Why using the same sum for each row/column/diagonal? In the anti-magic square each row/column/diagonal has a different (sequencial) magic sum.
3x3 anti-magic square
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1 |
8 |
7 |
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16 |
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9 |
5 |
4 |
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18 |
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3 |
2 |
6 |
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11 |
15 |
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12 |
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13 |
15 |
17 |
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Magic sum = 11 up to 18 (14 missing & 15 double)
4x4 anti-magic square
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11 |
14 |
1 |
4 |
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30 |
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5 |
2 |
16 |
10 |
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33 |
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15 |
3 |
8 |
9 |
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35 |
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6 |
12 |
7 |
13 |
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38 |
29 |
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34 |
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37 |
31 |
32 |
36 |
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Magic sum = 29 up to 38
5x5 anti-magic square
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21 |
18 |
6 |
17 |
4 |
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66 |
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7 |
3 |
13 |
16 |
24 |
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63 |
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5 |
20 |
23 |
11 |
1 |
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60 |
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15 |
8 |
19 |
2 |
25 |
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69 |
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14 |
12 |
9 |
22 |
10 |
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67 |
65 |
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59 |
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62 |
61 |
70 |
68 |
64 |
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Magic sum = 59 up to 70
6x6 anti-magic square
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10 |
25 |
32 |
13 |
16 |
9 |
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105 |
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22 |
7 |
3 |
24 |
21 |
30 |
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107 |
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20 |
27 |
18 |
26 |
11 |
6 |
|
108 |
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1 |
31 |
23 |
33 |
17 |
8 |
|
113 |
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19 |
5 |
36 |
12 |
15 |
29 |
|
116 |
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34 |
14 |
2 |
4 |
35 |
28 |
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117 |
118 |
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111 |
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106 |
109 |
114 |
112 |
115 |
110 |
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Magic sum = 105 up to 118
7x7 anti-magic square
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14 |
3 |
34 |
21 |
47 |
29 |
22 |
|
170 |
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43 |
16 |
13 |
25 |
6 |
26 |
44 |
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173 |
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30 |
48 |
24 |
8 |
12 |
9 |
45 |
|
176 |
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10 |
5 |
11 |
38 |
49 |
46 |
19 |
|
178 |
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4 |
41 |
37 |
36 |
33 |
27 |
1 |
|
179 |
|
39 |
17 |
40 |
20 |
7 |
35 |
23 |
|
181 |
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31 |
42 |
18 |
32 |
28 |
2 |
15 |
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168 |
183 |
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|
175 |
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171 |
172 |
177 |
180 |
182 |
174 |
169 |
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Magic sum = 168 up to 183
8x8 anti-magic square
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49 |
16 |
50 |
10 |
19 |
28 |
24 |
56 |
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252 |
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42 |
43 |
11 |
15 |
44 |
38 |
55 |
5 |
|
253 |
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25 |
21 |
48 |
46 |
9 |
37 |
6 |
63 |
|
255 |
|
29 |
47 |
8 |
40 |
51 |
30 |
52 |
1 |
|
258 |
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45 |
22 |
54 |
23 |
20 |
34 |
2 |
62 |
|
262 |
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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 |
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|
260 |
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257 |
259 |
254 |
256 |
264 |
261 |
263 |
266 |
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Magic sum = 252 up to 269
9x9 anti-magic square
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52 |
19 |
81 |
22 |
29 |
15 |
42 |
31 |
76 |
|
367 |
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61 |
10 |
67 |
23 |
54 |
79 |
25 |
33 |
16 |
|
368 |
|
57 |
9 |
71 |
24 |
38 |
1 |
51 |
47 |
75 |
|
373 |
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26 |
78 |
7 |
69 |
66 |
77 |
13 |
27 |
12 |
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375 |
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39 |
21 |
74 |
20 |
37 |
17 |
49 |
55 |
64 |
|
376 |
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8 |
65 |
4 |
62 |
50 |
34 |
73 |
41 |
40 |
|
377 |
|
56 |
68 |
2 |
63 |
14 |
72 |
35 |
44 |
6 |
|
360 |
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53 |
30 |
60 |
32 |
36 |
3 |
46 |
43 |
58 |
|
361 |
|
11 |
70 |
5 |
59 |
48 |
80 |
28 |
45 |
18 |
|
364 |
379 |
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|
369 |
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363 |
370 |
371 |
374 |
372 |
378 |
362 |
366 |
365 |
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Magic sum = 360 up to 379
Source: J.A. Lindon, Ant-magic squares, Recreational mathematic magazine, no. 7, feb. 1962, p. 16-19