Browsing Reddit I found this interesting submission which caught my attention because it seemed like a fun little project to complete.
I reverted to type and wrote up a script in CoffeeScript which you can find at the Github repository. Must try harder to use Elixir for these - maybe the next thing I can do is re-write it in Elixir.
There were a few false starts, but I think the final solution is pretty solid and seems to give the same sort of results as expected.
So for the grid:
1 2 3 4 5 6 7 8 9
The least efficient way to connect all the numbers is:
[ 2, 7, 6, 1, 8, 3, 4, 9, 5 ]
with a length of 17.066689404871624. Obviously there's a bunch of other similar paths, but none are any longer at least according to my calculations.
And that's what I learnt today!