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

6 7 8 9 10 11 12 0 1 2 3 4 5
5 6 7 8 9 10 11 12 0 1 2 3 4
4 5 6 7 8 9 10 11 12 0 1 2 3
3 4 5 6 7 8 9 10 11 12 0 1 2
2 3 4 5 6 7 8 9 10 11 12 0 1
1 2 3 4 5 6 7 8 9 10 11 12 0
0 1 2 3 4 5 6 7 8 9 10 11 12
12 0 1 2 3 4 5 6 7 8 9 10 11
11 12 0 1 2 3 4 5 6 7 8 9 10
10 11 12 0 1 2 3 4 5 6 7 8 9
9 10 11 12 0 1 2 3 4 5 6 7 8
8 9 10 11 12 0 1 2 3 4 5 6 7
7 8 9 10 11 12 0 1 2 3 4 5 6

 

 

+ 13x number from column grid

7 8 9 10 11 12 0 1 2 3 4 5 6
8 9 10 11 12 0 1 2 3 4 5 6 7
9 10 11 12 0 1 2 3 4 5 6 7 8
10 11 12 0 1 2 3 4 5 6 7 8 9
11 12 0 1 2 3 4 5 6 7 8 9 10
12 0 1 2 3 4 5 6 7 8 9 10 11
0 1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12 0
2 3 4 5 6 7 8 9 10 11 12 0 1
3 4 5 6 7 8 9 10 11 12 0 1 2
4 5 6 7 8 9 10 11 12 0 1 2 3
5 6 7 8 9 10 11 12 0 1 2 3 4
6 7 8 9 10 11 12 0 1 2 3 4 5

 

 

= 13x13 Lozenge magic square

98 112 126 140 154 168 13 14 28 42 56 70 84
110 124 138 152 166 11 25 39 40 54 68 82 96
122 136 150 164 9 23 37 51 65 66 80 94 108
134 148 162 7 21 35 49 63 77 91 92 106 120
146 160 5 19 33 47 61 75 89 103 117 118 132
158 3 17 31 45 59 73 87 101 115 129 143 144
1 15 29 43 57 71 85 99 113 127 141 155 169
26 27 41 55 69 83 97 111 125 139 153 167 12
38 52 53 67 81 95 109 123 137 151 165 10 24
50 64 78 79 93 107 121 135 149 163 8 22 36
62 76 90 104 105 119 133 147 161 6 20 34 48
74 88 102 116 130 131 145 159 4 18 32 46 60
86 100 114 128 142 156 157 2 16 30 44 58 72

 

 

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

 

Download
13x13, Lozenge method.xls
Microsoft Excel werkblad 49.0 KB