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