Final answer:
The usefulness of working backwards is not dependent on the number of directions from the goal state, so the statement is false. It is a strategy that simplifies the problem-solving process, regardless of the number of directions involved.
Step-by-step explanation:
The statement "Working backwards is most helpful when the number of directions backwards from the goal state is greater than the number of directions towards the goal state" is false. The reason for this is that the usefulness of working backwards as a strategy does not depend on the sheer number of directions, but rather on whether it simplifies the problem-solving process. Also, the fact that working backwards is helpful in many situations does not depend on a comparison of the number of directions from the goal state versus the number of directions towards it.
For example, consider the statement: "A person walks 2 blocks east and 5 blocks north, another person walks 5 blocks north and then two blocks east." The displacement (the shortest distance from the start point to the end point) for the first person will be the same as the displacement for the second person as both have covered the same distance in east and north directions albeit in different order. Therefore, the statement about the displacement being different based on the order of directions is false.