"3 x 3 x 3 strict magic cube - is impossible-but why?"
A strict 3x3x3 magic cube is one in which the numbers from 1 to 27 are arranged at the 27 matrix points in a 3x3x3 cubical matrix with integer co-ordinates in the 3-dimensional space such that each of the 3x3 arrays of the numbers in each of the the plane layers <3 parallel layers parallel to x-y plane, 3 parallel layers parallel to y-z plane and 3 parallel layers parallel to z-x plane> of the cube are magic squares having the same total AND the sum of the numbers along each of the 4 body diagonals also add up to the same total. I have been able to prove that such a 3x3x3 strict magic cube cannot exist.
Science is the queen of human knowledge. Mathematics is the essence of science. Logic is the basis of mathematics. Geometry is the vehicle of intuition.