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How Did They Design This Game? Swish: Complexity and Unplayable Positions

Authors Antoine Dailly, Pascal Lafourcade , Gaël Marcadet

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Author Details

Antoine Dailly
  • Université Clermont-Auvergne, CNRS, Mines de Saint-Étienne, Clermont-Auvergne-INP, LIMOS, 63000 Clermont-Ferrand, France
Pascal Lafourcade
  • Université Clermont-Auvergne, CNRS, Mines de Saint-Étienne, Clermont-Auvergne-INP, LIMOS, 63000 Clermont-Ferrand, France
Gaël Marcadet
  • Université Clermont-Auvergne, CNRS, Mines de Saint-Étienne, Clermont-Auvergne-INP, LIMOS, 63000 Clermont-Ferrand, France

Funding

  • Dailly, Antoine: This author was supported by the International Research Center "Innovation Transportation and Production Systems" of the I-SITE CAP 20-25 and by the ANR project GRALMECO (ANR-21-CE48-0004).
  • Marcadet, Gaël: This author was supported by the DataLake-For-Nuclear (D4N) project funded by the BPI institute.

Acknowledgements

We thank the anonymous referees for their useful suggestions and remarks.

Cite AsGet BibTex

Antoine Dailly, Pascal Lafourcade, and Gaël Marcadet. How Did They Design This Game? Swish: Complexity and Unplayable Positions. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.FUN.2024.10

Abstract

Swish is a competitive pattern recognition card-based game, in which players are trying to find a valid cards superposition from a set of cards, called a "swish". By the nature of the game, one may expect to easily recover the logic of the Swish’s designers. However, no justification appears to explain the number of cards, of duplicates, but also under which circumstances no player can find a swish. In this work, we formally investigate Swish. In the commercial version of the game, we observe that there exist large sets of cards with no swish, and find a construction to generate large sets of cards without swish. More importantly, in the general case with larger cards, we prove that Swish is NP-complete.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Backtracking
  • Mathematics of computing → Combinatorial algorithms
Keywords
  • Game
  • Complexity
  • Algorithms

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