How to tell if a Heuristic is monotonic I've applied a Heuristic to a puzzle where I need to move all off the B's the the right of the W's. my Heuristic is the total distance of the B's from the right most W's. my initial state is (B,B,B,*,W,W,W), where * represents a blank space. A piece can move into a blank space and can jump over one or two other pieces into a blank space. I've attached a picture of the graph.



This Heuristic is Admissible because the distance to the goal is ALWAYS more than the distance from the B's to the rightmost W. 

The thing I'm not sure of is if this Heuristic is monotonic. My understanding of Monotonic is that the cost of going to an adjacent node plus the estimate of the new node have to be less than the total distance to the goal. How would I determine if this Heuristic is monotonic?
If your heuristic is essentially the original problem, but with some constraints removed, it is monotonic. 
Otherwise, you must prove that there is no transition which does not uphold the formula in Caesar's answer.