Solving the General NxN Puzzle

Some domains can be scaled up or down by adjusting a certain parameter, such that the same operators are applicable in the scaled domain (perhaps by using the parameter in their definition). For example, we can define a family of domains called the NxN puzzle, where each N defines a different puzzle domain. When N=3 we get the 8-puzzle domain, when N=4 we get the 15-puzzle domain, etc. All the domains in this family use the same operators: Up, Down, Left and Right.