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Magic squares (most perfect, [Franklin] panmagic & inlaid)
Detailed explanation about the structure and construction of magic squares
10x10 magic square
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How to produce 10x10 magic squares?
 
 You can produce 10x10 magic squares by using the Medjig method, the method to produce bordered
squares, or the method of Strachey.

On this webpage I present the improved method of Strachey and the Medjig method without puzzling
(= LUX method) to produce a magic 10x10 square.
 


Improved method of Strachey 

A 10x10 magic square produced with the ordinary method of Strachey consists of a 2x2 carpet  of a
magic 5x5 square. You need to swap a lot of digits to get a correct magic square. A 10x10 magic
square produced with the improved method of Strachey consists of 4 panmagic 5x5 squares. The
5x5 squares are more proportional and you need to swap less digits to get a correct magic square.
 
 
Produce 4 panmagic 5x5 squares by using method 3 on page 3x extra magic 15x15 square. Take as
row coordinates each time the digits 0 up to 4 and take as column coordinates the digits 0 up to
(5 x 4 -/- 1 = ) 19.
 
 
 5x column coordinate  +   1x row coordinate + 1  =    panmagic 5x5 square
 
 
 
 
 
 
 
 
 
 
 
 
250
250
250
250
250
 
 
 
 
 
 
 
 
 
 
 
 
 
250
 
 
 
 
 
250
 
0
5
10
15
17
 
0
1
2
3
4
 
1
27
53
79
90
 
250
10
15
17
0
5
 
3
4
0
1
2
 
54
80
86
2
28
 
250
17
0
5
10
15
 
1
2
3
4
0
 
87
3
29
55
76
 
250
5
10
15
17
0
 
4
0
1
2
3
 
30
51
77
88
4
 
250
15
17
0
5
10
 
2
3
4
0
1
 
78
89
5
26
52
 
250
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
250
250
250
250
250
 
 
 
 
 
 
 
 
 
 
 
 
 
250
 
 
 
 
 
250
 
1
4
9
14
19
 
0
1
2
3
4
 
6
22
48
74
100
 
250
9
14
19
1
4
 
3
4
0
1
2
 
49
75
96
7
23
 
250
19
1
4
9
14
 
1
2
3
4
0
 
97
8
24
50
71
 
250
4
9
14
19
1
 
4
0
1
2
3
 
25
46
72
98
9
 
250
14
19
1
4
9
 
2
3
4
0
1
 
73
99
10
21
47
 
250
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
255
255
255
255
255
 
 
 
 
 
 
 
 
 
 
 
 
 
255
 
 
 
 
 
255
 
2
6
11
13
16
 
0
1
2
3
4
 
11
32
58
69
85
 
255
11
13
16
2
6
 
3
4
0
1
2
 
59
70
81
12
33
 
255
16
2
6
11
13
 
1
2
3
4
0
 
82
13
34
60
66
 
255
6
11
13
16
2
 
4
0
1
2
3
 
35
56
67
83
14
 
255
13
16
2
6
11
 
2
3
4
0
1
 
68
84
15
31
57
 
255
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
255
255
255
255
255
 
 
 
 
 
 
 
 
 
 
 
 
 
255
 
 
 
 
 
255
 
3
7
8
12
18
 
0
1
2
3
4
 
16
37
43
64
95
 
255
8
12
18
3
7
 
3
4
0
1
2
 
44
65
91
17
38
 
255
18
3
7
8
12
 
1
2
3
4
0
 
92
18
39
45
61
 
255
7
8
12
18
3
 
4
0
1
2
3
 
40
41
62
93
19
 
255
12
18
3
7
8
 
2
3
4
0
1
 
63
94
20
36
42
 
255
 

 
Put the 4 panmagic 5x5 squares together.

 
 
magic 10x10 square to be corrected
 
 
505
505
505
505
505
505
505
505
505
505
 
 
505
 
 
 
 
 
 
 
 
 
 
505
500
 
1
27
53
79
90
6
22
48
74
100
 
500
 
54
80
86
2
28
49
75
96
7
23
 
500
 
87
3
29
55
76
97
8
24
50
71
 
500
 
30
51
77
88
4
25
46
72
98
9
 
500
 
78
89
5
26
52
73
99
10
21
47
 
510
 
11
32
58
69
85
16
37
43
64
95
 
510
 
59
70
81
12
33
44
65
91
17
38
 
510
 
82
13
34
60
66
92
18
39
45
61
 
510
 
35
56
67
83
14
40
41
62
93
19
 
510
 
68
84
15
31
57
63
94
20
36
42
 
 

 
Swap the 2x five (not-diagonal) digits, to get a correct 10x10 magic square.

 
 
  10x10 magic square
1
32
53
79
90
6
22
48
74
100
59
80
86
2
28
49
75
96
7
23
87
3
29
60
76
97
8
24
50
71
35
51
77
88
4
25
46
72
98
9
78
89
5
31
52
73
99
10
21
47
11
27
58
69
85
16
37
43
64
95
54
70
81
12
33
44
65
91
17
38
82
13
34
55
66
92
18
39
45
61
30
56
67
83
14
40
41
62
93
19
68
84
15
26
57
63
94
20
36
42
 

 
This method can be also used to produce a magic 14x14 square (consisting of 4 as proportional as
possible panmagic 7x7 squares).



Medjig method without puzzling (= LUX method)

You can use the Medjig method without puzzling, better known as the LUX method. The three cha-
racters concern three different Medjig tiles. If you draw straight lines between the digits 1, 2, 3 [and 4]
on the tiles, you get the characters L (see red marked), U (see yellow marked) and X (see blue marked).
Take a digit from the LUX grid and add 4x [digit minus 1] from the same cell of the second grid with the
2x2 'blown up' 5x5 magic square.
 
 
1x digit from grid with Medjig tiles LUX
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
25
25
25
25
25
25
25
25
25
25
 
 
25
 
 
 
 
 
 
 
 
 
 
25
25
 
4
1
4
1
4
1
4
1
4
1
 
25
 
2
3
2
3
2
3
2
3
2
3
 
25
 
4
1
4
1
4
1
4
1
4
1
 
25
 
2
3
2
3
2
3
2
3
2
3
 
25
 
4
1
4
1
1
4
4
1
4
1
 
25
 
2
3
2
3
2
3
2
3
2
3
 
25
 
1
4
1
4
4
1
1
4
1
4
 
25
 
2
3
2
3
2
3
2
3
2
3
 
25
 
1
4
1
4
1
4
1
4
1
4
 
25
 
3
2
3
2
3
2
3
2
3
2
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
+4x [digit minus 1] from grid with 2x2 'blown up' 5x5 magic square
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
130
130
130
130
130
130
130
130
130
130
 
 
130
 
 
 
 
 
 
 
 
 
 
130
130
 
1
1
7
7
13
13
19
19
25
25
 
130
 
1
1
7
7
13
13
19
19
25
25
 
130
 
14
14
20
20
21
21
2
2
8
8
 
130
 
14
14
20
20
21
21
2
2
8
8
 
130
 
22
22
3
3
9
9
15
15
16
16
 
130
 
22
22
3
3
9
9
15
15
16
16
 
130
 
10
10
11
11
17
17
23
23
4
4
 
130
 
10
10
11
11
17
17
23
23
4
4
 
130
 
18
18
24
24
5
5
6
6
12
12
 
130
 
18
18
24
24
5
5
6
6
12
12
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
= 10x10 magic square