3 problems

Let $puz[d,1,l]$ denote the puzzle graph for the $d$-dimensional cube with one movable token and $l$ unoccupied vertices, and let $diam$ denote its diameter. Diameter conjecture. F…

Let $(d,k)$ be an admissible tuple of integers, and let $S(d,k)$ be the minimum integer such that $puz[d,k,S(d,k)]$ has the even solvability property. A configuration is $k$-mobile…

Let $B(h)$ be a hexagonal sliding-puzzle board, and let its puzzle graph have configurations as vertices and legal moves as edges. For a starting configuration, run breadth-first s…