[kevincox]

I think it has made be better. At the very least it shows some techniques like moving forward and back and highlights some approaches that I missed.

I generally solve the puzzle "backwards", looking at how the robot can approach the goal. So if you miss a possible approach it can definitely result in me missing a solution. Filling these gaps is valuable.

It also provides some intuition about how long puzzles are in different scenarios which helps you decide how to look.

But overall I would say that it is mainly curiosity why I use the solver. It is interesting to know if we actually found the best solution or how often we miss it.