10 Dec '04 19:49

As everyone knows, a 2x2 magic square is not possible in 2 dimensions. Similarly in 3 dimensions a 3x3x3 strict magic cube ,in which all row sums, lateral row sums, column sums, and diagonal sums , in each of the 3x3 squares in each of the 3 layers of each plane( x-y plane, y-z plane and z-x plane), aswell as the 4 body- diagonal sums are each equal(i.e. equal to 42), - is NOT possible. I have found a proof for the impossibility of the magic cube of order 3 i.e. 3x3x3 magic cube..

AS in 2 dimensions the smallest order of possible magic square is 2+1 i.e. 3 only, , my conjecture is that , in 3- dimensions , the smallest strict magic cube can be of order 3+1 i.e.4 or above only. There are some websites giving magic cubes of any order but they are not strict magic cubes in the sense that sums along all rows, lateral rows, columns , diagonals, body -diagonals ,are not equal.

AS in 2 dimensions the smallest order of possible magic square is 2+1 i.e. 3 only, , my conjecture is that , in 3- dimensions , the smallest strict magic cube can be of order 3+1 i.e.4 or above only. There are some websites giving magic cubes of any order but they are not strict magic cubes in the sense that sums along all rows, lateral rows, columns , diagonals, body -diagonals ,are not equal.