This question caught my atention recently. Most (if not all) of the answers aproached the problem via a brute force attack. Surely there is a more elegant way to deal with this, given the inherent symmetry.
My question is can this be generalised to an $n$ dimensional lattice? Clearly the placement of the nearest neighbour is critical in this problem (ie, it is unclear where $n=5$ in $2$ dimensions would be places in terms of the classical Descatrian coordinate system), but it could also be generalised to $n$ in any dimension. Is this a Hamiltonian path (ie NP hard problem), or can the symmetry be utilised to present a more analytic solution?
If standard MSE policy of questions being self-contained is desired, please note, and I will alter.