Since the author seems interested in the maximum number of moves required to solve the puzzle, a similar puzzle called Subway Shuffle far outdoes Rush Hour. For example, puzzle 100 involves 9 pieces on a 10-spot grid, but requires (as far as is known, maybe the solution isn't optimal?) 589 steps to solve. https://www.cs.brandeis.edu/~storer/JimPuzzles/ZPAGES/zzzSub...

Fun article.

The Rush Hour puzzle is quite fun when viewed as a planning problem. In standard PDDL the model becomes very messy. I like the extensions proposed in https://arxiv.org/abs/2412.06312v1 that makes the model intuitive.