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. <a href="https://www.cs.brandeis.edu/~storer/JimPuzzles/ZPAGES/zzzSubwayShuffle.html" rel="nofollow">https://www.cs.brandeis.edu/~storer/JimPuzzles/ZPAGES/zzzSub...</a>