Use 25 proportional (semi)magic 3x3 squares to produce a 15x15 magic square. Proportional means that all 25 (semi)magic 3x3 squares have the same magic sum of (1/5 x 1695 = ) 339. Use the row and column coordinates of the 3x3 magic square. Don't use the numbers 0 up to 2, but 1 up to (25x3 = ) 75 instead. You must divide the row coordinates proportional over the 25 magic 3x3 squares. Use the table and connect each of the 5 rows to the other 5 rows to get (5x5x3 =) 75 row coordinates:
1 | 3 | 5 | 9 | |
2 | 5 | 2 | 9 | |
3 | 2 | 4 | 9 | |
4 | 4 | 1 | 9 | |
5 | 1 | 3 | 9 |
Construct the 25 (semi)magic 3x3 squares.
Row coordinate +75x column coordinate = (semi)magic 3x3 square
38 | 1 | 75 | 0 | 2 | 1 | 38 | 151 | 150 | ||
75 | 38 | 1 | 2 | 1 | 0 | 225 | 113 | 1 | ||
1 | 75 | 38 | 1 | 0 | 2 | 76 | 75 | 188 | ||
40 | 2 | 72 | 0 | 2 | 1 | 40 | 152 | 147 | ||
72 | 40 | 2 | 2 | 1 | 0 | 222 | 115 | 2 | ||
2 | 72 | 40 | 1 | 0 | 2 | 77 | 72 | 190 | ||
37 | 3 | 74 | 0 | 2 | 1 | 37 | 153 | 149 | ||
74 | 37 | 3 | 2 | 1 | 0 | 224 | 112 | 3 | ||
3 | 74 | 37 | 1 | 0 | 2 | 78 | 74 | 187 | ||
39 | 4 | 71 | 0 | 2 | 1 | 39 | 154 | 146 | ||
71 | 39 | 4 | 2 | 1 | 0 | 221 | 114 | 4 | ||
4 | 71 | 39 | 1 | 0 | 2 | 79 | 71 | 189 | ||
36 | 5 | 73 | 0 | 2 | 1 | 36 | 155 | 148 | ||
73 | 36 | 5 | 2 | 1 | 0 | 223 | 111 | 5 | ||
5 | 73 | 36 | 1 | 0 | 2 | 80 | 73 | 186 | ||
48 | 6 | 60 | 0 | 2 | 1 | 48 | 156 | 135 | ||
60 | 48 | 6 | 2 | 1 | 0 | 210 | 123 | 6 | ||
6 | 60 | 48 | 1 | 0 | 2 | 81 | 60 | 198 | ||
50 | 7 | 57 | 0 | 2 | 1 | 50 | 157 | 132 | ||
57 | 50 | 7 | 2 | 1 | 0 | 207 | 125 | 7 | ||
7 | 57 | 50 | 1 | 0 | 2 | 82 | 57 | 200 | ||
47 | 8 | 59 | 0 | 2 | 1 | 47 | 158 | 134 | ||
59 | 47 | 8 | 2 | 1 | 0 | 209 | 122 | 8 | ||
8 | 59 | 47 | 1 | 0 | 2 | 83 | 59 | 197 | ||
49 | 9 | 56 | 0 | 2 | 1 | 49 | 159 | 131 | ||
56 | 49 | 9 | 2 | 1 | 0 | 206 | 124 | 9 | ||
9 | 56 | 49 | 1 | 0 | 2 | 84 | 56 | 199 | ||
46 | 10 | 58 | 0 | 2 | 1 | 46 | 160 | 133 | ||
58 | 46 | 10 | 2 | 1 | 0 | 208 | 121 | 10 | ||
10 | 58 | 46 | 1 | 0 | 2 | 85 | 58 | 196 | ||
33 | 11 | 70 | 0 | 2 | 1 | 33 | 161 | 145 | ||
70 | 33 | 11 | 2 | 1 | 0 | 220 | 108 | 11 | ||
11 | 70 | 33 | 1 | 0 | 2 | 86 | 70 | 183 | ||
35 | 12 | 67 | 0 | 2 | 1 | 35 | 162 | 142 | ||
67 | 35 | 12 | 2 | 1 | 0 | 217 | 110 | 12 | ||
12 | 67 | 35 | 1 | 0 | 2 | 87 | 67 | 185 | ||
32 | 13 | 69 | 0 | 2 | 1 | 32 | 163 | 144 | ||
69 | 32 | 13 | 2 | 1 | 0 | 219 | 107 | 13 | ||
13 | 69 | 32 | 1 | 0 | 2 | 88 | 69 | 182 | ||
34 | 14 | 66 | 0 | 2 | 1 | 34 | 164 | 141 | ||
66 | 34 | 14 | 2 | 1 | 0 | 216 | 109 | 14 | ||
14 | 66 | 34 | 1 | 0 | 2 | 89 | 66 | 184 | ||
31 | 15 | 68 | 0 | 2 | 1 | 31 | 165 | 143 | ||
68 | 31 | 15 | 2 | 1 | 0 | 218 | 106 | 15 | ||
15 | 68 | 31 | 1 | 0 | 2 | 90 | 68 | 181 | ||
43 | 16 | 55 | 0 | 2 | 1 | 43 | 166 | 130 | ||
