 
 
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
1
2
3
0
1
2
3
2
3
0
1
2
3
0
1
 
 
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
3
2
1
0
3
2
1
0
1
0
3
2
1
0
3
2
 
 
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
1
0
3
2
1
0
3
2
3
2
1
0
3
2
1
0
 
 
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
2
1
0
3
2
1
0
1
0
3
2
1
0
3
2
 
 
0
3
0
3
0
3
0
3
0
3
0