Waarom moet eigenlijk elke rij/kolom/diagonaal dezelfde magische som hebben? Met het anti-magische vierkant heeft elke rij/kolom/diagonaal haar (opeenvolgende) magische som.
3x3 anti-magisch vierkant
|
|
|
|
|
|
|
1 |
8 |
7 |
|
16 |
|
9 |
5 |
4 |
|
18 |
|
3 |
2 |
6 |
|
11 |
15 |
|
|
|
12 |
|
|
13 |
15 |
17 |
|
|
Magische som = 11 t/m 18 (14 ontbreekt & 15 dubbel)
4x4 anti-magisch vierkant
|
|
|
|
|
|
|
|
11 |
14 |
1 |
4 |
|
30 |
|
5 |
2 |
16 |
10 |
|
33 |
|
15 |
3 |
8 |
9 |
|
35 |
|
6 |
12 |
7 |
13 |
|
38 |
29 |
|
|
|
|
34 |
|
|
37 |
31 |
32 |
36 |
|
|
Magische som = 29 t/m 38
5x5 anti-magisch vierkant
|
|
|
|
|
|
|
|
|
21 |
18 |
6 |
17 |
4 |
|
66 |
|
7 |
3 |
13 |
16 |
24 |
|
63 |
|
5 |
20 |
23 |
11 |
1 |
|
60 |
|
15 |
8 |
19 |
2 |
25 |
|
69 |
|
14 |
12 |
9 |
22 |
10 |
|
67 |
65 |
|
|
|
|
|
59 |
|
|
62 |
61 |
70 |
68 |
64 |
|
|
Magische som = 59 t/m 70
6x6 anti-magisch vierkant
|
|
|
|
|
|
|
|
|
|
10 |
25 |
32 |
13 |
16 |
9 |
|
105 |
|
22 |
7 |
3 |
24 |
21 |
30 |
|
107 |
|
20 |
27 |
18 |
26 |
11 |
6 |
|
108 |
|
1 |
31 |
23 |
33 |
17 |
8 |
|
113 |
|
19 |
5 |
36 |
12 |
15 |
29 |
|
116 |
|
34 |
14 |
2 |
4 |
35 |
28 |
|
117 |
118 |
|
|
|
|
|
|
111 |
|
|
106 |
109 |
114 |
112 |
115 |
110 |
|
|
Magische som = 105 t/m 118
7x7 anti-magisch vierkant
|
|
|
|
|
|
|
|
|
|
|
14 |
3 |
34 |
21 |
47 |
29 |
22 |
|
170 |
|
43 |
16 |
13 |
25 |
6 |
26 |
44 |
|
173 |
|
30 |
48 |
24 |
8 |
12 |
9 |
45 |
|
176 |
|
10 |
5 |
11 |
38 |
49 |
46 |
19 |
|
178 |
|
4 |
41 |
37 |
36 |
33 |
27 |
1 |
|
179 |
|
39 |
17 |
40 |
20 |
7 |
35 |
23 |
|
181 |
|
31 |
42 |
18 |
32 |
28 |
2 |
15 |
|
168 |
183 |
|
|
|
|
|
|
|
175 |
|
|
171 |
172 |
177 |
180 |
182 |
174 |
169 |
|
|
Magische som = 168 t/m 183
8x8 anti-magisch vierkant
|
|
|
|
|
|
|
|
|
|
|
|
49 |
16 |
50 |
10 |
19 |
28 |
24 |
56 |
|
252 |
|
42 |
43 |
11 |
15 |
44 |
38 |
55 |
5 |
|
253 |
|
25 |
21 |
48 |
46 |
9 |
37 |
6 |
63 |
|
255 |
|
29 |
47 |
8 |
40 |
51 |
30 |
52 |
1 |
|
258 |
|
45 |
22 |
54 |
23 |
20 |
34 |
2 |
62 |
|
262 |
|
14 |
59 |
18 |
33 |
41 |
26 |
61 |
13 |
|
265 |
|
36 |
12 |
58 |
32 |
27 |
64 |
3 |
35 |
|
267 |
|
17 |
39 |
7 |
57 |
53 |
4 |
60 |
31 |
|
268 |
269 |
|
|
|
|
|
|
|
|
260 |
|
|
257 |
259 |
254 |
256 |
264 |
261 |
263 |
266 |
|
|
Magische som = 252 t/m 269
9x9 anti-magisch vierkant
|
|
|
|
|
|
|
|
|
|
|
|
|
52 |
19 |
81 |
22 |
29 |
15 |
42 |
31 |
76 |
|
367 |
|
61 |
10 |
67 |
23 |
54 |
79 |
25 |
33 |
16 |
|
368 |
|
57 |
9 |
71 |
24 |
38 |
1 |
51 |
47 |
75 |
|
373 |
|
26 |
78 |
7 |
69 |
66 |
77 |
13 |
27 |
12 |
|
375 |
|
39 |
21 |
74 |
20 |
37 |
17 |
49 |
55 |
64 |
|
376 |
|
8 |
65 |
4 |
62 |
50 |
34 |
73 |
41 |
40 |
|
377 |
|
56 |
68 |
2 |
63 |
14 |
72 |
35 |
44 |
6 |
|
360 |
|
53 |
30 |
60 |
32 |
36 |
3 |
46 |
43 |
58 |
|
361 |
|
11 |
70 |
5 |
59 |
48 |
80 |
28 |
45 |
18 |
|
364 |
379 |
|
|
|
|
|
|
|
|
|
369 |
|
|
363 |
370 |
371 |
374 |
372 |
378 |
362 |
366 |
365 |
|
|
Magische som = 360 t/m 379
Bron: J.A. Lindon, Ant-magic squares, Recreational mathematic magazine, no. 7, feb. 1962, p. 16-19