I have a directed graph that looks like the attached image, every node in a column is attached to all the nodes in the following column in the way that the first nodes illustrate

If I always want the path to be exactly 3 nodes I'm looking for a way to find a path of cost x, or be somewhat close to cost x. My starting point will either be random or selected by the 'user'. I'm guessing it needs to be some form of dijkstra's but I'm not looking for the shortest or cheapest, I'm looking for an exact cost.

Anyone have any advice or do I just traverse the graph randomly until I find an acceptable path?