[UPDATE 1/10/09: This post is fairly popular so I assume many people are looking for help on Scramble Squares and potentially hints or solutions.
Sadly, there is no way to shortcut these puzzles. I suppose if you look at the box, and your box shows you the completed puzzle, you can “cheat” that way.
If you just want to use an already coded “solver”, there are a few out there. Here’s a good one.
Read the instructions on how to encode your puzzle pieces so the solver can work properly.
Note that puzzles can sometimes have more than 1 solution.
Also note that the algorithmic solvers are not “shortcutting” the puzzle. They simply try more options than you do much faster. It’s pretty much just brute force. A modern computer can run through all 23 billion combinations in 30 seconds (and usually does it faster because it might pick the right center piece early on… which is what the popular algorithm uses as a starting point).
That said, humans can somehow solve these puzzles without “trying” a lot of configurations. As I discuss below I have some theories how this is possible, but I do not have a definitive answer.]
Here are some papers, code and blog posts (this is nice one too) on how to algorithmically search for solutions to squzzles/scramble square puzzles. You might have received one of these puzzles as a holiday gift over the last few years, they were quite popular.
The algorithm is straightforward – just one that searches through solutions.
What’s interesting is that I’ve seen people solve these puzzles, even brand new ones (no prior knowledge), very quickly. There’s something that happens with a persons vision or something that’s helping them not have to exhaustively search the full solution space. If I’d seen someone do this once or twice, I’d think it was just lucky picks. (these puzzles have enormous solution spaces (4^8 x 9! = 23,781,703,680 puzzle configurations) )
Is there something in this puzzle that “hints” to a human early in the solution testing that a solution is viable or not. That is, after 1 or 2 pieces placed, can the human see a promising solution “faster” than the basic algorithm that searches quickly through all piece placements and orientations. If so, what is that data (“hint”) the human sees and how can we factor it into the algorithm?
Possible hint data:
Rules of thumb on how all these puzzles are printed and cut (do the puzzles all get made with same orientations so exposure to one puzzle provides data on other puzzles?)
Humans can see the whole pattern in parallel even when pieces aren’t lined up so they don’t have to check each piece systematically
Are combinations of pieces eliminated as the humans solve it thus taking them out of future solution attempts, reducing solution space the more the human works on the puzzle
Great post (and thanks for the link). One observation … there just isn’t an algorithm that will clock through all possible combinations brute force … there just isn’t time enough in the world for that. Useful algorithms do a form of ‘pruning’ away big branches of combinations because the first couple of steps indicate a dead end and no point to continue. This very human-like heuristic helps to constrain the amount of brute-force needed by several orders of magnitude, and keeps it solvable.
I agree with you, though, that there is some sort of higher order visual processing that the human brain can do … some people do have a sort of knack for glancing at the pieces and putting it together fast.
I have a 16 square puzzle with 6 different bugs. I can’t solve it. Any suggestions? Ann
can you post a picture of it or give me a bit more of a description… i’m sure we can find an algo to solve it/search for a solution.
Do you know of an alog to solve it that can accept 16 squares.
Well, the general algos I pointed to will scale to 16 squares. we just need to adjust them. granted they might be kinda slow cause the solution space is that much bigger.
I think that Annie is looking for a way to do it sans work! But you’re right un1crom … the algo I coded is fairly general. Nothing tough about extending it to larger search spaces other than the longer processing times.
yeah, I figured…. so are you going to extend it or am i? 🙂
Have the same bug puzzle to do for my daughter’s 6th grade homework! It is CRAZY!!! Can e-mail someone the puzzle. It’ won’t let me post it here.
takes for ever
did anyone figure out the 16 piece bug puzzle for 6th grade as we have the same one now.
I have the same 16 square puzzle thing and I can’t figure it out if someone here has an answer I need it pronto because I have this assignment and I really need his to be turned in. if anyone has the soulotion I would be super grateful. please help thank you. publisher- frank schaffer publications, inc. copany- logic across the curriculum. I really need your help. no other site has the answer and I really need it.