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

7 8 9 10 11 12 13 14 0 1 2 3 4 5 6
6 7 8 9 10 11 12 13 14 0 1 2 3 4 5
5 6 7 8 9 10 11 12 13 14 0 1 2 3 4
4 5 6 7 8 9 10 11 12 13 14 0 1 2 3
3 4 5 6 7 8 9 10 11 12 13 14 0 1 2
2 3 4 5 6 7 8 9 10 11 12 13 14 0 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
14 0 1 2 3 4 5 6 7 8 9 10 11 12 13
13 14 0 1 2 3 4 5 6 7 8 9 10 11 12
12 13 14 0 1 2 3 4 5 6 7 8 9 10 11
11 12 13 14 0 1 2 3 4 5 6 7 8 9 10
10 11 12 13 14 0 1 2 3 4 5 6 7 8 9
9 10 11 12 13 14 0 1 2 3 4 5 6 7 8
8 9 10 11 12 13 14 0 1 2 3 4 5 6 7

 

 

+ 15x number from column grid

8 9 10 11 12 13 14 0 1 2 3 4 5 6 7
9 10 11 12 13 14 0 1 2 3 4 5 6 7 8
10 11 12 13 14 0 1 2 3 4 5 6 7 8 9
11 12 13 14 0 1 2 3 4 5 6 7 8 9 10
12 13 14 0 1 2 3 4 5 6 7 8 9 10 11
13 14 0 1 2 3 4 5 6 7 8 9 10 11 12
14 0 1 2 3 4 5 6 7 8 9 10 11 12 13
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0
2 3 4 5 6 7 8 9 10 11 12 13 14 0 1
3 4 5 6 7 8 9 10 11 12 13 14 0 1 2
4 5 6 7 8 9 10 11 12 13 14 0 1 2 3
5 6 7 8 9 10 11 12 13 14 0 1 2 3 4
6 7 8 9 10 11 12 13 14 0 1 2 3 4 5
7 8 9 10 11 12 13 14 0 1 2 3 4 5 6

 

 

= 15x15 Lozenge magic square

128 144 160 176 192 208 224 15 16 32 48 64 80 96 112
142 158 174 190 206 222 13 29 45 46 62 78 94 110 126
156 172 188 204 220 11 27 43 59 75 76 92 108 124 140
170 186 202 218 9 25 41 57 73 89 105 106 122 138 154
184 200 216 7 23 39 55 71 87 103 119 135 136 152 168
198 214 5 21 37 53 69 85 101 117 133 149 165 166 182
212 3 19 35 51 67 83 99 115 131 147 163 179 195 196
1 17 33 49 65 81 97 113 129 145 161 177 193 209 225
30 31 47 63 79 95 111 127 143 159 175 191 207 223 14
44 60 61 77 93 109 125 141 157 173 189 205 221 12 28
58 74 90 91 107 123 139 155 171 187 203 219 10 26 42
72 88 104 120 121 137 153 169 185 201 217 8 24 40 56
86 102 118 134 150 151 167 183 199 215 6 22 38 54 70
100 116 132 148 164 180 181 197 213 4 20 36 52 68 84
114 130 146 162 178 194 210 211 2 18 34 50 66 82 98

 

 

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

 

Download
15x15, Lozenge method.xls
Microsoft Excel werkblad 76.5 KB