Again we use 9 panmagic 5x5 squares to construct the 15x15 magic square, but this time we use 9 proportional panmagic 5x5 squares (shift). Proportional means that all 9 panmagic 5x5 squares have the same magic sum of (1/3 x 1695 = ) 565. We use the shift method to construct the panmagic 5x5 squares. Only as column coordinates we do not use the digits 0 up to 4 but 0 up to (9x5 -/- 1 = ) 44 and choose the column coordinates smart so we get 9 proportional panmagic 5x5 squares.
5x column coordinate + 1x row coordinate + 1 = panmagic 5x5 square
0 | 15 | 21 | 30 | 44 | 0 | 1 | 2 | 3 | 4 | 1 | 77 | 108 | 154 | 225 | ||
21 | 30 | 44 | 0 | 15 | 3 | 4 | 0 | 1 | 2 | 109 | 155 | 221 | 2 | 78 | ||
44 | 0 | 15 | 21 | 30 | 1 | 2 | 3 | 4 | 0 | 222 | 3 | 79 | 110 | 151 | ||
15 | 21 | 30 | 44 | 0 | 4 | 0 | 1 | 2 | 3 | 80 | 106 | 152 | 223 | 4 | ||
30 | 44 | 0 | 15 | 21 | 2 | 3 | 4 | 0 | 1 | 153 | 224 | 5 | 76 | 107 | ||
1 | 16 | 22 | 33 | 38 | 0 | 1 | 2 | 3 | 4 | 6 | 82 | 113 | 169 | 195 | ||
22 | 33 | 38 | 1 | 16 | 3 | 4 | 0 | 1 | 2 | 114 | 170 | 191 | 7 | 83 | ||
38 | 1 | 16 | 22 | 33 | 1 | 2 | 3 | 4 | 0 | 192 | 8 | 84 | 115 | 166 | ||
16 | 22 | 33 | 38 | 1 | 4 | 0 | 1 | 2 | 3 | 85 | 111 | 167 | 193 | 9 | ||
33 | 38 | 1 | 16 | 22 | 2 | 3 | 4 | 0 | 1 | 168 | 194 | 10 | 81 | 112 | ||
2 | 17 | 23 | 27 | 41 | 0 | 1 | 2 | 3 | 4 | 11 | 87 | 118 | 139 | 210 | ||
23 | 27 | 41 | 2 | 17 | 3 | 4 | 0 | 1 | 2 | 119 | 140 | 206 | 12 | 88 | ||
41 | 2 | 17 | 23 | 27 | 1 | 2 | 3 | 4 | 0 | 207 | 13 | 89 | 120 | 136 | ||
17 | 23 | 27 | 41 | 2 | 4 | 0 | 1 | 2 | 3 | 90 | 116 | 137 | 208 | 14 | ||
27 | 41 | 2 | 17 | 23 | 2 | 3 | 4 | 0 | 1 | 138 | 209 | 15 | 86 | 117 | ||
3 | 9 | 24 | 31 | 43 | 0 | 1 | 2 | 3 | 4 | 16 | 47 | 123 | 159 | 220 | ||
24 | 31 | 43 | 3 | 9 | 3 | 4 | 0 | 1 | 2 | 124 | 160 | 216 | 17 | 48 | ||
43 | 3 | 9 | 24 | 31 | 1 | 2 | 3 | 4 | 0 | 217 | 18 | 49 | 125 | 156 | ||
9 | 24 | 31 | 43 | 3 | 4 | 0 | 1 | 2 | 3 | 50 | 121 | 157 | 218 | 19 | ||
31 | 43 | 3 | 9 | 24 | 2 | 3 | 4 | 0 | 1 | 158 | 219 | 20 | 46 | 122 | ||
4 | 10 | 25 | 34 | 37 | 0 | 1 | 2 | 3 | 4 | 21 | 52 | 128 | 174 | 190 | ||
25 | 34 | 37 | 4 | 10 | 3 | 4 | 0 | 1 | 2 | 129 | 175 | 186 | 22 | 53 | ||
37 | 4 | 10 | 25 | 34 | 1 | 2 | 3 | 4 | 0 | 187 | 23 | 54 | 130 | 171 | ||
10 | 25 | 34 | 37 | 4 | 4 | 0 | 1 | 2 | 3 | 55 | 126 | 172 | 188 | 24 | ||
34 | 37 | 4 | 10 | 25 | 2 | 3 | 4 | 0 | 1 | 173 | 189 | 25 | 51 | 127 | ||
5 | 11 | 26 | 28 | 40 | 0 | 1 | 2 | 3 | 4 | 26 | 57 | 133 | 144 | 205 | ||
26 | 28 | 40 | 5 | 11 | 3 | 4 | 0 | 1 | 2 | 134 | 145 | 201 | 27 | 58 | ||
40 | 5 | 11 | 26 | 28 | 1 | 2 | 3 | 4 | 0 | 202 | 28 | 59 | 135 | 141 | ||
11 | 26 | 28 | 40 | 5 | 4 | 0 | 1 | 2 | 3 | 60 | 131 | 142 | 203 | 29 | ||
