The figure shows nine equilateral triangles each having sides of length 1.
We want to put each of the digits from 1 to 9 into the small triangles so
that the sum of the entries in any equilateral triangle with side length 2
is the same.
What are the smallest and largest possible values for this sum?
Source: U.K Junior Mathematical Olympiad
Up to symmetry (i.e. solutions that are rotations or reflections of one
another are considered to be the same) how many ways are there of placing
the digits subject to the constraint above?