Pebbling a Chessboard

Inspired by the Numberphile video of the same name, Free the Clones is a game where the player has to empty the "prison" area of a chessboard according to the particular movement rules of the "clones".

Each "clone" moves by creating two copies of itself to the right and below it, with the original disappearing in the process. Also, a "clone" can only move if both squares it would be moving into are unoccupied.

The embedded video provides a summary of the game, and also provides the solution, but I invite you to try out the game first, either on a chessboard of your own, or by downloading a digital version I have made here.