Rush Hour (puzzle)

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The Rush Hour puzzle set

Rush Hour is a sliding block puzzle invented by Nob Yoshigahara in the 1970s. It was first sold in the United States in 1996. It is now being manufactured by ThinkFun (formerly Binary Arts).

ThinkFun now sells Rush Hour spin-offs Rush Hour Jr., Safari Rush Hour, Railroad Rush Hour, Rush Hour Brain Fitness and Rush Hour Shift, with puzzles by Scott Kim.

Game[edit]

The Regular Edition comes with 40 puzzles in 1 split up into 4 different difficulties, ranging from Beginner to Expert. The Deluxe Edition has a black playing board, card box in place of the board's own card tray and 60 new puzzles with an extra difficulty: the Grand Master, which is harder than Expert. The Ultimate Collector's Edition also has a black playing board that can hold vehicles not in play and new way to display the current active card in a billboard like display. The Ultimate Collectors Edition also includes 155 new puzzles with some of them being from card set 3 and a white limo. The Regular Version includes a travel bag. Extra puzzle card packs (in addition to the 40, 60 or 155 cards included with the game) are also available. Also both the Deluxe Edition and the Ultimate Collector's Edition comes with all new shiny vehicles variant with the Ultimate Collector's Edition ones being slightly altered in design. Then in 2011, the board was changed to black, like the Deluxe Edition but with a card try and the cards was also changed to have new levels and design to match the new board color.

Description[edit]

The board is a 6x6 grid with grooves in the tiles to allow cars to slide, card tray to hold the cards, current active card holder and an exit hole. The game comes with 16 vehicles (12 cars, 4 trucks), each colored differently, and 40 puzzle cards. Cars and trucks are both one square wide, but cars are two squares long and trucks are three squares long. Vehicles can only be moved along a straight line on the grid; rotation is forbidden. Puzzle cards, each with a level number that indicates the difficulty of the challenge, show the starting positions of cars and trucks. Not all cars and trucks are used in all challenges.

Objective[edit]

The goal of the game is to get only the red car out through the exit of the board by moving the other vehicles out of its way. However, the cars and trucks (set up before play, according to a puzzle card) obstruct the path which makes the puzzle harder.

Expansions[edit]

Three expansions were released that are card set 2 which comes with a red conversable that take up 2 squares, card set 3 which comes with a white limo that take up 3 squares and card set 4 which comes with a taxi that take up 2 squares. The sets also come with 40 new exclusive challenges each from Intermediate to Grand Master that have use the new vehicles in place or with the red car. Additionally, all three of the expansions will work with all three editions that are the Regular Edition, the Deluxe Edition and the Ultimate Collector's Edition. Also, like the Regular Edition of the game in 2011, the cards of all three expansions was also changed to have new levels and design to match the new board color of the Regular Edition.

An iOS version of the game was released in 2010.

Computational complexity[edit]

When generalized so that it can be played on an arbitrarily large board, the problem of deciding if a Rush Hour problem has a solution is PSPACE-complete.[1] This is proved by reducing a graph game called Nondeterministic Constraint Logic, which is known to be PSPACE-complete, to generalized Rush Hour positions.

Tromp and Cilibrasi (2004)[2] showed that Rush Hour is still PSPACE-complete when the cars are of size 2 only. They also conjectured that Rush Hour is still nontrivial when the cars are of size 1 only.

See also[edit]

References[edit]

  1. ^ Gary Flake and Eric Baum (2002). "Rush Hour is PSPACE-complete, or why you should generously tip parking lot attendants". Theoretical Computer Science. 270: 895–911. doi:10.1016/S0304-3975(01)00173-6. 
  2. ^ John Tromp; Rudy Cilibrasi (2005). "Limits of Rush Hour Logic Complexity". arXiv:cs/0502068Freely accessible.