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).

 

 

Download
11x11, Shift method.xls
Microsoft Excel werkblad 42.0 KB