### Composite, Proportional (1) b

Use 9 proportional panmagic 5x5 squares (shift) to construct a 15x15 magic square. 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 numbers 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.

I have used composite method, proportional (1) to construct

15x15, Composite, Prop. (1) b.xls