Extra-sliding puzzles: Experiments in Cognitive Modeling and Representation for Problem Solving

We are studying the well known problem of the sliding puzzle or Npuzzle and we are modeling a number of consecutive extensions and their solution based on the known algorithmic solution. The usual approach to date has been to find optimal solutions (move sequences) to the N-puzzle with the aid of sophisticated special-purpose search methods. Our goal is to study it from a bottom up perspective and to do cognitive modeling of the scalable algorithmic solution that finds suboptimal move sequences but that can do so consistently for a large number of extensions with practically no increase in polynomial complexity. This approach claims both to model for fundamental cognitive skills that are exerted on top of existing intelligent problem-solving methods as well as to identify modules of reasoning that should be included in any scalably intelligent system.