Neil's off the grid for a week, but the url for his simple^3 version is http://nbickford.wordpress.com/category/sliding-block-puzzles/ --rwg We should bug him to post his 5x4 goodies. AdamG> (Hopefully this will help to provide the much-needed break from the inundation of math-fun messages entitled `yacht question'!) Subject to the constraint that pieces are only distinguished by shape, there is a sliding block puzzle in a 4-by-4 box that requires 217 moves (in the `steps' metric) to solve: http://cp4space.wordpress.com/2013/06/25/cipher-33-puzzling-ii/ The state-space of the puzzle is a graph with 9591 vertices and a diameter of 217: http://cp4space.files.wordpress.com/2013/06/sbp-graph.png Is there a harder (i.e. requiring more moves) sliding block puzzle in a 4-by-4 box? This is the most difficult pair of positions reachable from the configuration provided by Neil Bickford as the hardest `simple^3 sliding block puzzle'. Sincerely, Adam P. Goucher