Siamese method

 

Put digit 1 in the middle of the top row. Put the digits 2 up to n (= length of the square) each time one cell diagonal up and to the right. Put digit n+1 below digit n. Put the digits n+2 up to 2n each time one cell diagonal up and to the right. Put digit 2n+1 below digit 2n. Etcetera ...

 

 

15x15 symmetric magic square

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

 

 

You can use this method to construct magic squares of odd order from 3x3 to infinite and you get a symmetric (but not pan)magic square.

 

 

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15x15, Siamese method.xls
Microsoft Excel werkblad 10.4 KB