Put number 1 in the middle of the top row. Put the numbers 2 up to n (= lenght of the square) each time (using a chess knight movement) 1 cell to the right and 2 cells down. Put number n+1 below number n. Put the numbers n+2 up to 2n each time 1 cell to the right and 2 cells down. Put number 2n+1 below number 2n. Etcetera ...
1 | ||||||||||
7 | ||||||||||
2 | ||||||||||
8 | ||||||||||
3 | ||||||||||
9 | ||||||||||
4 | ||||||||||
10 | ||||||||||
5 | ||||||||||
11 | ||||||||||
12 | 6 |
11x11 symmetric magic square
116 | 93 | 70 | 47 | 24 | 1 | 110 | 87 | 64 | 41 | 18 |
7 | 105 | 82 | 59 | 36 | 13 | 111 | 99 | 76 | 53 | 30 |
19 | 117 | 94 | 71 | 48 | 25 | 2 | 100 | 88 | 65 | 42 |
31 | 8 | 106 | 83 | 60 | 37 | 14 | 112 | 89 | 77 | 54 |
43 | 20 | 118 | 95 | 72 | 49 | 26 | 3 | 101 | 78 | 66 |
55 | 32 | 9 | 107 | 84 | 61 | 38 | 15 | 113 | 90 | 67 |
56 | 44 | 21 | 119 | 96 | 73 | 50 | 27 | 4 | 102 | 79 |
68 | 45 | 33 | 10 | 108 | 85 | 62 | 39 | 16 | 114 | 91 |
80 | 57 | 34 | 22 | 120 | 97 | 74 | 51 | 28 | 5 | 103 |
92 | 69 | 46 | 23 | 11 | 109 | 86 | 63 | 40 | 17 | 115 |
104 | 81 | 58 | 35 | 12 | 121 | 98 | 75 | 52 | 29 | 6 |
You can use this method to construct magic squares of odd order from 3x3 to infinite and you get a symmetric (but not pan)magic square.
See 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29 and 31x31