How to Solve: To solve any of the puzzles on RattleRig.com, start with a clean screen. That cannot be stressed enough. Then, click the first square you wish to begin with, only once. Sometimes internet connections may present lag times (where you click and nothing seems to happen). On these puzzles, nothing will happen until you click the second (or destination square).
So, all you're doing is selecting 2 squares, to transpose. And you do that until the puzzle is solved. Good luck.
Or, click the destination first, and then the square to be moved second.
Either way, you'll see the two squares have transposed positions.

Press your space bar a time or two to better position the puzzle on the screen.