Research Article

The Settlers of “Catanbinatorics”

Published: 2019-5-27

Journal: Mathematics Magazine

DOI: 10.1080/0025570x.2019.1561096

Abstract

Catan is a dynamic property-building and trading board game in which players build a new board every time they play by arranging tiles, number tokens, and port markers. In this paper, we count the number of possible boards, consider different ways of counting the number tokens based on probability, and count the number of non-equivalent tile arrangements in two ways: one using a direct approach, the other taking advantage of more elegant techniques from abstract algebra. Summary.Catan is a dynamic property-building and trading board game in which players build a new board every time they play by arranging tiles, number tokens, and port markers. In this paper, we count the number of possible boards, consider different ways of counting the number tokens based on probability, and count the number of non-equivalent tile arrangements in two ways: one using a direct approach, the other taking advantage of more elegant techniques from abstract algebra. Keywords MSC: Primary 05A15 Secondary 20B30 Acknowledgements We would like to thank the anonymous reviewers for their helpful suggestions and Jonathon Miller for his contributions in our preliminary discussions. Additional information Notes on contributors Jathan Austin JATHAN AUSTIN (MR Author ID: 1040737) is an associate professor of mathematics at Salisbury University in Maryland. He earned a B.S. in mathematics from Salisbury University, and both an M.S. in mathematics and a Ph.D. in mathematics education from the University of Delaware. He teaches a range of mathematics courses, both for future and current teachers and for traditional mathematics majors. His research interests include the mathematics of games, elementary number theory with connections to linear algebra, and the mathematical development of prospective teachers. Brian G. Kronenthal BRIAN G. KRONENTHAL (MR Author ID: 863868) is an associate professor of mathematics at Kutztown University of Pennsylvania. He earned his B.S. in mathematics from Lafayette College (Easton, Pennsylvania), as well as his M.S. and Ph.D. in mathematics from the University of Delaware. His favorite research problems are combinatorial, often with an algebraic flair. In addition to teaching and research, he enjoys playing ping pong, watching movies, and rooting for Philadelphia sports teams. Susanna Molitoris Miller SUSANNA MOLITORIS MILLER (MR Author ID: 1284731) is an assistant professor of Mathematics Education at Kennesaw State University in GA where she teaches mathematics content courses for teachers. She earned her B.S. in mathematics from The University of Scranton, and M. S. in mathematics and Ph.D. in mathematics education from The University of Delaware. Susanna’s research focuses on how students learn mathematical concepts in both formal situations, such as those involving mathematical definitions, as well as non-conventional settings, such as through games or self-directed learning experiences. In her free time, she enjoys spending time with her family, fiber arts, tea and, of course, game night with friends.

Faculty Members

  • Brian G. Kronenthal - Kutztown University of Pennsylvania, Kutztown, PA 19530,
  • Jathan Austin - Salisbury University, Salisbury, MD 21801,
  • Susanna Molitoris Miller - Kennesaw State University, Kennesaw, GA 30144,

Themes

  • Mathematical structures in board games
  • Game theory
  • Combinatorial mathematics
  • Algebraic techniques in counting problems
  • Probability in games

Categories

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