Stories with Tag Constraint Satisfaction

• Solving a “Layton Puzzle” with Prolog

  permalink

  Posted: 2025-04-08 19:11:41

  Verbose tl;dr

  The post describes solving a logic puzzle reminiscent of Professor Layton games using Prolog. The author breaks down a seemingly complex word problem about arranging differently-sized boxes on shelves into a set of logical constraints. They then demonstrate how Prolog's declarative programming paradigm allows for a concise and elegant solution by simply defining the problem's rules and letting Prolog's inference engine find a valid arrangement. This showcases Prolog's strength in handling constraint satisfaction problems, contrasting it with a more imperative approach that would require manually iterating through possible solutions. The author also briefly touches on performance considerations and different strategies for optimizing the Prolog code.

  Hillel Wayne's blog post, "Solving a 'Layton Puzzle' with Prolog," details his experience using the logic programming language Prolog to solve a puzzle reminiscent of those found in the Professor Layton video game series. The puzzle involves arranging colored weights on a balance scale to achieve equilibrium. Specifically, the puzzle presents three distinct colored weights—red, blue, and yellow—and tasks the solver with determining how many of each color are needed to balance the scale, given that two red weights equal three blue weights and three yellow weights equal five blue weights.

  Wayne begins by outlining the problem and his initial, somewhat naive, approach using Python. He demonstrates how a brute-force method in Python, while functional, lacks the elegance and declarative power he desired. This leads him to explore Prolog as a more suitable tool for the task.

  He meticulously explains the process of translating the puzzle's constraints into Prolog's logical framework. He defines predicates representing the relationships between the different colored weights, expressing the given ratios as logical rules. For example, he defines a predicate that asserts the equivalence of two red weights and three blue weights. Furthermore, he introduces a predicate to represent the balanced state of the scale, where the total weight on both sides is equal.

  The core of his Prolog solution involves recursively generating potential combinations of weights and then testing each combination against the defined constraints. This recursive approach explores the solution space systematically, eliminating combinations that violate the weight ratios or the balance condition. Crucially, Prolog's backtracking mechanism simplifies this exploration, automatically discarding invalid solutions and pursuing alternative paths.

  Wayne highlights the conciseness and declarative nature of the Prolog solution compared to the more procedural Python approach. He emphasizes how Prolog allows him to express the problem's logic directly, letting the language's inference engine handle the search for a solution. This, he argues, makes Prolog an ideal tool for puzzles of this nature, where the focus is on defining the rules and constraints rather than specifying the exact steps to find the answer. The post concludes with a reflection on the satisfying experience of using Prolog to solve the puzzle and a general appreciation for the power of logic programming in tackling constraint-based problems.

  • Prolog
  • Logic Programming
  • Puzzle Solving
  • Layton Series
  • Professor Layton
  • Game AI
  • Constraint Satisfaction
  • Declarative Programming
  • Algorithm
  • Tutorial
  • Hillel Wayne

  Summary of Comments ( 24 )
  https://news.ycombinator.com/item?id=43625452

  Verbose tl;dr

  Hacker News users discuss the cleverness of using Prolog to solve a puzzle involving overlapping colored squares, with several expressing admiration for the elegance and declarative nature of the solution. Some commenters delve into the specifics of the Prolog code, suggesting optimizations and alternative approaches. Others discuss the broader applicability of logic programming to similar constraint satisfaction problems, while a few debate the practical limitations and performance characteristics of Prolog in real-world scenarios. A recurring theme is the enjoyment derived from using a tool perfectly suited to the task, highlighting the satisfaction of finding elegant solutions. A couple of users also share personal anecdotes about their experiences with Prolog and its unique problem-solving capabilities.

  The Hacker News post "Solving a “Layton Puzzle” with Prolog" sparked a lively discussion with several insightful comments. Many commenters focused on the elegance and declarative nature of Prolog for solving logic puzzles, echoing the author's points in the original blog post.

  One commenter highlighted Prolog's strength in constraint satisfaction problems, noting how naturally the puzzle's rules translate into Prolog code. They appreciated the clarity and conciseness of the solution compared to imperative approaches. This commenter also pointed out the power of declarative programming for expressing the what rather than the how, allowing the Prolog engine to handle the search and optimization.

  Another commenter discussed the learning curve associated with Prolog, acknowledging its initial difficulty but emphasizing the rewarding experience of mastering its logic programming paradigm. They expressed admiration for the elegance of Prolog solutions and the satisfaction of seeing complex problems elegantly solved.

  Several commenters delved into specific aspects of the Prolog code, discussing alternative approaches and optimizations. One suggested using clpfd, a constraint satisfaction library for Prolog, to further streamline the solution. Another commenter explored different ways to represent the puzzle's constraints, highlighting the flexibility of Prolog in modeling logical relationships.

  The discussion also touched upon the broader applicability of Prolog beyond puzzle solving. One commenter mentioned its use in natural language processing and knowledge representation, showcasing the versatility of this logic programming language. Another discussed the historical context of Prolog and its influence on other programming paradigms.

  A few commenters shared their personal experiences with Prolog, some recalling fond memories of using it in academic settings, while others expressed a renewed interest in exploring its capabilities after reading the post.

  Overall, the comments section reflected a general appreciation for the power and elegance of Prolog in solving logic puzzles, with many commenters praising the clarity and conciseness of the presented solution. The discussion also explored broader topics related to Prolog's capabilities, learning curve, and historical context, demonstrating the community's engagement with the topic.

