The latest articles on Forem by Jordan Maire (@teliance). https://forem.com/teliance https://media2.dev.to/dynamic/image/width=90,height=90,fit=cover,gravity=auto,format=auto/https:%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Fuser%2Fprofile_image%2F3771246%2Ffa2d0ef6-b648-448d-8a6c-e70ac9150943.jpg https://forem.com/teliance en Jordan Maire Fri, 13 Feb 2026 15:40:10 +0000 https://forem.com/teliance/building-a-playable-graeco-latin-sudoku-square-the-math-behind-suirodoku-gf3 https://forem.com/teliance/building-a-playable-graeco-latin-sudoku-square-the-math-behind-suirodoku-gf3 <p>In 1782, Euler imagined arranging 36 officers in a square so that no regiment and no rank repeated in any row or column. He couldn't solve it. The structure he imagined, Graeco-Latin squares, became a cornerstone of combinatorics.</p> <p>I turned it into a puzzle you can play.</p> <h2> What is Suirodoku? </h2> <p>A 9×9 grid where each cell contains a digit (1-9) AND a color (9 colors). The rules:</p> <ul> <li>Each row contains all 9 digits and all 9 colors</li> <li>Each column contains all 9 digits and all 9 colors </li> <li>Each 3×3 block contains all 9 digits and all 9 colors</li> <li>Each of the 81 digit-color pairs appears exactly once</li> </ul> <p>That last rule is what makes it fundamentally different from Sudoku. Every cell has a unique identity.</p> <h2> The interesting math </h2> <p>I formalized Suirodoku as a Constraint Satisfaction Problem. Classical Sudoku has 27 constraints. Suirodoku has 55.</p> <p>The global pair uniqueness constraint creates a bijection between cells and pairs. This means solving techniques exist that have no Sudoku equivalent:</p> <ul> <li> <strong>Rainbow Technique</strong>: track one digit across all 9 colors</li> <li> <strong>Chromatic Circle</strong>: track one color across all 9 digits</li> </ul> <h2> An open problem </h2> <p>The <strong>God Digit Problem</strong>: must every uniquely solvable Suirodoku puzzle contain all 9 digits among its clues? In Sudoku you can always relabel digits, but Suirodoku's global constraint breaks that symmetry.</p> <p>I proved a Dichotomy Theorem: either no digit is critical, or all are. Which one holds remains unsolved.</p> <h2> Try it <a href="https://suirodoku.com" rel="noopener noreferrer">suirodoku.com</a> </h2> <p>Research paper: <a href="https://zenodo.org/records/18625970" rel="noopener noreferrer">Zenodo</a></p> javascript algorithms webdev