Author:
Dickson Jessica,Perrier Rachel
Abstract
Abstract
Dots-and-Boxes is a popular children’s game whose winning strategies have been studied by Berlekamp, Conway, Guy, and others. In this article we consider two variations, Dots-and-Triangles and Dots-and-Polygons, both of which utilize the same lattice game board structure as Dots-and-Boxes. The nature of these variations along with this lattice structure lends itself to applying Pick’s theorem to calculate claimed area. Several strategies similar to those studied in Dots-and-Boxes are used to analyze these new variations.
Subject
General Chemical Engineering
Reference9 articles.
1. [Aic+05] Oswin Aichholzer et al. “Games on triangulations”. In: Theoretical Computer Science 343 (2005), pp. 42–71. doi: http://doi.org/10.1016/j.tcs.2005.05.007.10.1016/j.tcs.2005.05.007
2. [Apo76] Tom M. Apostol. Introduction to Analytic Number Theory. New York: Springer Science-Busines Media, 1976, pp. 62–63.10.1007/978-1-4757-5579-4
3. [BCG82] Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy. Winning Ways for Your Mathematical Plays. Vol. 2. New York, New York: Academic Press Inc., 1982.
4. [Ber00] Elwyn Berlekamp. The Dots and Boxes Game: Sophisticated Child’s Play. Natick, MA: A K Peters, Lrd., 2000.10.1201/b14452
5. [GKW76] RW Gaskell, MS Klamkin, and P Watson. “Triangulations and Pick’s theorem”. In: Mathematics Magazine 49.1 (1976), pp. 35–37.10.1080/0025570X.1976.11976535