28 | 40 | 5 | 11 | 26 | 2 | 3 | 4 | 0 | 1 | 143 | 204 | 30 | 56 | 132 | ||
6 | 12 | 18 | 32 | 42 | 0 | 1 | 2 | 3 | 4 | 31 | 62 | 93 | 164 | 215 | ||
18 | 32 | 42 | 6 | 12 | 3 | 4 | 0 | 1 | 2 | 94 | 165 | 211 | 32 | 63 | ||
42 | 6 | 12 | 18 | 32 | 1 | 2 | 3 | 4 | 0 | 212 | 33 | 64 | 95 | 161 | ||
12 | 18 | 32 | 42 | 6 | 4 | 0 | 1 | 2 | 3 | 65 | 91 | 162 | 213 | 34 | ||
32 | 42 | 6 | 12 | 18 | 2 | 3 | 4 | 0 | 1 | 163 | 214 | 35 | 61 | 92 | ||
7 | 13 | 19 | 35 | 36 | 0 | 1 | 2 | 3 | 4 | 36 | 67 | 98 | 179 | 185 | ||
19 | 35 | 36 | 7 | 13 | 3 | 4 | 0 | 1 | 2 | 99 | 180 | 181 | 37 | 68 | ||
36 | 7 | 13 | 19 | 35 | 1 | 2 | 3 | 4 | 0 | 182 | 38 | 69 | 100 | 176 | ||
13 | 19 | 35 | 36 | 7 | 4 | 0 | 1 | 2 | 3 | 70 | 96 | 177 | 183 | 39 | ||
35 | 36 | 7 | 13 | 19 | 2 | 3 | 4 | 0 | 1 | 178 | 184 | 40 | 66 | 97 | ||
8 | 14 | 20 | 29 | 39 | 0 | 1 | 2 | 3 | 4 | 41 | 72 | 103 | 149 | 200 | ||
20 | 29 | 39 | 8 | 14 | 3 | 4 | 0 | 1 | 2 | 104 | 150 | 196 | 42 | 73 | ||
39 | 8 | 14 | 20 | 29 | 1 | 2 | 3 | 4 | 0 | 197 | 43 | 74 | 105 | 146 | ||
14 | 20 | 29 | 39 | 8 | 4 | 0 | 1 | 2 | 3 | 75 | 101 | 147 | 198 | 44 | ||
29 | 39 | 8 | 14 | 20 | 2 | 3 | 4 | 0 | 1 | 148 | 199 | 45 | 71 | 102 |
Combine the 9 panmagic 5x5 squares in sequence.
15x15 magic square consisting of 9 proportional panmagic 5x5 squares
1 | 77 | 108 | 154 | 225 | 6 | 82 | 113 | 169 | 195 | 11 | 87 | 118 | 139 | 210 |
109 | 155 | 221 | 2 | 78 | 114 | 170 | 191 | 7 | 83 | 119 | 140 | 206 | 12 | 88 |
222 | 3 | 79 | 110 | 151 | 192 | 8 | 84 | 115 | 166 | 207 | 13 | 89 | 120 | 136 |
80 | 106 | 152 | 223 | 4 | 85 | 111 | 167 | 193 | 9 | 90 | 116 | 137 | 208 | 14 |
153 | 224 | 5 | 76 | 107 | 168 | 194 | 10 | 81 | 112 | 138 | 209 | 15 | 86 | 117 |
16 | 47 | 123 | 159 | 220 | 21 | 52 | 128 | 174 | 190 | 26 | 57 | 133 | 144 | 205 |
124 | 160 | 216 | 17 | 48 | 129 | 175 | 186 | 22 | 53 | 134 | 145 | 201 | 27 | 58 |
217 | 18 | 49 | 125 | 156 | 187 | 23 | 54 | 130 | 171 | 202 | 28 | 59 | 135 | 141 |
50 | 121 | 157 | 218 | 19 | 55 | 126 | 172 | 188 | 24 | 60 | 131 | 142 | 203 | 29 |
158 | 219 | 20 | 46 | 122 | 173 | 189 | 25 | 51 | 127 | 143 | 204 | 30 | 56 | 132 |
31 | 62 | 93 | 164 | 215 | 36 | 67 | 98 | 179 | 185 | 41 | 72 | 103 | 149 | 200 |
94 | 165 | 211 | 32 | 63 | 99 | 180 | 181 | 37 | 68 | 104 | 150 | 196 | 42 | 73 |
212 | 33 | 64 | 95 | 161 | 182 | 38 | 69 | 100 | 176 | 197 | 43 | 74 | 105 | 146 |
65 | 91 | 162 | 213 | 34 | 70 | 96 | 177 | 183 | 39 | 75 | 101 | 147 | 198 | 44 |
163 | 214 | 35 | 61 | 92 | 178 | 184 | 40 | 66 | 97 | 148 | 199 | 45 | 71 | 102 |
This 15x15 magic square is panmagic, 5x5 compact and each 1/3 row/column/diagonal gives 1/3 of the magic sum.