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 digit 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 digit 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).
