adventures and experiments in bringing new puzzles to life
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puzzles The paper “Mathematical Definition and Systematization of Puzzle Rules” by Itsuki Maeda and Yasuhiro Inoue details a mathematical framework for logic pencil
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puzzles with formulas defining 10 different puzzle types. Nikoli, the company that popularized “Number Place” puzzles under the Japanese trademark ‘Sudoku’, publishes
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collections in Japan and describes each on their website: Slitherlink Sudoku Shikaku Choco Banana Inshi no Heya Fillomino Kurotto Sukoro Norinori Hitori. As I get my
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⟪Silver⟫ Solver working on each, I'll post my ⟪Sapphire⟫ definitions.
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I started on a formulation of Slitherlink rules in ⟪Sapphire⟫. Connectivity, as a pairwise relation could be easily satisfied by being true for any vertices that are
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connected to anything. I ended up defining a distance function with a special value (rather than a distinct relation) for ‘not connected’. In the next day or two,
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I'll see how ⟪Silver⟫ does trying to find a satisfying model (aka solution).
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Here's a link to the Sudoku rules I'm using for my experiments, written in my Sapphire logic syntax. So far, Sapphire supports first order formulae, integer
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operations and sets of integers. My ad-hoc "Silver Solver" supports partial evaluation and rewriting to try to find a satisfying model.
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Square Routes playtesting is just about happening!
