Reflecting grids (1)
Look how René Chrétien used reflecting grids to produce a 14x14 magic square. Notify that the second (column) grid is a reflection of the first (row) grid.
1x number + 1
| 0 | 1 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 12 | 13 |
| 0 | 1 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 12 | 13 |
| 0 | 12 | 2 | 10 | 9 | 5 | 7 | 6 | 8 | 4 | 3 | 11 | 1 | 13 |
| 13 | 12 | 11 | 10 | 4 | 5 | 7 | 6 | 8 | 9 | 3 | 2 | 1 | 0 |
| 13 | 12 | 2 | 3 | 4 | 5 | 7 | 6 | 8 | 9 | 10 | 11 | 1 | 0 |
| 13 | 12 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 1 | 0 |
| 13 | 12 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 1 | 0 |
| 13 | 12 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 1 | 0 |
| 13 | 12 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 1 | 0 |
| 0 | 1 | 11 | 3 | 4 | 8 | 6 | 7 | 5 | 9 | 10 | 2 | 12 | 13 |
| 0 | 1 | 11 | 10 | 9 | 8 | 6 | 7 | 5 | 4 | 3 | 2 | 12 | 13 |
| 0 | 1 | 2 | 3 | 9 | 8 | 6 | 7 | 5 | 4 | 10 | 11 | 12 | 13 |
| 13 | 1 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 12 | 0 |
| 0 | 1 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 12 | 13 |
+14x number
| 0 | 0 | 0 | 13 | 13 | 13 | 13 | 13 | 13 | 0 | 0 | 0 | 13 | 0 |
| 1 | 1 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 1 | 1 | 1 | 1 | 1 |
| 11 | 11 | 2 | 11 | 2 | 2 | 2 | 2 | 2 | 11 | 11 | 2 | 11 | 11 |
| 10 | 10 | 10 | 10 | 3 | 3 | 3 | 3 | 3 | 3 | 10 | 3 | 10 | 10 |
| 9 | 9 | 9 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 9 | 9 | 9 | 9 |
| 8 | 8 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 8 | 8 | 8 | 8 | 8 |
| 7 | 7 | 7 | 7 | 7 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 7 |
| 6 | 6 | 6 | 6 | 6 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 6 | 6 |
| 5 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 5 | 5 | 5 | 5 |
| 4 | 4 | 4 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 4 | 4 | 4 | 4 |
| 3 | 3 | 3 | 3 | 10 | 10 | 10 | 10 | 10 | 10 | 3 | 10 | 3 | 3 |
| 2 | 2 | 11 | 2 | 11 | 11 | 11 | 11 | 11 | 2 | 2 | 11 | 2 | 2 |
| 12 | 12 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 12 | 12 | 12 | 12 | 12 |
| 13 | 13 | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 13 | 13 | 13 | 0 | 13 |
= 14x14 magic square
| 1 | 2 | 12 | 193 | 192 | 191 | 190 | 189 | 188 | 5 | 4 | 3 | 195 | 14 |
| 15 | 16 | 180 | 179 | 178 | 177 | 176 | 175 | 174 | 19 | 18 | 17 | 27 | 28 |
| 155 | 167 | 31 | 165 | 38 | 34 | 36 | 35 | 37 | 159 | 158 | 40 | 156 | 168 |
| 154 | 153 | 152 | 151 | 47 | 48 | 50 | 49 | 51 | 52 | 144 | 45 | 142 | 141 |
| 140 | 139 | 129 | 60 | 61 | 62 | 64 | 63 | 65 | 66 | 137 | 138 | 128 | 127 |
| 126 | 125 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 122 | 123 | 124 | 114 | 113 |
| 112 | 111 | 101 | 102 | 103 | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 100 | 99 |
| 98 | 97 | 87 | 88 | 89 | 104 | 105 | 106 | 107 | 108 | 109 | 110 | 86 | 85 |
| 84 | 83 | 115 | 116 | 117 | 118 | 119 | 120 | 121 | 80 | 81 | 82 | 72 | 71 |
| 57 | 58 | 68 | 130 | 131 | 135 | 133 | 134 | 132 | 136 | 67 | 59 | 69 | 70 |
| 43 | 44 | 54 | 53 | 150 | 149 | 147 | 148 | 146 | 145 | 46 | 143 | 55 | 56 |
| 29 | 30 | 157 | 32 | 164 | 163 | 161 | 162 | 160 | 33 | 39 | 166 | 41 | 42 |
| 182 | 170 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | 173 | 172 | 171 | 181 | 169 |
| 183 | 184 | 194 | 11 | 10 | 9 | 8 | 7 | 6 | 187 | 186 | 185 | 13 | 196 |
Use the method of reflecting grids (1) to construct magic squares of order is double odd. See 6x6, 10x10, 14x14, 18x18, 22x22, 26x26 en 30x30
