SONGKLANAKARIN JOURNAL OF SCIENCE & TECHNOLOGY

Volume 43, No. 01, Month JANUARY, Year 2021, Pages 105 - 110

Greedy strategy for some normal m x n closing octagons games and winning strategy for normal 1 x n and 2 x n closing octagons games

Ratinan Boonklurb, Thitiphut Leelathanakit

Abstract Download PDF

m x n Closing Octagons (CO) game is a combinatorial game for two players. The game starts with an m x n array of octagons such that every two adjacent octagons has one common side and 0 points. Players alternately turn by the following rules. (i) A player moves by coloring one side of an octagon. (ii) A player who colors the eighth side of k octagons earns k points and gets one more move. The game ends when every side of the octagons has been colored and the player with the most points wins. This game is formulated into a new CO game using graphs. In order to analyze it, more rules are added and the game with these additional rules is called a normal m x n CO game. In this article, we give a greedy strategy for some normal m x n CO games and a winning strategy for normal 1 x n and 2 x n CO games.

Keywords

closing octagons game, combinatorial game, 2-person game, strategy

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