Take as first grid 9x the same 4x4 in 6x6 magic square and with the second fixed grid you get a magic 18x18 square consisting of 9 proportional 4x4 in 6x6 magic squares.
1x number from grid with 9x the same 4x4 in 6x6 magic square |
|||||||||||||||||
1 |
6 |
9 |
34 |
32 |
29 |
1 |
6 |
9 |
34 |
32 |
29 |
1 |
6 |
9 |
34 |
32 |
29 |
35 |
11 |
18 |
23 |
22 |
2 |
35 |
11 |
18 |
23 |
22 |
2 |
35 |
11 |
18 |
23 |
22 |
2 |
33 |
25 |
20 |
13 |
16 |
4 |
33 |
25 |
20 |
13 |
16 |
4 |
33 |
25 |
20 |
13 |
16 |
4 |
27 |
14 |
15 |
26 |
19 |
10 |
27 |
14 |
15 |
26 |
19 |
10 |
27 |
14 |
15 |
26 |
19 |
10 |
7 |
24 |
21 |
12 |
17 |
30 |
7 |
24 |
21 |
12 |
17 |
30 |
7 |
24 |
21 |
12 |
17 |
30 |
8 |
31 |
28 |
3 |
5 |
36 |
8 |
31 |
28 |
3 |
5 |
36 |
8 |
31 |
28 |
3 |
5 |
36 |
1 |
6 |
9 |
34 |
32 |
29 |
1 |
6 |
9 |
34 |
32 |
29 |
1 |
6 |
9 |
34 |
32 |
29 |
35 |
11 |
18 |
23 |
22 |
2 |
35 |
11 |
18 |
23 |
22 |
2 |
35 |
11 |
18 |
23 |
22 |
2 |
33 |
25 |
20 |
13 |
16 |
4 |
33 |
25 |
20 |
13 |
16 |
4 |
33 |
25 |
20 |
13 |
16 |
4 |
27 |
14 |
15 |
26 |
19 |
10 |
27 |
14 |
15 |
26 |
19 |
10 |
27 |
14 |
15 |
26 |
19 |
10 |
7 |
24 |
21 |
12 |
17 |
30 |
7 |
24 |
21 |
12 |
17 |
30 |
7 |
24 |
21 |
12 |
17 |
30 |
8 |
31 |
28 |
3 |
5 |
36 |
8 |
31 |
28 |
3 |
5 |
36 |
8 |
31 |
28 |
3 |
5 |
36 |
1 |
6 |
9 |
34 |
32 |
29 |
1 |
6 |
9 |
34 |
32 |
29 |
1 |
6 |
9 |
34 |
32 |
29 |
35 |
11 |
18 |
23 |
22 |
2 |
35 |
11 |
18 |
23 |
22 |
2 |
35 |
11 |
18 |
23 |
22 |
2 |
33 |
25 |
20 |
13 |
16 |
4 |
33 |
25 |
20 |
13 |
16 |
4 |
33 |
25 |
20 |
13 |
16 |
4 |
27 |
14 |
15 |
26 |
19 |
10 |
27 |
14 |
15 |
26 |
19 |
10 |
27 |
14 |
15 |
26 |
19 |
10 |
7 |
24 |
21 |
12 |
17 |
30 |
7 |
24 |
21 |
12 |
17 |
30 |
7 |
24 |
21 |
12 |
17 |
30 |
8 |
31 |
28 |
3 |
5 |
36 |
8 |
31 |
28 |
3 |
5 |
36 |
8 |
31 |
28 |
3 |
5 |
36 |
+ 36x number from fixed grid |
|||||||||||||||||
8 |
0 |
8 |
0 |
8 |
0 |
7 |
1 |
7 |
1 |
7 |
1 |
6 |
2 |
6 |
2 |
6 |
2 |
0 |
8 |
0 |
8 |
0 |
8 |
1 |
7 |
1 |
7 |
1 |
7 |
2 |
6 |
2 |
6 |
2 |
6 |
8 |
0 |
8 |
0 |
8 |
0 |
7 |
1 |
7 |
1 |
7 |
1 |
6 |
2 |
6 |
2 |
6 |
2 |
0 |
0 |
8 |
0 |
8 |
8 |
1 |
1 |
7 |
1 |
7 |
7 |
2 |
2 |
6 |
2 |
6 |
6 |
0 |
8 |
0 |
8 |
0 |
8 |
1 |
7 |
1 |
7 |
1 |
7 |
2 |
6 |
2 |
6 |
2 |
6 |
8 |
8 |
0 |
8 |
0 |
0 |
7 |
7 |
1 |
7 |
1 |
1 |
6 |
6 |
2 |
6 |
2 |
2 |
5 |
3 |
5 |
3 |
5 |
3 |
4 |
4 |
4 |
4 |
4 |
4 |
3 |
5 |
3 |
5 |
3 |
5 |
3 |
5 |
3 |
5 |
3 |
5 |
4 |
4 |
4 |
4 |
4 |
4 |
5 |
3 |
5 |
3 |
5 |
3 |
5 |
3 |
5 |
3 |
5 |
3 |
4 |
4 |
4 |
4 |
4 |
4 |
3 |
5 |
3 |
5 |
3 |
5 |
3 |
3 |
5 |
3 |
5 |
5 |
4 |
4 |
4 |
4 |
4 |
4 |
5 |
5 |
3 |
5 |
3 |
3 |
3 |
5 |
3 |
5 |
3 |
5 |
4 |
4 |
4 |
4 |
4 |
4 |
5 |
3 |
5 |
3 |
