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How to make perfect magic squares & cubes
The sky is the limit!!!
Basic pattern method (3b)
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How to use a panmagic 4x4 square to produce a most perfect magic
16x16 square?
 
Just like basic pattern method 3a, the first pattern is a carpet of 4x4 the same panmagic 4x4
square. You need the carpet and 2 fixed patterns to produce a most perfect (Franklin pan)magic
16x16 square.
 
 
  1x digit from carpet of 4x4 the same panmagic 4x4 square
3
6
12
13
3
6
12
13
3
6
12
13
3
6
12
13
16
9
7
2
16
9
7
2
16
9
7
2
16
9
7
2
5
4
14
11
5
4
14
11
5
4
14
11
5
4
14
11
10
15
1
8
10
15
1
8
10
15
1
8
10
15
1
8
3
6
12
13
3
6
12
13
3
6
12
13
3
6
12
13
16
9
7
2
16
9
7
2
16
9
7
2
16
9
7
2
5
4
14
11
5
4
14
11
5
4
14
11
5
4
14
11
10
15
1
8
10
15
1
8
10
15
1
8
10
15
1
8
3
6
12
13
3
6
12
13
3
6
12
13
3
6
12
13
16
9
7
2
16
9
7
2
16
9
7
2
16
9
7
2
5
4
14
11
5
4
14
11
5
4
14
11
5
4
14
11
10
15
1
8
10
15
1
8
10
15
1
8
10
15
1
8
3
6
12
13
3
6
12
13
3
6
12
13
3
6
12
13
16
9
7
2
16
9
7
2
16
9
7
2
16
9
7
2
5
4
14
11
5
4
14
11
5
4
14
11
5
4
14
11
10
15
1
8
10
15
1
8
10
15
1
8
10
15
1
8
 
 
  + 16x digit from fixed pattern 1
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
 
 
  + 64x digit from fixed pattern 2 (= reflected version of fixed pattern 1)
0
1
3
2
1
0
2
3
3
2
0
1
2
3
1
0
3
2
0
1
2
3
1
0
0
1
3
2
1
0
2
3
0
1
3
2
1
0
2
3
3
2
0
1
2
3
1
0
3
2
0
1
2
3
1
0
0
1
3
2
1
0
2
3
0
1
3
2
1
0
2
3
3
2
0
1
2
3
1
0
3
2
0
1
2
3
1
0
0
1
3
2
1
0
2
3
0
1
3
2
1
0
2
3
3
2
0
1
2
3
1
0
3
2
0
1
2
3
1
0
0
1
3
2
1
0
2
3
0
1
3
2
1
0
2
3
3
2
0
1
2
3
1
0
3
2
0
1
2
3
1
0
0
1
3
2
1
0
2
3
0
1
3
2
1
0
2
3
3
2
0
1
2
3
1
0
3
2
0
1
2
3
1
0
0
1
3
2
1
0
2
3
0
1
3
2
1
0
2
3
3
2
0
1
2
3
1
0
3
2
0
1
2
3
1
0
0
1
3
2
1
0
2
3
0
1
3
2
1
0
2
3
3
2
0
1
2
3
1
0
3
2
0
1
2
3
1
0
0
1
3
2
1
0
2
3
 
 
  = most perfect (Franklin pan)magic 16x16 square
3
118
204
189
67
54
140
253
195
182
12
125
131
246
76
61
224
169
23
98
160
233
87
34
32
105
215
162
96
41
151
226
53
68
254
139
117
4
190
203
245
132
62
75
181
196
126
11
234
159
33
88
170
223
97
24
42
95
225
152
106
31
161
216
19
102
220
173
83
38
156
237
211
166
28
109
147
230
92
45
208
185
7
114
144
249
71
50
16
121
199
178
80
57
135
242
37
84
238
155
101
20
174
219
229
148
46
91
165
212
110
27
250
143
49
72
186
207
113
8
58
79
241
136
122
15
177
200
51
70
252
141
115
6
188
205
243
134
60
77
179
198
124
13
240
153
39
82
176
217
103
18
48
89
231
146
112
25
167
210
5
116
206
187
69
52
142
251
197
180
14
123
133
244
78
59
218
175
17
104
154
239
81
40
26
111
209
168
90
47
145
232
35
86
236
157
99
22
172
221
227
150
44
93
163
214
108
29
256
137
55
66
192
201
119
2
64
73
247
130
128
9
183
194
21
100
222
171
85
36
158
235
213
164
30
107
149
228
94
43
202
191
1
120
138
255
65
56
10
127
193
184
74
63
129
248
 
 
N.B.: It is also possible to use (in stead of 4x4 unsplitted panmagic 4x4 square,) 8x2x splitted
panmagic 4x4 squares of basic pattern method 1.



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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|symmetric & semi (pan)magic 5x5x5 cube|Symmetric & panmagic 7x7x7 cube|Perfect (Nasik) & compact 8x8x8 cube|[More than] perfect magic 9x9x9 cube|Perfect (Nasik) magic 11x11x11 cube|Perfect (Nasik) magic 15x15x15 cube|Trick with 8x8 bimagic square|Favorite Links