### Anti-magic square

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

 1 8 7 16 9 5 4 18 3 2 6 11 15 12 13 15 17

Magic sum = 11 up to 18 (14 missing & 15 double)

4x4 anti-magic square

 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

Magic sum = 29 up to 38

5x5 anti-magic square

 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

Magic sum = 59 up to 70

6x6 anti-magic square

 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

Magic sum = 105 up to 118

7x7 anti-magic square

 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

Magic sum = 168 up to 183

8x8 anti-magic square

 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

Magic sum = 252 up to 269

9x9 anti-magic square

 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

Magic sum = 360 up to 379

Source: J.A. Lindon, Ant-magic squares, Recreational mathematic magazine, no. 7, feb. 1962, p. 16-19

Specials, Anti-magic square.xls