We consider coin sliding puzzles of the following type, also referred to as non-adjacent token puzzles. Given a graph G with tokens on some of the vertices (this token arrangement is called a configuration), we must slide the tokens along the edges of G to move them into a given goal configuration. The constraint is that tokens can never be on adjacent vertices. This type of puzzle turns out to be PSPACE-complete, as proven by Bob Hearn and Erik Demaine. This is discussed here. [in-depth link]
The problem is PSPACE-complete in general, but what if the graph is a hex lattice, i.e. the dual graph of a honeycomb configuration? Is the problem then in P? Is it in NP? Is it PSPACE-complete? Here is a honeycomb configuration that can be printed out (thanks to Bob Hearn for this). In this case, coins go on the faces and cannot lie on adjacent faces.