it is a question of "operational research"

Provide the solution of following by satisfying the given constraints Consider the game below, the goal is to move all a's to the right and all b's to the left (as shown in picture below). Rules for moving elements are given in constraints. There is one empty space on which elements can move. Start: a a_bb End: bb_aa Example Move: a_ a bb Variable: Move element in the empty space X Domain: (a, b): Each entry can contain either a orb Constraints 1. a only moves to the right 2. bonly moves to the left 3. only one move at a time 4. No back up moves 5. Entry can either slide or hop