Are there any mathematical or other strategies that can be imployed on 4x4 slider puzzles. These puzzles are sometimes numeric but more than often they are scrambled up pictures.
Ex. These little Doohickies:
http://plink.sonic.net/slider/slider.cgi?begin=yes&puzzle=plant
Thanks,
The MeatBeast
This puzzle is commonly referred to as the 15 Puzzle. That link goes into some detail on which initial positions are solvable, but not a general algorithm for the solution. I’m sure such an algorithm exists; I can solve the puzzle, but I’ve never thought it through enough to give a rigorous algorithm for the solution. Basically, the idea is to work row by row, so that your final row is the one which should contain the final “empty” spot. Some of the references in the above link probably do give appropriate algorithms, so that could be a place to start.
It depends on whether we are talking computers or humans. For a computer, the standard algorithm is known as Iterative Deepening A* (if you are into programming, a search for that and “15-puzzle” should give you whatever you need). It works by calculating and summing the “distance” that each tile is from its target location, and then figuring out which set of moves will get you a smaller sum (moving tiles closer to their target locations).
It is still basically a brute-force search (technically a depth-first search), just, I guess you could say guided. AFAIK, there is no algorithm which can simply “look” at a 15-puzzle problem and generate a solution. It is easy to tell whether or not a solution exists, but not so easy to generate it.
If you want to screw someone who’s trying to solve one of those, pop any two tiles out and swap their positions, leaving the others where they are. This introduces a parity error, and the puzzle will be unsolvable unless they pop the tiles out again. You can also do this with a Rubik’s Cube; use a screwdriver to pop out an edge piece, and the rest will follow easily.