Call to Action: I need a long term mentally challenging puzzle of some sort...
Yesterday I posted on the game Rush Hour Spatially oriented puzzles, density, and perceived complexity... and about it's various types of complexity. Today, I'm desperately seeking some puzzle game that is going to last more than a few hours. When all was said and done for this particular puzzle game I was out about 30 bucks and only got around 6 hours of gameplay between the 120 puzzle cards. I've been to quite a few game stores and I can honestly say this was one of the more challenging puzzle games that I've managed to find compared to all the others, so similar games with a much deeper focus on creating complex solutions might be something to look at (they have a railroad version that adds a new piece type that can move horizontally and vertically).
Since I love giving content I'll go ahead and provide an examination of the game for you in case you might be willing to play Rush Hour yourself.
- Initial Game - $18 after tax with 40 game cards. The game cards have 4 levels of difficulty (Beginner, Intermediate, Advanced, and Expert). Each level is set apart from the previous by requiring more moves in order to complete the puzzle. I find that some of the Intermediate and most of the Advanced are probably the most difficult in this particular deck based on the spatial orientation and density discussion I had in my previous entry.
- Deck 2 - $8 after tax with an additional 40 game cards and a new 2 square car. This car is generally just a replacement for the old red car that you need to remove from the board in order to win. With a new 2 square car, new types of puzzles are available that weren't previously enabled. Only puzzles that make use of all of the two part cars are new puzzles. The rest were previously available with the existing set of cars. One of the new puzzle types allows you to remove more than one car from the playing field. These are often very easy and the first of the two cars can be removed in about 3 - 5 moves leaving you with the real problem. These could just as easily have been made without the 3 - 5 extraneous moves.
- Deck 3 - $8 after tax with an additional 40 game cards and a new 3 square car. The new car is a limousine and you often have to remove this car from the board in place of the red car. Decks 2 and 3 are exclusive, so you don't need Deck 2 to play Deck 3. This isn't really a problem since the board isn't large enough to support all the cars of both 2 and 3 square types. The new puzzle types enabled with the new car rely on having all of the 3 part cars on the board at once. Because 3 part cars take up half the board, they heavily restrict freedom of movement, and it is often quite obvious where the cars need to wind up if you are going to escape the traffic jam. Based on the freedom of movement principle I find this entire deck to be much easier than both the initial game and the second deck.
The game strategy breaks down quite nicely. There are three types of puzzles that revolve around the movement of the red car and an initial examination phase that will enable you to beat even the most difficult cards with ease.
- Initial Examination - During this step, you need to identify where each piece should wind up if the red car is going to escape. The more dense the board the more obvious this is because you know that empty spots on the board need to be filled in order for filled spots in front of the red car to open up. You can often pick a single empty space and begin mentally finding what I'll call the critical cars. Generally there are between 1 and 4 critical cars that have to change position and consume different parts of the board for the red car to escape.
- Green Light - This is the first puzzle type. A green light puzzle means you can solve the puzzle without moving the red car or only having to move it slightly. This involves mentally finding where the critical cars are up front and moving them into place to open up the path for the red car. These are almost non-existent at higher densities.
- Jams - Jams are much harder than green light puzzles, but I don't think they classify as the hardest puzzle type. In a jam, the red car will be forced to move backwards and forwards several times to let cars pass around it and into position. In a jam, the movement of the red car is fairly localized so the visualization step is still fairly easy. Jams aren't all that hard because they are like knots that unravel. As you solve portions of the jam the pattern gets easier and easier to solve for.
- Stop & Go - Stop and Go puzzles are by far the hardest. Generally these puzzles are very dense and they feature a kind of figure 8 pattern of cars. You are forced to put the cars into a specific sequence in order to transfer the red car between two locations within the puzzle. You work on each side of the puzzle to move the critical cars and have to put the game back into the specific sequence several times, each time with a different car layout (because you are moving critical cars) to pass the red car around and unblock other cars. Unlike jams, the complexity of a Stop & Go never unravels.
I'm thinking of doing an algorithmic study of this game using the Zobrist hash for solving. And then showing how the same memory techniques can be used for creating an entire database of new puzzles. The end result would hopefully be some very solid puzzle cards with great freedom of movement and complex decision trees. There must be an optimally hard puzzle in there somewhere. If the longest time spent on any of the 120 existing puzzles is only about 10 minutes, then maybe I can squeak out a card that takes me 20?
Play the Game!