I have a set of numbers and I have to order them for maximum MSSD (mean successive squared difference). For example, if I have the ordered set
(1,2,3,4,5,6)
this would give me an MSSD of (1^2+1^2+1^2+1^2+1^2+1^2)/5=5/5=1
This is obviously not the best order. The maximum is reached at
(3,5,1,6,2,4)
Here one has MSSD=(2^2+4^2+5^2+4^2+2^2)/5.

I have a simple heuristic in mind for this problem. Start with an empty set and then always add the elements that will enlarge the sum of squared differences the most. With this example it would give the following:
Start with ()
Then add 1 and 6 (this adds 5^2):
(1,6)
then add 5 (this adds 4^2)
(5,1,6)
then 2 (also adds 4^2):
(5,1,6,2)
and then 3 and 4 (both add 2^2):
(3,5,1,6,2,4)

Using simulations, this simple algorithm indeed always gives the best solution. Moreover this solution seems to be unique (except for the reverse order, (4,2,6,1,5,3), which obviously gives the same result). However, I can't proof this. Is this a known problem? Can somebody help me to proof that this heuristic gives indeed the optimal order?

Thanks!