Imagine if like to investigate the structure of solutions made from various puzzle pieces. What area of math is this?
A good analogy is how Rubix cube solutions are related to group theory.
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Do you mean combinatorics? – null Sep 12 '15 at 21:34
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@null I mean more like the way we determine if a puzzle has a solution, what the solution looks like etc...what symmetries does it have, what conditions have to exist for unique solutions...I guess combinatorics is part of that, but I'm more interested in the nitty gritty of the actual solution theory. – Zach466920 Sep 12 '15 at 22:37
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Maybe take the red pill and see how deep the rabbit hole goes. Matrix provides such things like telling if there are solutions, what they look like etc. Question is how to get your problem into the matrix. I have no idea how that'd work or if at all. – null Sep 12 '15 at 23:25
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As far as ensuring unique solutions, I would think graph theory would be applicable. That would be if fits could be determined precisely enough to be able to say definitively whether the edges of two different pieces mesh or not. Most puzzles are cut in a fair approximation to a grid (with some "waviness" and the notches of course) - if pieces can be assigned row and column coordinates this is a further simplification. If you are interested in a computer jigsaw solver, then I guess computer vision would be important - detecting colour, patterns and shapes, e.g. tapering pieces, etc. – Marconius Sep 13 '15 at 05:47