• A new Sudoku layout with 81 uniquely shaped cells

  permalink

  Posted: 2025-03-13 01:04:50

  Verbose tl;dr

  Daniel Chase Hooper created a Sudoku variant called "Cracked Sudoku" where all 81 cells have unique shapes, eliminating the need for row and column lines. The puzzle maintains the standard Sudoku rules, requiring digits 1-9 to appear only once in each traditional row, column, and 3x3 block. Hooper generated these puzzles algorithmically, starting with a solved grid and then fracturing it into unique, interlocking pieces like a jigsaw puzzle. This introduces an added layer of visual complexity, making the puzzle more challenging by obfuscating the traditional grid structure and relying solely on the shapes for positional clues.

  Daniel Chase Hooper, in his blog post "Cracked Sudoku," details his creation of a novel Sudoku variant distinguished by its 81 uniquely shaped cells, referred to as "Cracked Sudoku." Hooper meticulously outlines his design process, starting with the initial concept sparked by a desire to move beyond the standard 9x9 grid of squares. He aimed to construct a puzzle with a single solution, maintaining the core logic of Sudoku while offering a visually distinct and potentially more challenging experience.

  He articulates the challenges faced during development, emphasizing the complexity of ensuring each cell has a distinct shape while also guaranteeing a contiguous overall design. His initial attempts involved hand-drawing various cell configurations, a process he found both time-consuming and ultimately unsuccessful in producing a viable puzzle. This led him to adopt a computational approach.

  Hooper leverages a combination of algorithms and programming. He details his utilization of a backtracking algorithm, a common technique for solving constraint satisfaction problems, to explore the vast space of potential cell arrangements. This algorithm systematically tests possible cell shapes and their placements, discarding configurations that violate Sudoku rules or result in duplicate cell shapes.

  Furthermore, the post explains the visual representation of the puzzle. The algorithm outputs SVG (Scalable Vector Graphics) data, which precisely defines the intricate borders of each uniquely shaped cell. This ensures the final puzzle maintains both its mathematical validity and aesthetic appeal. The use of SVG also allows for scalable rendering, ensuring the puzzle looks crisp and clear on various devices.

  The post culminates in the presentation of the completed Cracked Sudoku puzzle, a testament to Hooper's blend of artistic vision and computational prowess. He highlights the intricate network of interlocking shapes, a striking departure from the conventional Sudoku grid, while preserving the underlying logical framework of the game. He also reflects on the potential of this approach for creating further variations of Sudoku and other logic puzzles, suggesting a pathway for future exploration in this domain. Finally, the post briefly touches on the possibility of incorporating a solver for this new Sudoku variant, hinting at the next stage in the development of Cracked Sudoku.

  • Sudoku
  • Puzzle
  • Logic Puzzle
  • Game Design
  • mathematics
  • Constraint Satisfaction
  • Algorithm
  • Combinatorics
  • Unique Solution
  • Variant Sudoku
  • Grid Puzzle
  • Recreation
  • Geometric Puzzle

  Summary of Comments ( 58 )
  https://news.ycombinator.com/item?id=43349385

  Verbose tl;dr

  HN commenters generally found the uniquely shaped Sudoku variant interesting and visually appealing. Several praised its elegance and the cleverness of its design. Some discussed the difficulty of the puzzle, wondering if the unique shapes made it easier or harder to solve, and speculating about solving techniques. A few commenters expressed skepticism about its solvability or uniqueness, while others linked to similar previous attempts at uniquely shaped Sudoku grids. One commenter pointed out the potential for this design to be adapted for colorblind individuals by using patterns instead of colors. There was also brief discussion about the possibility of generating such puzzles algorithmically.

  The Hacker News post discussing the "new Sudoku layout with 81 uniquely shaped cells" has generated several comments, mostly focusing on the novelty and solvability of the puzzle, as well as its aesthetic appeal.

  Several commenters discuss the puzzle's difficulty. Some suggest that having uniquely shaped cells might make the puzzle easier because it reduces the search space, while others argue that the unusual shapes could increase the cognitive load, making it harder to recognize patterns. One commenter points out that the puzzle could potentially be more challenging because conventional Sudoku-solving techniques that rely on recognizing number patterns within rows, columns, and 3x3 blocks might not be as readily applicable. Another notes that removing the constraint of the regular 3x3 blocks could drastically increase the number of valid puzzle arrangements, and wonders about the implications of this for generating puzzles.

  The aesthetic quality of the puzzle is also a topic of conversation. Some commenters praise the elegance and novelty of the design, while others find it visually cluttered or difficult to parse. One comment highlights the potential accessibility issues of such a design, suggesting that it may be challenging for people with visual impairments or cognitive processing difficulties.

  The discussion touches on the practicalities of implementing this new format, with one user mentioning the need for a specialized input method or physical pieces.

  The originality of the design is also questioned, with some commenters linking to similar past attempts at creating variations on the standard Sudoku grid. One comment provides a link to a previous discussion on Hacker News about a Sudoku variant with similar properties. This raises questions about the true novelty of the presented puzzle and whether it represents a significant departure from existing variations.

  Finally, the post sparks some theoretical discussions on the mathematics of Sudoku, including the number of possible valid Sudoku grids and the computational complexity of solving them. One comment suggests that the unique shape constraint could potentially simplify the process of generating valid Sudoku puzzles, a topic that others express interest in exploring further.