Benjamin Franklin, an 18th-century American printer, politician, diplomat, scientist, inventor, etc., etc., enjoyed creating magic squares in his free time.
52 | 61 | 4 | 13 | 20 | 29 | 36 | 45 |
14 | 3 | 62 | 51 | 46 | 35 | 30 | 19 |
53 | 60 | 5 | 12 | 21 | 28 | 37 | 44 |
11 | 6 | 59 | 54 | 43 | 38 | 27 | 22 |
55 | 58 | 7 | 10 | 23 | 26 | 39 | 42 |
9 | 8 | 57 | 56 | 41 | 40 | 25 | 24 |
50 | 63 | 2 | 15 | 18 | 31 | 34 | 47 |
16 | 1 | 64 | 49 | 48 | 33 | 32 | 17 |
Later on in his life, Franklin created a 16×16 semi-magic square with similar properties; in other words, each row or column sums to the magic sum, 2056, each half-row sums to half of 2056, and each "bent row" sums to 2056. In addition, the numbers in any 4×4 square drawn within the magic square sum to 2056. Here is the square that Franklin created:
200 | 217 | 232 | 249 | 8 | 25 | 40 | 57 | 72 | 89 | 104 | 121 | 136 | 153 | 168 | 185 |
58 | 39 | 26 | 7 | 250 | 231 | 218 | 199 | 186 | 167 | 154 | 135 | 122 | 103 | 90 | 71 |
198 | 219 | 230 | 251 | 6 | 27 | 38 | 59 | 70 | 91 | 102 | 123 | 134 | 155 | 166 | 187 |
60 | 37 | 28 | 5 | 252 | 229 | 220 | 197 | 188 | 165 | 156 | 133 | 124 | 101 | 92 | 69 |
201 | 216 | 233 | 238 | 9 | 24 | 41 | 56 | 73 | 88 | 105 | 120 | 137 | 152 | 169 | 184 |
55 | 42 | 23 | 10 | 247 | 234 | 215 | 202 | 183 | 170 | 151 | 138 | 119 | 106 | 87 | 74 |
203 | 214 | 235 | 246 | 11 | 22 | 43 | 54 | 75 | 86 | 107 | 118 | 139 | 150 | 171 | 182 |
53 | 44 | 21 | 12 | 245 | 236 | 213 | 204 | 181 | 172 | 149 | 140 | 117 | 108 | 85 | 76 |
205 | 212 | 237 | 244 | 13 | 20 | 45 | 52 | 77 | 84 | 109 | 116 | 141 | 148 | 173 | 180 |
51 | 46 | 19 | 14 | 243 | 238 | 211 | 206 | 179 | 174 | 147 | 142 | 115 | 110 | 83 | 78 |
207 | 210 | 239 | 242 | 15 | 18 | 47 | 50 | 79 | 82 | 111 | 114 | 143 | 146 | 175 | 178 |
49 | 48 | 17 | 16 | 241 | 240 | 209 | 208 | 177 | 176 | 145 | 144 | 113 | 112 | 81 | 80 |
196 | 221 | 228 | 253 | 4 | 29 | 36 | 61 | 68 | 93 | 100 | 125 | 132 | 157 | 164 | 189 |
62 | 35 | 30 | 3 | 254 | 227 | 222 | 195 | 190 | 163 | 158 | 131 | 126 | 99 | 94 | 67 |
194 | 223 | 226 | 255 | 2 | 31 | 34 | 63 | 66 | 95 | 98 | 127 | 130 | 159 | 162 | 191 |
64 | 33 | 32 | 1 | 256 | 225 | 224 | 193 | 192 | 161 | 160 | 129 | 128 | 97 | 96 | 65 |
You may also be interested in Euler's Knight's Tour Magic Square.
Sources used (see bibliography page for titles corresponding to numbers): 33.