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2 player game with red, bluec chips on n-gon 2017 May Olympiad L1 p4

Source:

August 25, 2021
gamecombinatoricswinning strategy

Problem Statement

Let nn be an even integer greater than 22. On the vertices of a regular polygon with n sides we can place red or blue chips. Two players, AA and BB, play alternating turns of the next mode: each player, on their turn, chooses two vertices that have no tiles and places on one of them a red chip and in the other a blue chip. The goal of AA is to get three vertices consecutive with tiles of the same color. BB's goal is to prevent this from happening. To the beginning of the game there are no tiles in any of the vertices. Show that regardless of who starts to play, Player BB can always achieve his goal.