### Basic pattern method (2)

Use as first grid 16x the shifted versions of a 4x4 panmagic square and as second grid 16x the same or another (not shifted version of the) 4x4 panmagic square to construct a most perfect (Franklin pan)magic 16x16 square.

In the first grid we need a panmagic 4x4 square (top left) and 15x a (different) shifted version of the panmagic 4x4 square. To get 15x shifted version of the panmagic 4x4 square we use starting positions (= coordinates) on a 2x2 carpet of the panmagic 4x4 square. We must arrange the shifted versions systematically in the 16x16 square to get a most perfect (franklin pan)magic 16x16 square.

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

The second grid is 16x a (not shifted version of a) panmagic 4x4 square..

1x number of grid with 16x shifted version of a panmagic 4x4 square

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

+16x number of a (not shifted version of a) panmagic 4x4 square

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

= most perfect (Franklin pan)magic 16x16 square

 34 85 187 204 35 93 186 196 43 92 178 197 42 84 179 205 255 136 102 17 254 128 103 25 246 129 111 24 247 137 110 16 68 51 221 170 69 59 220 162 77 58 212 163 76 50 213 171 153 238 0 119 152 230 1 127 144 231 9 126 145 239 8 118 38 81 191 200 39 89 190 192 47 88 182 193 46 80 183 201 253 138 100 19 252 130 101 27 244 131 109 26 245 139 108 18 64 55 217 174 65 63 216 166 73 62 208 167 72 54 209 175 155 236 2 117 154 228 3 125 146 229 11 124 147 237 10 116 36 83 189 202 37 91 188 194 45 90 180 195 44 82 181 203 249 142 96 23 248 134 97 31 240 135 105 30 241 143 104 22 66 53 219 172 67 61 218 164 75 60 210 165 74 52 211 173 159 232 6 113 158 224 7 121 150 225 15 120 151 233 14 112 32 87 185 206 33 95 184 198 41 94 176 199 40 86 177 207 251 140 98 21 250 132 99 29 242 133 107 28 243 141 106 20 70 49 223 168 71 57 222 160 79 56 214 161 78 48 215 169 157 234 4 115 156 226 5 123 148 227 13 122 149 235 12 114

16x16, Basic pattern method (2).xls