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Magic squares (most perfect, [Franklin] panmagic & inlaid)
Detailed explanation about the structure and construction of magic squares
Basic key method (1)
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How to produce a most perfect (Franklin pan)magic square
 
 
A perfect Franklin panmagic square (for each multiple of 8) can be produced using the basic key method
of construction. See the basic key method of construction executed to produce a most perfect 16x16
(Franklin pan)magic square below.

 
1
2
 
 
3
4
 
 
5
6
 
 
7
8
 
 
 
 
1
2
 
 
3
4
 
 
5
6
 
 
7
8

 
Ensure that the sum of each column is the size of the magic square plus 1 (so 16 + 1 = 17).

 
1
2
16
15
3
4
14
13
5
6
12
11
7
8
10
9
16
15
1
2
14
13
3
4
12
11
5
6
10
9
7
8
 
 
Copy the two rows to the bottom of the square until the size of the magic square has been reached.
 
 
 Column:
1
2
16
15
3
4
14
13
5
6
12
11
7
8
10
9
16
15
1
2
14
13
3
4
12
11
5
6
10
9
7
8
1
2
16
15
3
4
14
13
5
6
12
11
7
8
10
9
16
15
1
2
14
13
3
4
12
11
5
6
10
9
7
8
1
2
16
15
3
4
14
13
5
6
12
11
7
8
10
9
16
15
1
2
14
13
3
4
12
11
5
6
10
9
7
8
1
2
16
15
3
4
14
13
5
6
12
11
7
8
10
9
16
15
1
2
14
13
3
4
12
11
5
6
10
9
7
8
1
2
16
15
3
4
14
13
5
6
12
11
7
8
10
9
16
15
1
2
14
13
3
4
12
11
5
6
10
9
7
8
1
2
16
15
3
4
14
13
5
6
12
11
7
8
10
9
16
15
1
2
14
13
3
4
12
11
5
6
10
9
7
8
1
2
16
15
3
4
14
13
5
6
12
11
7
8
10
9
16
15
1
2
14
13
3
4
12
11
5
6
10
9
7
8
1
2
16
15
3
4
14
13
5
6
12
11
7
8
10
9
16
15
1
2
14
13
3
4
12
11
5
6
10
9
7
8
 
 
Produce a second square by rotating the first square (a quarter turn to the left).
 
 
 Row:
9
8
9
8
9
8
9
8
9
8
9
8
9
8
9
8
10
7
10
7
10
7
10
7
10
7
10
7
10
7
10
7
8
9
8
9
8
9
8
9
8
9
8
9
8
9
8
9
7
10
7
10
7
10
7
10
7
10
7
10
7
10
7
10
11
6
11
6
11
6
11
6
11
6
11
6
11
6
11
6
12
5
12
5
12
5
12
5
12
5
12
5
12
5
12
5
6
11
6
11
6
11
6
11
6
11
6
11
6
11
6
11
5
12
5
12
5
12
5
12
5
12
5
12
5
12
5
12
13
4
13
4
13
4
13
4
13
4
13
4
13
4
13
4
14
3
14
3
14
3
14
3
14
3
14
3
14
3
14
3
4
13
4
13
4
13
4
13
4
13
4
13
4
13
4
13
3
14
3
14
3
14
3
14
3
14
3
14
3
14
3
14
15
2
15
2
15
2
15
2
15
2
15
2
15
2
15
2
16
1
16
1
16
1
16
1
16
1
16
1
16
1
16
1
2
15
2
15
2
15
2
15
2
15
2
15
2
15
2
15
1
16
1
16
1
16
1
16
1
16
1
16
1
16
1
16
 
 
Take a digit (= column coordinate) from a cell of the column square and take a digit (= row coordinate)
from the same cell of the row square and look up in the table below the digit you need to fill in.
 


 
 
Column:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Row:
1
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
 
2
 
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
 
3
 
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
 
4
 
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
 
5
 
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
 
6
 
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
 
7
 
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
 
8
 
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
 
9
 
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
 
10
 
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
 
11
 
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
 
12
 
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
 
13
 
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
 
14
 
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
 
15
 
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
 
16
 
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
 
  
Result:
 
129
114
144
127
131
116
142
125
133
118
140
123
135
120
138
121
160
111
145
98
158
109
147
100
156
107
149
102
154
105
151
104
113
130
128
143
115
132
126
141
117
134
124
139
119
136
122
137
112
159
97
146
110
157
99
148
108
155
101
150
106
153
103
152
161
82
176
95
163
84
174
93
165
86
172
91
167
88
170
89
192
79
177
66
190
77
179
68
188
75
181
70
186
73
183
72
81
162
96
175
83
164
94
173
85
166
92
171
87
168
90
169
80
191
65
178
78
189
67
180
76
187
69
182
74
185
71
184
193
50
208
63
195
52
206
61
197
54
204
59
199
56
202
57
224
47
209
34
222
45
211
36
220
43
213
38
218
41
215
40
49
194
64
207
51
196
62
205
53
198
60
203
55
200
58
201
48
223
33
210
46
221
35
212
44
219
37
214
42
217
39
216
225
18
240
31
227
20
238
29
229
22
236
27
231
24
234
25
256
15
241
2
254
13
243
4
252
11
245
6
250
9
247
8
17
226
32
239
19
228
30
237
21
230
28
235
23
232
26
233
16
255
1
242
14
253
3
244
12
251
5
246