55 | 43 | 16 | 2 | 1 | 0 | 205 | 118 | 16 | ||
16 | 55 | 43 | 1 | 0 | 2 | 91 | 55 | 193 | ||
45 | 17 | 52 | 0 | 2 | 1 | 45 | 167 | 127 | ||
52 | 45 | 17 | 2 | 1 | 0 | 202 | 120 | 17 | ||
17 | 52 | 45 | 1 | 0 | 2 | 92 | 52 | 195 | ||
42 | 18 | 54 | 0 | 2 | 1 | 42 | 168 | 129 | ||
54 | 42 | 18 | 2 | 1 | 0 | 204 | 117 | 18 | ||
18 | 54 | 42 | 1 | 0 | 2 | 93 | 54 | 192 | ||
44 | 19 | 51 | 0 | 2 | 1 | 44 | 169 | 126 | ||
51 | 44 | 19 | 2 | 1 | 0 | 201 | 119 | 19 | ||
19 | 51 | 44 | 1 | 0 | 2 | 94 | 51 | 194 | ||
41 | 20 | 53 | 0 | 2 | 1 | 41 | 170 | 128 | ||
53 | 41 | 20 | 2 | 1 | 0 | 203 | 116 | 20 | ||
20 | 53 | 41 | 1 | 0 | 2 | 95 | 53 | 191 | ||
28 | 21 | 65 | 0 | 2 | 1 | 28 | 171 | 140 | ||
65 | 28 | 21 | 2 | 1 | 0 | 215 | 103 | 21 | ||
21 | 65 | 28 | 1 | 0 | 2 | 96 | 65 | 178 | ||
30 | 22 | 62 | 0 | 2 | 1 | 30 | 172 | 137 | ||
62 | 30 | 22 | 2 | 1 | 0 | 212 | 105 | 22 | ||
22 | 62 | 30 | 1 | 0 | 2 | 97 | 62 | 180 | ||
27 | 23 | 64 | 0 | 2 | 1 | 27 | 173 | 139 | ||
64 | 27 | 23 | 2 | 1 | 0 | 214 | 102 | 23 | ||
23 | 64 | 27 | 1 | 0 | 2 | 98 | 64 | 177 | ||
29 | 24 | 61 | 0 | 2 | 1 | 29 | 174 | 136 | ||
61 | 29 | 24 | 2 | 1 | 0 | 211 | 104 | 24 | ||
24 | 61 | 29 | 1 | 0 | 2 | 99 | 61 | 179 | ||
26 | 25 | 63 | 0 | 2 | 1 | 26 | 175 | 138 | ||
63 | 26 | 25 | 2 | 1 | 0 | 213 | 101 | 25 | ||
25 | 63 | 26 | 1 | 0 | 2 | 100 | 63 | 176 |
Put the 25 (semi)magic 3x3 squares together (for example in sequence of the middle number of the 3x3 sub-square):
15x15 magic square
26 | 175 | 138 | 27 | 173 | 139 | 28 | 171 | 140 | 29 | 174 | 136 | 30 | 172 | 137 |
213 | 101 | 25 | 214 | 102 | 23 | 215 | 103 | 21 | 211 | 104 | 24 | 212 | 105 | 22 |
100 | 63 | 176 | 98 | 64 | 177 | 96 | 65 | 178 | 99 | 61 | 179 | 97 | 62 | 180 |
31 | 165 | 143 | 32 | 163 | 144 | 33 | 161 | 145 | 34 | 164 | 141 | 35 | 162 | 142 |
218 | 106 | 15 | 219 | 107 | 13 | 220 | 108 | 11 | 216 | 109 | 14 | 217 | 110 | 12 |
90 | 68 | 181 | 88 | 69 | 182 | 86 | 70 | 183 | 89 | 66 | 184 | 87 | 67 | 185 |
36 | 155 | 148 | 37 | 153 | 149 | 38 | 151 | 150 | 39 | 154 | 146 | 40 | 152 | 147 |
223 | 111 | 5 | 224 | 112 | 3 | 225 | 113 | 1 | 221 | 114 | 4 | 222 | 115 | 2 |
80 | 73 | 186 | 78 | 74 | 187 | 76 | 75 | 188 | 79 | 71 | 189 | 77 | 72 | 190 |
41 | 170 | 128 | 42 | 168 | 129 | 43 | 166 | 130 | 44 | 169 | 126 | 45 | 167 | 127 |
203 | 116 | 20 | 204 | 117 | 18 | 205 | 118 | 16 | 201 | 119 | 19 | 202 | 120 | 17 |
95 | 53 | 191 | 93 | 54 | 192 | 91 | 55 | 193 | 94 | 51 | 194 | 92 | 52 | 195 |
46 | 160 | 133 | 47 | 158 | 134 | 48 | 156 | 135 | 49 | 159 | 131 | 50 | 157 | 132 |
208 | 121 | 10 | 209 | 122 | 8 | 210 | 123 | 6 | 206 | 124 | 9 | 207 | 125 | 7 |
85 | 58 | 196 | 83 | 59 | 197 | 81 | 60 | 198 | 84 | 56 | 199 | 82 | 57 | 200 |
Each 1/5 row/column give 1/5 of the magic sum and the 15x15 magic square is 3x3 compact.