The 8-puzzle has been one of the popular workbenches in the artificial intelligence research. This paper analyzes the problem space of this puzzle to better understand the relationship among many problem instances. Optimal solutions of many problems can be easily obtained without search by transforming optimal solutions of one original problem. By making use of this result, all optimal solutions of all possible problems are efficiently calculated. Accurate distributions of solution lengths, number of solutions per problem and estimation error of the Manhattan distance are shown together with several important problem instances with maximum solution length(31),maximum number of solutions(86),maximum estimation error(18),etc.