Magic squaresContact / guestbookMost magic square per order3x3 magic square3x3 magic square, explanationSudoku method (1)Sudoku method (2)Sudoku method (3)Pan magic 4x4 squarePan magic 4x4 square, explanationPan magic 4x4 square, binaryDürer & Franklin transformationTransformation methodTransformation method, analysis[ultra] pan magic 5x5 squarePan magic 5x5 square, explanation6x6 magic squareUltra (pan)magic 8x8 squareMost perfect magic squares, explanation8x8 most perfect magic squares, binaryKhajuraho methodKhajuraho method, explanationBasic pattern method (1a)Basic pattern method (1b)Basic pattern method (2)Basic pattern method (3a)Basic pattern method (3b)Basic pattern method (3c)Basic pattern method (4)Basic pattern method (5)Basic pattern method (6)Basic pattern method (7a)Basic pattern method (7b)Analysis Franklin panm. 8x8 (1)Analysis Franklin panm. 8x8 (2)Basic key method (1)Basic key method (2)Quadrant method (Willem Barink)Quadrant method group 1 up to 5Quadrant method group 6 up to 10Quadrant method group 11 up to 19[ultra] pan magic 9x9 square (1)pan magic 9x9 square (2)pan magic 9x9 square (3)3x extra magic 9x9 square10x10 magic squareComposite 12x12 magic square14x14 magic square[Ultra] pan magic 15x15 square3x extra magic 15x15 squareThe perfect magic square3x extra magic 18x18 squareUltra pan magic 25x25 square[ultra] pan magic 27x27 square[ultra] pan magic 35x35 squareextra magic 35x35 squareBordered squaresInlaid square (1)Inlaid square (2)Each magic sumWater retention challengeMost magic 4x4x4 cubePerfect (Nasik) magic 8x8x8 cube[More than] perfect magic 9x9x9 cubeTrick with 8x8 bimagic squareFavorite Links
Magic squares (most perfect, [Franklin] panmagic & inlaid)
Detailed explanation about the structure and construction of magic squares
Basic pattern method (3a)
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How to produce a Franklin panmagic 16x16 square from a panmagic
4x4 square
 
It is possible to use a 4x4 carpet of the pattern (don’t split it up!) of a pan magic 4x4 square to pro-
duce a perfect Franklin pan magic 16x16 square. You need a 4x4 carpet of a pan magic 4x4 square
and a (second) 4x4 carpet of the shifted versions of the pan magic 4x4 square (notify that this is
comparable with the production of an ultra pan magic 25x25 square by using the shifted versions of
a pan magic 5x5 square).
 
 
● The first 4x4 carpet consist of (top left) a pan magic 4x4 square plus 15x the shifted versions of the
    pan magic 4x4 square. To produce the shifted versions of the  pan magic 4x4 square you need a
    2x2 carpet of the panmagic 4x4 square. Two (= red and blue) coordinates give the starting positions
    (is digits at the top left) of the shifted versions of the 4x4 pan magic square.
 
 
 
0
1
2
3
 
 
 
 
 
 
 
 
 
 
0
2
5
11
12
2
5
11
12
 
 
0,0
1,2
2,0
3,2
1
15
8
6
1
15
8
6
1
 
 
2,1
3,3
0,1
1,3
2
4
3
13
10
4
3
13
10
 
 
0,2
1,0
2,2
3,0
3
9
14
0
7
9
14
0
7
 
 
2,3
3,1
0,3
1,1
 
2
5
11
12
2
5
11
12
 
 
 
 
 
 
 
15
8
6
1
15
8
6
1
 
 
 
 
 
 
 
4
3
13
10
4
3
13
10
 
 
 
 
 
 
 
9
14
0
7
9
14
0
7
 
 
 
 
 
 
 
 
● The second 4x4 carpet consists of 4x4 the same pan magic 4x4 square.
 
 
 
 1x digit from 4x4 carpet of shifted versions of panmagic 4x4 square
2
5
11
12
3
13
10
4
11
12
2
5
10
4
3
13
15
8
6
1
14
0
7
9
6
1
15
8
7
9
14
0
4
3
13
10
5
11
12
2
13
10
4
3
12
2
5
11
9
14
0
7
8
6
1
15
0
7
9
14
1
15
8
6
6
1
15
8
7
9
14
0
15
8
6
1
14
0
7
9
13
10
4
3
12
2
5
11
4
3
13
10
5
11
12
2
0
7
9
14
1
15
8
6
9
14
0
7
8
6
1
15
11
12
2
5
10
4
3
13
2
5
11
12
3
13
10
4
4
3
13
10
5
11
12
2
13
10
4
3
12
2
5
11
9
14
0
7
8
6
1
15
0
7
9
14
1
15
8
6
2
5
11
12
3
13
10
4
11
12
2
5
10
4
3
13
15
8
6
1
14
0
7
9
6
1
15
8
7
9
14
0
0
7
9
14
1
15
8
6
9
14
0
7
8
6
1
15
11
12
2
5
10
4
3
13
2
5
11
12
3
13
10
4
6
1
15
8
7
9
14
0
15
8
6
1
14
0
7
9
13
10
4
3
12
2
5
11
4
3
13
10
5
11
12
2
 
