The First Playable Graeco-Latin Puzzle
Rainbow Technique
Because of orthogonal structure, each digit appears across all 9 colors. Scan a digit through the grid to locate the missing color. The number reveals the color.
A logical deduction method that emerges directly from the Graeco-Latin architecture.
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Chromatic Circle
The structure is fully symmetric: each color also covers all 9 digits. Follow a color through the grid to isolate the missing digit. The color reveals the number.
A deduction technique native to the orthogonal sudoku format.
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Sudoku was the warm-up.
Tsuidoku is the real game.
What is Tsuidoku?
Tsuidoku, also known as Suirodoku, is the first playable Graeco-Latin square puzzle: a 9×9 grid where every cell holds a unique digit-color pair. Digits and colors each independently obey sudoku constraints. That combination of digits and colors is precisely what makes it playable, guaranteeing all 81 pairs appear exactly once.
Graeco-Latin Orthogonality in 4 Rules
This free online orthogonal sudoku puzzle enforces 4 simultaneous constraints across every row, column and block:
- Each row contains numbers 1-9 and all 9 colors
- Each column contains numbers 1-9 and all 9 colors
- Each 3×3 region contains numbers 1-9 and all 9 colors
- Each digit-color pair appears exactly once: the Graeco-Latin orthogonality
81 Orthogonal Pairs
Graeco-Latin orthogonality produces a perfect bijection: every one of the 81 digit-color pairings is unique across the grid. This is what makes Tsuidoku the first truly playable Graeco-Latin square: digits and colors together create a structure that can actually be solved as a puzzle.
81 cells.
81 combinations.
0 duplicates.
1 solution.Sudoku vs Tsuidoku
Sudoku
- 3 constraints
- Numbers only
- Each number repeated 9 times
- Classic techniques
Tsuidoku
- 4 constraints: rows, columns, regions + colors
- Colors are full players, not decoration
- 81 unique digit-color pairs, 0 repetition
- Rainbow & Chromatic Circle exclusive techniques
Frequently Asked Questions
What is a Graeco-Latin square?
A Graeco-Latin square is a mathematical structure where two sets of symbols (here digits and colors) are combined so that each pair appears exactly once. Euler studied them in the 18th century. Tsuidoku, also known as Suirodoku, is the first version ever designed as a playable puzzle game.
What does Graeco-Latin orthogonality mean in Tsuidoku?
Like Sudoku, each row/column/3×3 region must contain numbers 1-9. Additionally, each row/column/region must contain all 9 colors, and each digit-color pair appears exactly once in the grid: the Graeco-Latin orthogonality constraint.
Is Tsuidoku free to play?
Yes. Tsuidoku is completely free to play online in your browser, no download or registration needed. The same game is also available as Suirodoku on suirodoku.com.
Why is Tsuidoku the first playable Graeco-Latin square?
Previous Graeco-Latin squares were mathematical objects with no real game structure. Tsuidoku adds Sudoku constraints on top of the orthogonality, creating a puzzle with a unique solution and a complete set of logical solving techniques. This combination had never been achieved before.