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The research investigates the structural properties of Suirodoku, particularly the minimum number of clues required.

March 3, 2026Open Access

There Is a 13-Clue Suirodoku

Puntos clave

The research investigates the structural properties of Suirodoku, particularly the minimum number of clues required.
Analyzed the back-circulant configurations of Suirodoku.
Calculated the number of orthogonal mates and structural orbits.
Examined the fusion rates under paratopism.
Compared findings with classical Sudoku properties.
The back-circulant has 3,622,317,453 orthogonal mates.
Identified 740 structural orbits and 734 species with a fusion rate of 0.8%.
The Sudoku-162 shows a high fusion rate of 87.4%, resulting in 1,129 orbits and 142 species.
Demonstrated that 13 clues are sufficient for Suirodoku, compared to 17 required for classical Sudoku.

Resumen

A Suirodoku is an order-9 Graeco-Latin square in which each component satisfies the 3×3 block constraint of Sudoku. We show that the back-circulant alone admits 3,622,317,453 orthogonal mates, revealing 740 structural orbits and 734 species — a fusion rate of 0.8% under paratopism. The Sudoku-162 reveals an opposite regime: 1,129 orbits merge into 142 species (87.4% fusion). At the top of the hierarchy sits the Crystal Grid (1,296 symmetries), and the Sudoku-162 produces a stabilizer of order 81 — forbidden in classical Sudoku. On the minimum number of clues: classical Sudoku requires 17 (McGuire et al., 2014); for Suirodoku, 13 suffice. Full source code: https://github.com/teliance23/suirodoku-lab

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Jordan Maire (Sun,) studied this question.

synapsesocial.com/papers/69a67f12f353c071a6f0ae2a https://doi.org/https://doi.org/10.5281/zenodo.18820235

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