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A variation on
the game Set
David Clark, George Fisk and Nurullah Goren
Vol. 9 (2016), No. 2, 249–264
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Abstract |
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Set is a very popular card game with strong mathematical structure. In this paper, we describe “anti-Set”, a variation on Set in which we reverse the objective of the game by trying to avoid drawing “sets”. In anti-Set, two players take turns selecting cards from the Set deck into their hands. The first player to hold a set loses the game. By examining the geometric structure behind Set, we determine a winning strategy for the first player. We extend this winning strategy to all nontrivial affine geometries over , of which Set is only one example. Thus we find a winning strategy for an infinite class of games and prove this winning strategy in geometric terms. We also describe a strategy for the second player which allows her to lengthen the game. This strategy demonstrates a connection between strategies in anti-Set and maximal caps in affine geometries. |
Keywords
SET (game), combinatorics, finite geometry, cap
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Mathematical Subject Classification 2010
Primary: 97A20, 51EXX
Secondary: 51E15, 51E22
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Milestones
Received: 13 October 2014
Revised: 29 January 2015
Accepted: 6 February 2015
Published: 2 March 2016
Communicated by Kenneth S. Berenhaut
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Authors |
| David Clark | |
| Department of Mathematics Grand Valley State University 1 Campus Drive Allendale, MI 49401 United States |
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| George Fisk | |
| Department of Mathematics University of Minnesota Minneapolis, MN 55455 United States |
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| Nurullah Goren | |
| Department of Mathematics Pomona College Claremont, CA 91711 United States |
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