Shift method
Use this method to construct magic squares of odd order which are no multiple of 3 (= 5x5, 7x7, 11x11, 13x13, 17x17, ... magic squares). To construct an 11x11 magic square, the first row is 0-a-b-c-d-e-f-g-h-i-j (fill in 1 up to 10 instead of a up to j; that gives 10x9x8x7x6x5x4x3x2 = 3.628.800 possibilities).
To construct row 2 up to 11 of the first grid shift the first row of the first grid each time two places to the left. To construct row 2 up to 11 of the second grid shift the first row of the second grid each time two places to the right.
Take 1x number from first grid +1
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 |
| 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 |
| 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 |
| 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 |
| 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+11x number from second grid
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 |
| 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 |
= panmagic 11x11 square
| 1 | 13 | 25 | 37 | 49 | 61 | 73 | 85 | 97 | 109 | 121 |
| 102 | 114 | 5 | 17 | 29 | 41 | 53 | 65 | 77 | 78 | 90 |
| 82 | 94 | 106 | 118 | 9 | 21 | 33 | 34 | 46 | 58 | 70 |
| 62 | 74 | 86 | 98 | 110 | 111 | 2 | 14 | 26 | 38 | 50 |
| 42 | 54 | 66 | 67 | 79 | 91 | 103 | 115 | 6 | 18 | 30 |
| 22 | 23 | 35 | 47 | 59 | 71 | 83 | 95 | 107 | 119 | 10 |
| 112 | 3 | 15 | 27 | 39 | 51 | 63 | 75 | 87 | 99 | 100 |
| 92 | 104 | 116 | 7 | 19 | 31 | 43 | 55 | 56 | 68 | 80 |
| 72 | 84 | 96 | 108 | 120 | 11 | 12 | 24 | 36 | 48 | 60 |
| 52 | 64 | 76 | 88 | 89 | 101 | 113 | 4 | 16 | 28 | 40 |
| 32 | 44 | 45 | 57 | 69 | 81 | 93 | 105 | 117 | 8 | 20 |
It is possible to shift this 11x11 magic square on a 2x2 carpet of the 11x11 magic square and you get 120 more solutions .
Instead of shift 2 to the left and shift 2 to the right, you can also shift 3, 4 or 5 to the right and/or to the left (e.g. in the first grid shift 3 to the right and in the second grid shift 4 to the left ór 4 to the right). In total you can construct all 89.227.651.645.440.000 panmagic 11x 11 squares (= more than 89 milion x billion possibilities).
Use the shift method to construct magic squares of odd order from 5x5 to infinity.
See 5x5, 7x7, 9x9 (1), 9x9 (2), 11x11, 13x13, 15x15 (1), 15x15 (2), 17x17, 19x19, 21x21 (1), 21x21 (2), 23x23, 25x25, 27x27 (1), 27x27 (2), 29x29 and 31x31
