>>14275869Im writing them as vectors in 3d then projecting to the plane perpendicular to <1,1,1>.
<x,y,z> goes to <X,Y> = <x - (y+z)/2, sqrt(3)(y-z)/2>
You get points on a an equilateral triangular lattice.
Then I'm working backwards from the points that correspond to single objects.
The valid moves (to work backwards) are to hop left by 2, hop up to the right by 2, hop down to the right by 2.
Clearly there are 4 sublattices corresponding to initial points <0,0,0>, <1,0,0>, <0,1,0>, <0,0,1>.
Right now I'm looking at the set of points that are 1 hop, 2 hops, 3 hops, etc from the start.
There appears to be a distance related to number of hops mod 3 that says if you can reach the start or not.
The distance is max(X, sqrt(3)|Y|/2 - X/2)
If you let T = x+y+z then you should be able to find a relation between T and the distance mod 3 that says if it works.
