Solving Rush Hour, the Puzzle (2018)

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

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...

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

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

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.