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In Rush Hour, a sliding block logic game, you have to battle the gridlock as you slide the blocking vehicles out of the way for the red car to exit. With 40 all-new challenges, ranging in difficulty, players can progress at their own speed.
- 2 min
- Terminology
- Prior Art
- Interesting Puzzles
- Combinatorial Explosion
- Enumerating States
- Lexicographical Ordering
- Visualizing Clusters
- Go vs. C++
- The Cloud
- Hardest Puzzles
Piece: a vehicle on the puzzle board. Each piece has a position, a size, and an orientation (horizontal or vertical). In Rush Hour there are 2-pieces (cars) and 3-pieces (trucks).Primary Piece: the "red car" in the puzzle, the piece that must reach the exit on the right side of the board.Step: moving a piece by one unit.Move: moving a piece by N steps at once.I didn't do a whole lot of research or anything, but did find these papers: 1. Finding hard initial configurations of Rush Hour with Binary Decision Diagrams- by Frédéric Servais 2. On the Hardness of 6x6 Rush Hour - An exploration of the entire configuration space- by Jelle van Assema The first one was rather academic and not particularly helpful....
So, what do I mean by "interesting"? I established a set of rules to filter out a lot of nonsense puzzles. Interesting puzzles follow these rules: 1. No row may be completely filled with horizontal pieces and no column may be completely filled with vertical pieces. These just form walls of pieces that can never move. Not very interesting. 2. No hor...
Rush Hour is a perfect example of combinatorial explosion. So, writing efficient code and using clever algorithms will be important but will only get us so far. I think solving the 7x7 case may be doable but would require extensive computing resources that I can't afford! (It would probably require decades of CPU time.) Even adding walls increases ...
To examine all possible puzzles, we need an efficient way to enumerate all possible piece placements based on our rules. Let's break it down by looking at individual rows and columns first. For the 6x6 puzzle with 2-pieces and 3-pieces, the following table shows all of the possible ways that horizontal pieces may appear on a row (or vertical pieces...
The enumeration scheme above will produce billions of states that we can then evaluate. But we only need to evaluate each distinct cluster (connected graph of mutually reachable states) once. We really only need the enumerator to give us onestate per cluster, and then we can find the other reachable states during further evaluation. In theory, we c...
Clusters are just directed graphs where each node is a puzzle state and each edge is a valid move. (Actually, all moves are reversible, so it could be considered an undirected graph as well.) So we can render them using Graphviz. Here are some examples (click to enlarge). In these graphs, unsolved states are red, goal states are green, and an optim...
All of my code was initially written in Go. But when I started trying to "solve" the entire game I decided to use C++ to get the most performance possible. I made a lot of improvements along the way in porting my code to C++, so I don't have a direct apples-to-apples comparison between Go and C++ for the full program. But I did run benchmarks on se...
Solving the 6x6 case with no walls took 3h10m on my iMac. But to compute puzzles with up to two walls, I used an EC2 instance with 72 cores (3.0 GHz Intel Xeon Scalable) to crank through it faster. It took 16h50m to complete and cost me about $50. But it sure was fun! I estimate it would have taken 170 hours (about one week) on my iMac.
Quantifying the difficulty of Rush Hour puzzles is... difficult... so normally when I say "hardest" I mean "requiring the most moves." I now present to you the hardest 6x6 puzzles with 0, 1, and 2 walls.
Uno de los juegos más emblemáticos de la empresa es el Rush Hour, un juego lógico que ayuda a desarrollar las habilidades para la resolución de problemas, la geometría y, como no podía faltar, la lógica también. Fue uno de los primeros juegos que crearon y ha recibido numerosos premios internacionales.
11 de feb. de 2021 · How to play Rush Hour - YouTube. Triple S Games. 226K subscribers. Subscribed. 271. 26K views 3 years ago. Learn the rules to the single player logic puzzle game Rush Hour quickly and...
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- Triple S Games
Rush Hour is a sliding block puzzle originally invented by Nob Yoshigahara in the late 1970s and first sold in the United States in 1996. Objective. The objective of the game is to get the red car out of a six-by-six grid full of automobiles by moving the other vehicles out of its way.
Ahora no solo puedes jugar a Rush Hour® Deluxe en solitario, ¡sino que también puedes enfrentarte a otros jugadores para demostrar tu inteligencia! ¿Quién resolverá los desafíos con menos tiempo y movimientos? Diseño original del popular juego de mesa. Entrenamiento lógico y divertido para la mente. 60 desafíos. 5 niveles de dificultad.
