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• Knight Walk Construction Method

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Franklin Squares
Knight Walk

16x16
15 14 2 3 4 5 9 8 0 1 13 12 11 10 6 7
0 1 13 12 11 10 6 7 15 14 2 3 4 5 9 8
15 14 2 3 4 5 9 8 0 1 13 12 11 10 6 7
0 1 13 12 11 10 6 7 15 14 2 3 4 5 9 8
15 14 2 3 4 5 9 8 0 1 13 12 11 10 6 7
0 1 13 12 11 10 6 7 15 14 2 3 4 5 9 8
15 14 2 3 4 5 9 8 0 1 13 12 11 10 6 7
0 1 13 12 11 10 6 7 15 14 2 3 4 5 9 8
15 14 2 3 4 5 9 8 0 1 13 12 11 10 6 7
0 1 13 12 11 10 6 7 15 14 2 3 4 5 9 8
15 14 2 3 4 5 9 8 0 1 13 12 11 10 6 7
0 1 13 12 11 10 6 7 15 14 2 3 4 5 9 8
15 14 2 3 4 5 9 8 0 1 13 12 11 10 6 7
0 1 13 12 11 10 6 7 15 14 2 3 4 5 9 8
15 14 2 3 4 5 9 8 0 1 13 12 11 10 6 7
0 1 13 12 11 10 6 7 15 14 2 3 4 5 9 8
 
 
15 0 15 0 15 0 15 0 15 0 15 0 15 0 15 0
14 1 14 1 14 1 14 1 14 1 14 1 14 1 14 1
2 13 2 13 2 13 2 13 2 13 2 13 2 13 2 13
3 12 3 12 3 12 3 12 3 12 3 12 3 12 3 12
4 11 4 11 4 11 4 11 4 11 4 11 4 11 4 11
5 10 5 10 5 10 5 10 5 10 5 10 5 10 5 10
9 6 9 6 9 6 9 6 9 6 9 6 9 6 9 6
8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7
0 15 0 15 0 15 0 15 0 15 0 15 0 15 0 15
1 14 1 14 1 14 1 14 1 14 1 14 1 14 1 14
13 2 13 2 13 2 13 2 13 2 13 2 13 2 13 2
12 3 12 3 12 3 12 3 12 3 12 3 12 3 12 3
11 4 11 4 11 4 11 4 11 4 11 4 11 4 11 4
10 5 10 5 10 5 10 5 10 5 10 5 10 5 10 5
6 9 6 9 6 9 6 9 6 9 6 9 6 9 6 9
7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8
 
 
256 225 48 49 80 81 160 129 16 17 224 193 192 161 112 113
15 18 223 194 191 162 111 114 255 226 47 50 79 82 159 130
243 238 35 62 67 94 147 142 3 30 211 206 179 174 99 126
4 29 212 205 180 173 100 125 244 237 36 61 68 93 148 141
245 236 37 60 69 92 149 140 5 28 213 204 181 172 101 124
6 27 214 203 182 171 102 123 246 235 38 59 70 91 150 139
250 231 42 55 74 87 154 135 10 23 218 199 186 167 106 119
9 24 217 200 185 168 105 120 249 232 41 56 73 88 153 136
241 240 33 64 65 96 145 144 1 32 209 208 177 176 97 128
2 31 210 207 178 175 98 127 242 239 34 63 66 95 146 143
254 227 46 51 78 83 158 131 14 19 222 195 190 163 110 115
13 20 221 196 189 164 109 116 253 228 45 52 77 84 157 132
252 229 44 53 76 85 156 133 12 21 220 197 188 165 108 117
11 22 219 198 187 166 107 118 251 230 43 54 75 86 155 134
247 234 39 58 71 90 151 138 7 26 215 202 183 170 103 122
8 25 216 201 184 169 104 121 248 233 40 57 72 89 152 137

This is a knight move construction with the first move into column nine row two in the top square and column two row nine in the second square. It makes a most perfect pandiagonal magic square. Because of that all 2x2s have the same total. I used a sequence that produced bent diagonals and half rows and columns with the proper totals to be a Franklin type square.

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