The diameter 5 problem has (ignoring roations and reflections) http://www.comm.toronto.edu/~frank/hexagon.html an unique solution

10,12,16
13,4,2,19
15,8,5,7,3
14,6,1,17
9,11,18


There is also a (trivial) diameter 1 magic hexagon. These are the only two sizes of magic hexagon possible.

Eliminating symmetry is important. The diameter 5 problem has 12 symmetries (rotation, reflection, …) which need to be considered.