Research Team Led by Professor Kim Jon-lark Publishes “5th-Order Sudoku Game” in IEEE Transactions on Games
A research team led by Professor Kim Jon-lark of the Department of Mathematics at Sogang University has developed a new form of Sudoku game using perfect codes and published their research findings in the international academic journal IEEE Transactions on Games (Early Access).
This research was conducted jointly by a team of graduate students—Ahn Jun-min, Baek Jae-hyun, Kim Geon-hwi, and Lim Ha-eun—led by Professor Kim Jon-lark (Director of the Institute for Mathematical and Data Sciences) from the Department of Mathematics. The title of the paper is "Symmetric Sudoku-Type Games from Perfect Codes."
Unlike the traditional 9×9 Sudoku, the research team used perfect codes—a mathematical structure from the field of coding theory—to construct new Sudoku-type games in 5×5 and 8×8 formats. Perfect codes are mathematical structures originally used to detect and correct errors in the process of transmitting information. The research team focused on the fact that these structures have the property of dividing space without gaps and linked this to the Sudoku rule that “each number must appear only once within each region.”
While many existing Sudoku variations focus on changing the shape of the grids, this can weaken the rotational and reflective symmetry inherent in traditional Sudoku. In contrast, the Sudoku proposed in this study is characterized by its ability to create grids with new shapes using the structure of perfect codes while maintaining a high level of symmetry.
In particular, 5×5 Sudoku is smaller than the standard 9×9 Sudoku, making it suitable for mobile environments or a puzzle game to enjoy in short bursts. To analyze the difficulty of the generated puzzles, the research team implemented a solver that mimics human solving methods and confirmed that puzzles of varying difficulty levels—ranging from easy to medium to hard—can be created. The paper concludes that 5×5 perfect Sudoku can serve as an alternative to traditional 9×9 Sudoku.
This research is also significant from a commercial perspective. Due to its short playtime, simple rules, and the ability to adjust difficulty levels, 5×5 Sudoku can be expanded into mobile puzzle apps, educational math content, brain training games, and web-based casual games. In particular, the fact that it is a “mathematically verified new Sudoku” can serve as a brand differentiator from existing Sudoku games.
The game is currently available to play directly on the website (https://cicagolab.pythonanywhere.com/).
Professor Kim Jon-lark stated, “This research demonstrates that abstract mathematical theories such as error-correcting codes can be applied to popular puzzle games,” adding, “There is great potential for developing new games and educational content based on mathematical structures in the future.”
This research was conducted with support from the Ministry of Education’s BK21 FOUR program, the Ministry of Science and ICT’s Pioneer Research program, and Sogang University’s G-LAMP.
Paper Link: https://ieeexplore.ieee.org/document/11479876
[SEO Keyword]
IEEE Transactions on Games, Perfect Codes in Coding Theory, Mathematically Verified Sudoku
This research was conducted jointly by a team of graduate students—Ahn Jun-min, Baek Jae-hyun, Kim Geon-hwi, and Lim Ha-eun—led by Professor Kim Jon-lark (Director of the Institute for Mathematical and Data Sciences) from the Department of Mathematics. The title of the paper is "Symmetric Sudoku-Type Games from Perfect Codes."
Unlike the traditional 9×9 Sudoku, the research team used perfect codes—a mathematical structure from the field of coding theory—to construct new Sudoku-type games in 5×5 and 8×8 formats. Perfect codes are mathematical structures originally used to detect and correct errors in the process of transmitting information. The research team focused on the fact that these structures have the property of dividing space without gaps and linked this to the Sudoku rule that “each number must appear only once within each region.”
While many existing Sudoku variations focus on changing the shape of the grids, this can weaken the rotational and reflective symmetry inherent in traditional Sudoku. In contrast, the Sudoku proposed in this study is characterized by its ability to create grids with new shapes using the structure of perfect codes while maintaining a high level of symmetry.
In particular, 5×5 Sudoku is smaller than the standard 9×9 Sudoku, making it suitable for mobile environments or a puzzle game to enjoy in short bursts. To analyze the difficulty of the generated puzzles, the research team implemented a solver that mimics human solving methods and confirmed that puzzles of varying difficulty levels—ranging from easy to medium to hard—can be created. The paper concludes that 5×5 perfect Sudoku can serve as an alternative to traditional 9×9 Sudoku.
This research is also significant from a commercial perspective. Due to its short playtime, simple rules, and the ability to adjust difficulty levels, 5×5 Sudoku can be expanded into mobile puzzle apps, educational math content, brain training games, and web-based casual games. In particular, the fact that it is a “mathematically verified new Sudoku” can serve as a brand differentiator from existing Sudoku games.
The game is currently available to play directly on the website (https://cicagolab.pythonanywhere.com/).
Professor Kim Jon-lark stated, “This research demonstrates that abstract mathematical theories such as error-correcting codes can be applied to popular puzzle games,” adding, “There is great potential for developing new games and educational content based on mathematical structures in the future.”
This research was conducted with support from the Ministry of Education’s BK21 FOUR program, the Ministry of Science and ICT’s Pioneer Research program, and Sogang University’s G-LAMP.
Paper Link: https://ieeexplore.ieee.org/document/11479876
[SEO Keyword]
IEEE Transactions on Games, Perfect Codes in Coding Theory, Mathematically Verified Sudoku