16x16 magic square

Medjig 16x16 magic square

 

You can use the Medjig method of Willem Barink (see the 6x6 magic square) to construct a 16x16 magic square. The first grid consists of 'the 2x2 blown up' version of the 8x8 magic square and the second grid consist of the 2x2 Medjig tiles. If you use a Franklin panmagic 8x8 square and a tight grid of Medjig tiles you can construct a panmagic 16x16 square.

 

Take a number from a cell of the first grid and add 64 x number from the same cell of the second grid.

 

 

+ 1x number

1 1 56 56 27 27 46 46 17 17 40 40 11 11 62 62
1 1 56 56 27 27 46 46 17 17 40 40 11 11 62 62
63 63 10 10 37 37 20 20 47 47 26 26 53 53 4 4
63 63 10 10 37 37 20 20 47 47 26 26 53 53 4 4
38 38 19 19 64 64 9 9 54 54 3 3 48 48 25 25
38 38 19 19 64 64 9 9 54 54 3 3 48 48 25 25
28 28 45 45 2 2 55 55 12 12 61 61 18 18 39 39
28 28 45 45 2 2 55 55 12 12 61 61 18 18 39 39
33 33 24 24 59 59 14 14 49 49 8 8 43 43 30 30
33 33 24 24 59 59 14 14 49 49 8 8 43 43 30 30
31 31 42 42 5 5 52 52 15 15 58 58 21 21 36 36
31 31 42 42 5 5 52 52 15 15 58 58 21 21 36 36
6 6 51 51 32 32 41 41 22 22 35 35 16 16 57 57
6 6 51 51 32 32 41 41 22 22 35 35 16 16 57 57
60 60 13 13 34 34 23 23 44 44 29 29 50 50 7 7
60 60 13 13 34 34 23 23 44 44 29 29 50 50 7 7

 

 

+ 64 x number

0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

 

 

= 16x16 panmagic square

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

 

 

N.B.: Each 1/2 row/colum/diagonal gives 1/2 of the magic sum (1/2 x 2056 = 1028) and each random chosen 4x4 subsquare inside the 16x16 magic square gives the magic sum of 2056.

 

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16x16, Medjig.xls
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16x16 magic square