Perfect magic squaresContact / guestbook3x3 magic square3x3 magic square, explanationSudoku method (1)Sudoku method (2)Sudoku method (3)Pan magic 4x4 squarePan magic 4x4 square, explanationTransformation methodPan magic 5x5 squarePan magic 5x5 square, explanation6x6 magic squareMost perfect magic squares, explanationKhajuraho methodKhajuraho method, explanationBasic pattern method (1)Basic pattern method (2)Basic pattern method (3)Analysis Franklin panm. 8x8Basic key method (1)Basic key method (2)pan magic 9x9 squarePan magic 15x15 squareThe perfect magic squareUltra pan magic 25x25 squarePan magic 27x27 squarePan magic 35x35 squareBordered squaresInlaid squareEach magic sumWater retention challengeMost magic 4x4x4 cubePerfect magic 8x8x8 cubeFavorite Links
Perfect magic squares
Basic pattern method (3)
<HOME>                         <<PREVIOUS]                         [NEXT>>



Information for whiz kids:  How to produce a Franklin panmagic 16x16 square from a panmagic
                                           4x4 square
 
 
 
PERFECT FRANKLIN PAN MAGIC 16x16 SQUARE:
 
It is possible to use a 4x4 carpet of the pattern (don’t split it up!) of a pan magic 4x4 square to produce 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 pan
    magic 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 the 4x4 carpet of the shifted versions of the pan magic 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
 
 
 
 = 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
 


<HOME>                         <<PREVIOUS]                         [NEXT>>

Perfect magic squares|Contact / guestbook|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|Transformation method|Pan magic 5x5 square|Pan magic 5x5 square, explanation|6x6 magic square|Most perfect magic squares, explanation|Khajuraho method|Khajuraho method, explanation|Basic pattern method (1)|Basic pattern method (2)|Basic pattern method (3)|Analysis Franklin panm. 8x8|Basic key method (1)|Basic key method (2)|pan magic 9x9 square|Pan magic 15x15 square|The perfect magic square|Ultra pan magic 25x25 square|Pan magic 27x27 square|Pan magic 35x35 square|Bordered squares|Inlaid square|Each magic sum|Water retention challenge|Most magic 4x4x4 cube|Perfect magic 8x8x8 cube|Favorite Links