2) Probably the smallest possible example of 11x11 pandiagonal multiplicative magic square.
Christian
Did you fill in any of the smaller values?
--Ed Pegg Jr
My two best examples of 11x11 pandiagonal multiplicative squares, meaning that each square has 44 alignments to get the same product: -with the smallest possible product (P=160986670580736000000, SLE=580): 260 160 85 38 345 200 116 1 84 54 33 14 135 88 52 16 204 114 69 500 290 5 100 29 12 42 27 220 130 80 34 285 184 102 57 460 250 145 2 105 72 44 13 192 110 65 32 255 152 92 25 348 6 21 180 15 56 36 11 156 96 51 380 230 125 58 23 300 174 3 140 90 55 26 240 136 76 48 340 190 115 50 435 8 28 9 132 78 45 22 195 128 68 19 276 150 87 20 70 232 4 7 108 66 39 320 170 95 46 375 228 138 75 580 10 35 18 165 104 64 17 -with the smallest largest entry: (P=1441031935035813120000, SLE=341): 104 85 38 220 161 100 27 252 174 93 11 290 217 4 13 153 114 66 253 200 135 56 25 243 168 87 341 8 65 34 190 154 92 57 242 184 125 54 280 203 124 1 117 102 5 26 170 133 88 23 225 162 84 319 248 196 116 31 9 78 51 209 176 115 50 270 207 150 81 308 232 155 2 130 119 76 22 187 152 110 46 250 189 112 29 279 6 39 62 10 91 68 19 198 138 75 297 224 145 108 28 261 186 3 143 136 95 44 230 175 132 69 275 216 140 58 310 7 52 17 171 First square checked OK by Edwin Clark and Don Reble. But first time that I send the second square = not checked by somebody else. The 44 products should be OK, and all integers should be distinct. I think that it will be impossible to construct 11x11 pandiagonal multiplicative squares with best values. Christian.