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