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[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.

C and Perl Implemenations

General Backtracking Approach

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