Eternal Picaria

Open access


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.


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

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

Journal Information

Mathematical Citation Quotient (MCQ) 2016: 0.05

Target Group

researchers in the fields of games and puzzles, problems, mathmagic, mathematics and arts, math and fun with algorithms


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