Toads And Frogs Puzzle
in 2D

The puzzle is solved by the following observation. The middle vertical column may be looked at as a simple 1-dimensional puzzle. In the course of a successful solution of that puzzle, the empty square will eventually move over all squares in that column. (This is because all pieces will have to be moved from their original positions.) The row in which the empty square is located may be looked at as another 1-dimensional puzzle, this time horizontal. The process of solution of the vertical puzzle serves as an index into a sequence of horizontal puzzles that are solved successively.