 
 
 +16x digit from the 4x4 carpet of the pan magic 4x4 square
2
5
11
12
2
5
11
12
2
5
11
12
2
5
11
12
15
8
6
1
15
8
6
1
15
8
6
1
15
8
6
1
4
3
13
10
4
3
13
10
4
3
13
10
4
3
13
10
9
14
0
7
9
14
0
7
9
14
0
7
9
14
0
7
2
5
11
12
2
5
11
12
2
5
11
12
2
5
11
12
15
8
6
1
15
8
6
1
15
8
6
1
15
8
6
1
4
3
13
10
4
3
13
10
4
3
13
10
4
3
13
10
9
14
0
7
9
14
0
7
9
14
0
7
9
14
0
7
2
5
11
12
2
5
11
12
2
5
11
12
2
5
11
12
15
8
6
1
15
8
6
1
15
8
6
1
15
8
6
1
4
3
13
10
4
3
13
10
4
3
13
10
4
3
13
10
9
14
0
7
9
14
0
7
9
14
0
7
9
14
0
7
2
5
11
12
2
5
11
12
2
5
11
12
2
5
11
12
15
8
6
1
15
8
6
1
15
8
6
1
15
8
6
1
4
3
13
10
4
3
13
10
4
3
13
10
4
3
13
10
9
14
0
7
9
14
0
7
9
14
0
7
9
14
0
7
 
 
 
 = Most perfect (Franklin pan)magic 16x16 square
34
85
187
204
35
93
186
196
43
92
178
197
42
84
179
205
255
136
102
17
254
128
103
25
246
129
111
24
247
137
110
16
68
51
221
170
69
59
220
162
77
58
212
163
76
50
213
171
153
238
0
119
152
230
1
127
144
231
9
126
145
239
8
118
38
81
191
200
39
89
190
192
47
88
182
193
46
80
183
201
253
138
100
19
252
130
101
27
244
131
109
26
245
139
108
18
64
55
217
174
65
63
216
166
73
62
208
167
72
54
209
175
155
236
2
117
154
228
3
125
146
229
11
124
147
237
10
116
36
83
189
202
37
91
188
194
45
90
180
195
44
82
181
203
249
142
96
23
248
134
97
31
240
135
105
30
241
143
104
22
66
53
219
172
67
61
218
164
75
60
210
165
74
52
211
173
159
232
6
113
158
224
7
121
150
225
15
120
151
233
14
112
32
87
185
206
33
95
184
198
41
94
176
199
40
86
177
207
251
140
98
21
250
132
99
29
242
133
107
28
243
141
106
20
70
49
223
168
71
57
222
160
79
56
214
161
78
48
215
169
157
234
4
115
156
226
5
123
148
227
13
122
149
235
12
114
 



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Magic squares|Contact / guestbook|Most magic square per order|3x3 magic square|3x3 magic square, explanation|Sudoku method (1)|Sudoku method (2)|Sudoku method (3)|Pan magic 4x4 square|Pan magic 4x4 square, explanation|Pan magic 4x4 square, binary|Dürer & Franklin transformation|Transformation method|Transformation method, analysis|[ultra] pan magic 5x5 square|Pan magic 5x5 square, explanation|6x6 magic square|Ultra (pan)magic 8x8 square|Most perfect magic squares, explanation|8x8 most perfect magic squares, binary|Khajuraho method|Khajuraho method, explanation|Basic pattern method (1a)|Basic pattern method (1b)|Basic pattern method (2)|Basic pattern method (3a)|Basic pattern method (3b)|Basic pattern method (3c)|Basic pattern method (4)|Basic pattern method (5)|Basic pattern method (6)|Basic pattern method (7a)|Basic pattern method (7b)|Analysis Franklin panm. 8x8 (1)|Analysis Franklin panm. 8x8 (2)|Basic key method (1)|Basic key method (2)|Quadrant method (Willem Barink)|Quadrant method group 1 up to 5|Quadrant method group 6 up to 10|Quadrant method group 11 up to 19|[ultra] pan magic 9x9 square (1)|pan magic 9x9 square (2)|pan magic 9x9 square (3)|3x extra magic 9x9 square|10x10 magic square|Composite 12x12 magic square|14x14 magic square|[Ultra] pan magic 15x15 square|3x extra magic 15x15 square|The perfect magic square|3x extra magic 18x18 square|Ultra pan magic 25x25 square|[ultra] pan magic 27x27 square|[ultra] pan magic 35x35 square|extra magic 35x35 square|Bordered squares|Inlaid square (1)|Inlaid square (2)|Each magic sum|Water retention challenge|Most magic 4x4x4 cube|Perfect (Nasik) magic 8x8x8 cube|[More than] perfect magic 9x9x9 cube|Trick with 8x8 bimagic square|Favorite Links