I was browsing Mathematica user communities for original projects and came by the following question: "How can I calculate a jigsaw puzzle cut path?" Such creative problems are in abundance at our user forums, the Wolfram Demonstrations Project, and The Mathematica Journal, which tells me that Mathematica, at its heart, is a conduit for creativity: it's a programing language that likes the challenge of convoluted problems and inspires elegant, often unexpected solutions. In its essence, a jigsaw puzzle is a tiling or tessellation, which means there are no gaps or overlaps between the pieces. Moreover, every piece is unique and has a definite place in the puzzle. Uniqueness is achieved by making a piece be a part of a large image, have a specific shape, or a combination of these. There are many approaches to producing such patterns. For instance, this single mathematical formula from our graphics examples produces a beautiful tessellation: However, since this question was asked on Mathematica Stack Exchange, a young, modern technical Q&A site, it was very specific in accordance with the community rules. Here are the author's requirements: All pieces must be unique to preclude placing a piece in the wrong spot. Pieces must be interlocking such that each piece is held by adjacent pieces. It must be possible to generate different paths (sets) for a specific shape that are not merely rotations or reflections of the first. Additionally, the author of the question notes that he seeks original designs alternative to typical mass-produced shapes.

UPDATE: The solution to the puzzle and more comments from Jon have been added at the bottom of the post. On the long flight to the recent Wolfram Technology Conference, I ended up on the puzzle page of a newspaper. My attention was drawn to a word ladder puzzle, where you must fill in a sequence of words from clues, but each word differs from the previous by only a single letter. Here, for example, is a simple puzzle already solved:

best	from a position of superiority or authority
bast	strong woody fibers obtained especially from the phloem of from various plants
bash	a vigorous blow
bath	a vessel containing liquid in which something is immersed (as to process it or to maintain it at a constant temperature or to lubricate it)
math	a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement

I wasn't going to do a blog entry on this, as it is a very similar task to my "Exploring Synonym Chains" post that I wrote some time ago, but that changed with a chance conversation at the (excellent) Technology Conference. Proving that one never stops learning, Charles Pooh, one of our graph theory developers, pointed out to me that my synonyms item could have been done much better. I had broken one of the very rules that I wrote about in my "10 Tips for Fast Mathematica Code" entry—"Use built-in functions." I had effectively re-implemented the built-in Mathematica commands GraphPeriphery and GraphDiameter. So, armed with these two new functions, let's find the longest word ladder puzzle that can be made using Mathematica's English dictionary.