### Composite, Proportional (1) a

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.

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

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