Game on triangular board
Source: Mexico National Olympiad Mock Exam 2017 P2
November 2, 2019
combinatoricsboardTrianglesgame
Problem Statement
Alice and Bob play on an infinite board formed by equilateral triangles. In each turn, Alice first places a white token on an unoccupied cell, and then Bob places a black token on an unoccupied cell. Alice's goal is to eventually have white tokens on a line. Determine the maximum value of for which Alice can achieve this no matter how Bob plays.Proposed by Oriol Solé