Ratinan Boonklurb and Thitiphut Leelathanakit

DOI: 10.14456/sjst-psu.2021.14

pp. 105 - 110

Abstract

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.