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Recreational Mathematics Magazine

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Mathematical Citation Quotient (MCQ) 2016: 0.05

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2182-1976
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Eternal Picaria

Urban Larsson
  • Corresponding author
  • Department of Mathematics and Statistics, Dalhousie University, 6316 Coburg Road, PO BOX 15000, Halifax, Nova Scotia, Canada
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/ Israel Rocha
  • Department of Mathematics and Statistics, Dalhousie University, 6316 Coburg Road, PO BOX 15000, Halifax, Nova Scotia, Canada
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Published Online: 2017-06-09 | DOI: https://doi.org/10.1515/rmm-2017-0016

Abstract

Picaria is a traditional board game, played by the Zuni tribe of the American Southwest and other parts of the world, such as a rural Southwest region in Sweden. It is related to the popular children’s game of Tic-tac-toe, but the 2 players have only 3 stones each, and in the second phase of the game, pieces are slided, along specified move edges, in attempts to create the three-in-a-row. We provide a rigorous solution, and prove that the game is a draw; moreover our solution gives insights to strategies that players can use.

Keywords: Abstract strategy game; Alignment game; Board game; Cyclic game; Loopy game; Luffarschack; Play-proof; Tapatan; Three-in-a-row; Three men’s morris; Zuni tribe

References

  • [1] Culin, Stewart. Games of North American Indians, Washington DC: US gov Printing Office, 1907.Google Scholar

  • [2] Philip D. Straffin, Jr. “Position Graphs for Pong Hau K’i and Mu Torere”, Mathematics Magazine, 68, 5, pp. 382-386, 1995.Google Scholar

About the article

Published Online: 2017-06-09

Published in Print: 2017-05-24


Citation Information: Recreational Mathematics Magazine, Volume 4, Issue 7, Pages 119–133, ISSN (Online) 2182-1976, DOI: https://doi.org/10.1515/rmm-2017-0016.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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