### Basic pattern method (2)

Use (as first grid) a splitted 4x4 panmagic square to construct a 16x16 most perfect (Franklin pan)magic square.

Choose one of the 4x4 panmagic squares and split it as follows:

 16 3 10 5 16 5 3 10 2 13 8 11 13 8 2 11 7 12 1 14 12 1 7 14 9 6 15 4 9 4 6 15

Fill in the empty cells, crosswise, with the same numbers of the 4x4 square:

 16 4 9 5 15 3 10 6 1 13 8 12 2 14 7 11 8 12 1 13 7 11 2 14 9 5 16 4 10 6 15 3

Fill the first grid of the 16x16 magic square with the two 4x4 squares.

The second grid is a fixed grid.

Take 1x number from first grid

 16 4 9 5 15 3 10 6 16 4 9 5 15 3 10 6 1 13 8 12 2 14 7 11 1 13 8 12 2 14 7 11 8 12 1 13 7 11 2 14 8 12 1 13 7 11 2 14 9 5 16 4 10 6 15 3 9 5 16 4 10 6 15 3 16 4 9 5 15 3 10 6 16 4 9 5 15 3 10 6 1 13 8 12 2 14 7 11 1 13 8 12 2 14 7 11 8 12 1 13 7 11 2 14 8 12 1 13 7 11 2 14 9 5 16 4 10 6 15 3 9 5 16 4 10 6 15 3 16 4 9 5 15 3 10 6 16 4 9 5 15 3 10 6 1 13 8 12 2 14 7 11 1 13 8 12 2 14 7 11 8 12 1 13 7 11 2 14 8 12 1 13 7 11 2 14 9 5 16 4 10 6 15 3 9 5 16 4 10 6 15 3 16 4 9 5 15 3 10 6 16 4 9 5 15 3 10 6 1 13 8 12 2 14 7 11 1 13 8 12 2 14 7 11 8 12 1 13 7 11 2 14 8 12 1 13 7 11 2 14 9 5 16 4 10 6 15 3 9 5 16 4 10 6 15 3

+ 16x number from second grid

 1 15 0 14 1 15 0 14 0 14 1 15 0 14 1 15 0 14 1 15 0 14 1 15 1 15 0 14 1 15 0 14 15 1 14 0 15 1 14 0 14 0 15 1 14 0 15 1 14 0 15 1 14 0 15 1 15 1 14 0 15 1 14 0 3 13 2 12 3 13 2 12 2 12 3 13 2 12 3 13 2 12 3 13 2 12 3 13 3 13 2 12 3 13 2 12 13 3 12 2 13 3 12 2 12 2 13 3 12 2 13 3 12 2 13 3 12 2 13 3 13 3 12 2 13 3 12 2 5 11 4 10 5 11 4 10 4 10 5 11 4 10 5 11 4 10 5 11 4 10 5 11 5 11 4 10 5 11 4 10 11 5 10 4 11 5 10 4 10 4 11 5 10 4 11 5 10 4 11 5 10 4 11 5 11 5 10 4 11 5 10 4 7 9 6 8 7 9 6 8 6 8 7 9 6 8 7 9 6 8 7 9 6 8 7 9 7 9 6 8 7 9 6 8 9 7 8 6 9 7 8 6 8 6 9 7 8 6 9 7 8 6 9 7 8 6 9 7 9 7 8 6 9 7 8 6

= most perfect (Franklin pan)magic 16x16 square

 32 244 9 229 31 243 10 230 16 228 25 245 15 227 26 246 1 237 24 252 2 238 23 251 17 253 8 236 18 254 7 235 248 28 225 13 247 27 226 14 232 12 241 29 231 11 242 30 233 5 256 20 234 6 255 19 249 21 240 4 250 22 239 3 64 212 41 197 63 211 42 198 48 196 57 213 47 195 58 214 33 205 56 220 34 206 55 219 49 221 40 204 50 222 39 203 216 60 193 45 215 59 194 46 200 44 209 61 199 43 210 62 201 37 224 52 202 38 223 51 217 53 208 36 218 54 207 35 96 180 73 165 95 179 74 166 80 164 89 181 79 163 90 182 65 173 88 188 66 174 87 187 81 189 72 172 82 190 71 171 184 92 161 77 183 91 162 78 168 76 177 93 167 75 178 94 169 69 192 84 170 70 191 83 185 85 176 68 186 86 175 67 128 148 105 133 127 147 106 134 112 132 121 149 111 131 122 150 97 141 120 156 98 142 119 155 113 157 104 140 114 158 103 139 152 124 129 109 151 123 130 110 136 108 145 125 135 107 146 126 137 101 160 116 138 102 159 115 153 117 144 100 154 118 143 99

Use the basic pattern method (2) also to construct a most perfect 8x8 magic square.

16x16, Basic pattern method (2).xls
Microsoft Excel werkblad 529.0 KB