The smallest possible multiplicative magic cube (here smallest = using the smallest possible integers) is an unsolved problem. It is also a good factorization problem. Until now, the best known cube used integers <= 416, in a 4x4x4 cube. A 3x3x3 cube can't be "smaller", because the best possible 3x3x3 use 900. Here is the NEW best known cube: it uses integers <= 364, again in a 4x4x4 cube. You can check that its integers are distinct, that its rows, columns, pillars and 4 main diagonals give the same product P = 17 297 280, each line being a different factorization of this same P. It was not asked (it is not a "perfect" magic cube), but a supplemental property: some small diagonals give again the same product. 52 168 15 132 36 55 273 32 231 12 96 65 40 156 44 63 42 11 234 160 260 144 3 154 8 182 220 54 198 60 112 13 165 72 16 91 56 26 264 45 312 120 21 22 6 77 195 192 48 130 308 9 33 84 80 78 30 66 39 224 364 24 18 110 Is it possible to construct a multiplicative magic cube with smaller integers? Christian. www.multimagie.com/indexengl.htm