If you like factorization problems and/or magic object, you should like this 3 dimensions problem. > What is the smallest composite integer MM(3) > from which we can pick and organize distinct factors in a CUBE > multiplicatively magic in any line of any direction, > including any broken diagonal? > I.e. multiplying entries of any line = always MM(3). > And what is the nxnxn size of this CUBE? I do not have the answer, but my smallest integer is: 89518183823250314294722560000 using 512 different factors organized in a 8x8x8 cube. Many thanks to Edwin CLARK to have checked this cube, confirming that all its different possible ways to multiply entries give always the above integer. There are 832 different ways to get this number in the case of a 8x8x8 cube. With 2 dimensions, the answer MM(2) is known. We have seen in October that MM(2) = 14400 organizing factors in a square that way: 1 24 10 60 30 20 3 8 12 2 120 5 40 15 4 6 When we multiply the integers of any row, column, or diagonal (including broken diagonals), we get always 14400. Christian.