Building a playable Graeco-Latin Sudoku square: the math behind Suirodoku

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. I turned it into a puzzle you can play. What is Suirodoku? A 9×9 grid where each cell contains a digit (1-9) AND a color (9 colors). The rules: Each row contains all 9 digits and all 9 colors Each column contains all 9 digits and all 9 colors Each 3×3 block contains all 9 digits and all 9 colors Each of the 81 digit-color pairs appears exactly once That last rule is what makes it fundamentally different from Sudoku. Every cell has a unique identity. The interesting math I formalized Suirodoku as a Constraint Satisfaction Problem. Classical Sudoku has 27 constraints. Suirodoku has 55. The global pair uniqueness constraint creates a bijection between cells and pairs. This means solving techniques exist that have no Sudoku equivalent: Rainbow Technique : track o