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...

It turns out that Rush Hour becomes much harder if we shrink the cars from size 2x1 to size 1x1, while maintaining their direction to be either horizontal or vertical [1]. While the hardest 6x6 Rush Hour puzzle takes 51 moves, the hardest Unit Rush Hour puzzle takes a whopping 732 moves [2].

[1] https://tromp.github.io/orimaze.html

[2] https://tromp.github.io/rh.ps

Great article, very impressive to solve the entire game, rather than just individual puzzles.

PS: Good chance that if you're reading these comments that you will appreciate this video by 2swap, visualising solutions to Rush Hour in 3D: https://youtu.be/YGLNyHd2w10?si=fGFqzEbmV3utbA0O

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.

Thanks for the article, perfect timing. Was stuck on a secret Santa gift for the brother in law. Rush hour is perfect!