Basic pattern method (1) a
Use as first grid 16x the same panmagic 4x4 square and as second and third grid two reflecting grids.
1x number from first grid with 16x 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 number from second grid
|
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 number from third grid (= reflection of second grid)
|
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 |
Use basic pattern method (1) to construct magic squares of order is multiple of 4 from 8x8 to infinity. See 8x8, 12x12, 16x16a, 16x16b, 16x16c, 20x20, 24x24a, 24x24b, 28x28, 32x32a, 32x32b, 32x32c and 32x32d