5 |
3 |
5 |
5 |
3 |
5 |
3 |
3 |
4 |
4 |
4 |
4 |
4 |
4 |
3 |
3 |
5 |
3 |
5 |
5 |
2 |
6 |
2 |
6 |
2 |
6 |
1 |
7 |
1 |
7 |
1 |
7 |
0 |
8 |
0 |
8 |
0 |
8 |
6 |
2 |
6 |
2 |
6 |
2 |
7 |
1 |
7 |
1 |
7 |
1 |
8 |
0 |
8 |
0 |
8 |
0 |
2 |
6 |
2 |
6 |
2 |
6 |
1 |
7 |
1 |
7 |
1 |
7 |
0 |
8 |
0 |
8 |
0 |
8 |
6 |
6 |
2 |
6 |
2 |
2 |
7 |
7 |
1 |
7 |
1 |
1 |
8 |
8 |
0 |
8 |
0 |
0 |
6 |
2 |
6 |
2 |
6 |
2 |
7 |
1 |
7 |
1 |
7 |
1 |
8 |
0 |
8 |
0 |
8 |
0 |
2 |
2 |
6 |
2 |
6 |
6 |
1 |
1 |
7 |
1 |
7 |
7 |
0 |
0 |
8 |
0 |
8 |
8 |
= 18x18 magic square consisting of 9x proportional 4x4 in 6x6 |
|||||||||||||||||
289 |
6 |
297 |
34 |
320 |
29 |
253 |
42 |
261 |
70 |
284 |
65 |
217 |
78 |
225 |
106 |
248 |
101 |
35 |
299 |
18 |
311 |
22 |
290 |
71 |
263 |
54 |
275 |
58 |
254 |
107 |
227 |
90 |
239 |
94 |
218 |
321 |
25 |
308 |
13 |
304 |
4 |
285 |
61 |
272 |
49 |
268 |
40 |
249 |
97 |
236 |
85 |
232 |
76 |
27 |
14 |
303 |
26 |
307 |
298 |
63 |
50 |
267 |
62 |
271 |
262 |
99 |
86 |
231 |
98 |
235 |
226 |
7 |
312 |
21 |
300 |
17 |
318 |
43 |
276 |
57 |
264 |
53 |
282 |
79 |
240 |
93 |
228 |
89 |
246 |
296 |
319 |
28 |
291 |
5 |
36 |
260 |
283 |
64 |
255 |
41 |
72 |
224 |
247 |
100 |
219 |
77 |
108 |
181 |
114 |
189 |
142 |
212 |
137 |
145 |
150 |
153 |
178 |
176 |
173 |
109 |
186 |
117 |
214 |
140 |
209 |
143 |
191 |
126 |
203 |
130 |
182 |
179 |
155 |
162 |
167 |
166 |
146 |
215 |
119 |
198 |
131 |
202 |
110 |
213 |
133 |
200 |
121 |
196 |
112 |
177 |
169 |
164 |
157 |
160 |
148 |
141 |
205 |
128 |
193 |
124 |
184 |
135 |
122 |
195 |
134 |
199 |
190 |
171 |
158 |
159 |
170 |
163 |
154 |
207 |
194 |
123 |
206 |
127 |
118 |
115 |
204 |
129 |
192 |
125 |
210 |
151 |
168 |
165 |
156 |
161 |
174 |
187 |
132 |
201 |
120 |
197 |
138 |
188 |
211 |
136 |
183 |
113 |
144 |
152 |
175 |
172 |
147 |
149 |
180 |
116 |
139 |
208 |
111 |
185 |
216 |
73 |
222 |
81 |
250 |
104 |
245 |
37 |
258 |
45 |
286 |
68 |
281 |
1 |
294 |
9 |
322 |
32 |
317 |
251 |
83 |
234 |
95 |
238 |
74 |
287 |
47 |
270 |
59 |
274 |
38 |
323 |
11 |
306 |
23 |
310 |
2 |
105 |
241 |
92 |
229 |
88 |
220 |
69 |
277 |
56 |
265 |
52 |
256 |
33 |
313 |
20 |
301 |
16 |
292 |
243 |
230 |
87 |
242 |
91 |
82 |
279 |
266 |
51 |
278 |
55 |
46 |
315 |
302 |
15 |
314 |
19 |
10 |
223 |
96 |
237 |
84 |
233 |
102 |
259 |
60 |
273 |
48 |
269 |
66 |
295 |
24 |
309 |
12 |
305 |
30 |
80 |
103 |
244 |
75 |
221 |
252 |
44 |
67 |
280 |
39 |
257 |
288 |
8 |
31 |
316 |
3 |
293 |
324 |
Notify that in the magic 18x18 square each 1/3 row/column/diagonal gives 1/3 of the magic sum.
I have used method composite, proportional (2) to construct
12x12, 18x18, 24x24, 30x30a and 30x30b