Year: 2025
Type: article
Abstract: EvenQuads is a new card game that is a generalization of the SET game, where each card is characterized by three attributes, each taking four possible values. Four cards form a quad when, for each attribute, the values are the same, all different, or half and half. For any $$\ell$$ ℓ cards selected from the deck of EvenQuads, it is possible to construct an error-correcting linear binary code of length $$\ell$$ ℓ and Hamming distance 4, where quads correspond to codewords of weight 4. Using error-correcting codes, we calculate the number of possible quads that can be formed with up to 8 cards. We also estimate the number of cards that do not contain quads for decks of different sizes. In addition, we discuss properties of error-correcting codes built on semimagic, magic, and strongly magic quad squares. This highlights a rich interplay between recreational mathematics games and coding theory and encourages others to explore similar combinatorial games for hidden connections!
Source: SN Computer Science
Authors: Nikhil Byrapuram, Hwiseo Choi, Adam Ge, Selena Ge, Sylvia Zia Lee, Evin Liang, Rajarshi Mandal, Aika Oki, Daniel Wu, Michael Yang, Tanya Khovanova
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4413426938