Lozenge method of John Horton Conway

 

With the Lozenge method of John Horton Conway you get a magic square of odd order and you find all odd numbers in the (white) 'diamond' and all even numbers outside the diamond (in the dark area). See for detailed explanation: Lozenge 5x5 magic square.

 

 

Take 1x number from row grid +1

5 6 7 8 9 10 0 1 2 3 4
4 5 6 7 8 9 10 0 1 2 3
3 4 5 6 7 8 9 10 0 1 2
2 3 4 5 6 7 8 9 10 0 1
1 2 3 4 5 6 7 8 9 10 0
0 1 2 3 4 5 6 7 8 9 10
10 0 1 2 3 4 5 6 7 8 9
9 10 0 1 2 3 4 5 6 7 8
8 9 10 0 1 2 3 4 5 6 7
7 8 9 10 0 1 2 3 4 5 6
6 7 8 9 10 0 1 2 3 4 5

 

 

+ 11x number from column grid

6 7 8 9 10 0 1 2 3 4 5
7 8 9 10 0 1 2 3 4 5 6
8 9 10 0 1 2 3 4 5 6 7
9 10 0 1 2 3 4 5 6 7 8
10 0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10 0
2 3 4 5 6 7 8 9 10 0 1
3 4 5 6 7 8 9 10 0 1 2
4 5 6 7 8 9 10 0 1 2 3
5 6 7 8 9 10 0 1 2 3 4

 

 

= 11x11 Lozenge magic square

72 84 96 108 120 11 12 24 36 48 60
82 94 106 118 9 21 33 34 46 58 70
92 104 116 7 19 31 43 55 56 68 80
102 114 5 17 29 41 53 65 77 78 90
112 3 15 27 39 51 63 75 87 99 100
1 13 25 37 49 61 73 85 97 109 121
22 23 35 47 59 71 83 95 107 119 10
32 44 45 57 69 81 93 105 117 8 20
42 54 66 67 79 91 103 115 6 18 30
52 64 76 88 89 101 113 4 16 28 40
62 74 86 98 110 111 2 14 26 38 50

 

 

Use this method to construct magic squares of odd order (= 3x3, 5x5, 7x7, ... magic square).

 

Download
11x11, Lozenge method.xls
Microsoft Excel werkblad 44.5 KB