Toads And Frogs puzzle in two dimensions . Here's a 2-dimensional variant of the Toads and Frogs puzzle. The rules are virtually identical.
Frogs only move rightward or downward, toads can only move leftward and upward.
A piece can jump over another piece of a different kind, provided the square on which it lands is empty. The goal of the puzzle of course is to cause frogs and toads to swap their positions. 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.