### Panmagic & 5x5 compact 15x15 magic square

Use 3x3 the same panmagic 5x5 square (as first grid) to construct a panmagic 15x15 and 5x5 compact square.

Construct the first row of the second grid:

The sum of the numbers of each colour is 5

 0 1 2 0 0 1 2 0 1 2 2 0 1 2 1

The sum of the numbers of each colour is 3

 0 1 2 0 0 1 2 0 1 2 2 0 1 2 1

Construct row 2 up to 15 by shifting the first row each time 3 places to the left.

The third grid is a reflection (rotated by a quarter and mirrored) of the second grid.

 Take 1x number from 3x3 the same panmagic 5x5 square 1 7 13 19 25 1 7 13 19 25 1 7 13 19 25 14 20 21 2 8 14 20 21 2 8 14 20 21 2 8 22 3 9 15 16 22 3 9 15 16 22 3 9 15 16 10 11 17 23 4 10 11 17 23 4 10 11 17 23 4 18 24 5 6 12 18 24 5 6 12 18 24 5 6 12 1 7 13 19 25 1 7 13 19 25 1 7 13 19 25 14 20 21 2 8 14 20 21 2 8 14 20 21 2 8 22 3 9 15 16 22 3 9 15 16 22 3 9 15 16 10 11 17 23 4 10 11 17 23 4 10 11 17 23 4 18 24 5 6 12 18 24 5 6 12 18 24 5 6 12 1 7 13 19 25 1 7 13 19 25 1 7 13 19 25 14 20 21 2 8 14 20 21 2 8 14 20 21 2 8 22 3 9 15 16 22 3 9 15 16 22 3 9 15 16 10 11 17 23 4 10 11 17 23 4 10 11 17 23 4 18 24 5 6 12 18 24 5 6 12 18 24 5 6 12 + 25x number from second grid 0 1 2 0 0 1 2 0 1 2 2 0 1 2 1 0 0 1 2 0 1 2 2 0 1 2 1 0 1 2 2 0 1 2 2 0 1 2 1 0 1 2 0 0 1 2 2 0 1 2 1 0 1 2 0 0 1 2 0 1 1 2 1 0 1 2 0 0 1 2 0 1 2 2 0 0 1 2 0 0 1 2 0 1 2 2 0 1 2 1 0 0 1 2 0 1 2 2 0 1 2 1 0 1 2 2 0 1 2 2 0 1 2 1 0 1 2 0 0 1 2 2 0 1 2 1 0 1 2 0 0 1 2 0 1 1 2 1 0 1 2 0 0 1 2 0 1 2 2 0 0 1 2 0 0 1 2 0 1 2 2 0 1 2 1 0 0 1 2 0 1 2 2 0 1 2 1 0 1 2 2 0 1 2 2 0 1 2 1 0 1 2 0 0 1 2 2 0 1 2 1 0 1 2 0 0 1 2 0 1 1 2 1 0 1 2 0 0 1 2 0 1 2 2 0 + 75x number from third grid 0 0 2 2 1 0 0 2 2 1 0 0 2 2 1 1 0 0 2 2 1 0 0 2 2 1 0 0 2 2 2 1 1 0 1 2 1 1 0 1 2 1 1 0 1 0 2 2 1 0 0 2 2 1 0 0 2 2 1 0 0 0 2 2 1 0 0 2 2 1 0 0 2 2 1 1 1 0 1 2 1 1 0 1 2 1 1 0 1 2 2 2 1 0 0 2 2 1 0 0 2 2 1 0 0 0 2 2 1 0 0 2 2 1 0 0 2 2 1 0 1 0 1 2 1 1 0 1 2 1 1 0 1 2 1 2 1 0 0 2 2 1 0 0 2 2 1 0 0 2 2 2 1 0 0 2 2 1 0 0 2 2 1 0 0 0 1 2 1 1 0 1 2 1 1 0 1 2 1 1 1 0 0 2 2 1 0 0 2 2 1 0 0 2 2 2 1 0 0 2 2 1 0 0 2 2 1 0 0 2 1 2 1 1 0 1 2 1 1 0 1 2 1 1 0 = panmagic 15x15 square 1 32 213 169 100 26 57 163 194 150 51 7 188 219 125 89 20 46 202 158 114 70 71 152 183 139 45 21 177 208 222 78 109 65 141 172 103 134 40 91 197 128 84 15 116 60 211 167 123 54 35 161 192 148 4 10 186 217 98 29 43 74 180 156 112 68 24 155 181 137 18 49 205 206 87 76 107 63 94 175 101 132 13 119 225 126 82 38 144 200 164 170 121 52 8 189 220 146 2 33 214 195 96 27 58 72 153 184 140 66 22 178 209 115 16 47 203 159 90 41 135 61 92 198 129 110 11 117 223 79 85 36 142 173 104 193 149 30 6 187 218 99 5 31 212 168 124 55 56 162 151 182 138 19 25 176 207 88 44 75 201 157 113 69 50 14 95 196 127 83 39 145 221 77 108 64 120 171 102 133 147 3 34 215 216 97 28 59 190 166 122 53 9 165 191 210 136 17 48 204 185 86 42 73 154 160 111 67 23 179 118 224 105 81 37 143 174 80 106 62 93 199 130 131 12

This panmagic 15x15 square is also 5x5 compact.

You can use this method also to construct a 21x21 magic square (take 3x3 the same panmagic 7x7 square).

15x15, Panmagic & 5x5 compact.xls