If player B plays correctly, then player A cannot win
Source: Austrian Mathematical Olympiad 1999, Part 2, D2, P3
June 28, 2011
Online Math Opensymmetrycombinatorics proposedcombinatorics
Problem Statement
Two players and play the following game. An even number of cells are placed on a circle. begins and and play alternately, where each move consists of choosing a free cell and writing either or in it. The player after whose move the word (OMO = Osterreichische Mathematik Olympiade) occurs for the first time in three successive cells wins the game. If no such word occurs, then the game is a draw. Prove that if player plays correctly, then player cannot win.