equilateral 2-player game in 72-gon (I Soros Olympiad 1994-95 R1 9.2)
Source:
July 30, 2021
combinatoricscombinatorial geometryRegularEquilateralgameStrategy
Problem Statement
Given a regular -gon. Lenya and Kostya play the game "Make an equilateral triangle." They take turns marking with a pencil on one still unmarked angle of the -gon: Lenya uses red. Kostya uses blue. Lenya starts the game, and the one who marks first wins if its color is three vertices that are the vertices of some equilateral triangle, if all the vertices are marked and no such a triangle exists, the game ends in a draw. Prove that Kostya can play like this so as not to lose.