a circular game board is divided into n sectors, empty or occupied by marker
Source: 2000 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p4
January 27, 2020
combinatoricsgame
Problem Statement
A circular game board is divided into sectors. Each sector is either empty or occupied by a marker. In each step one chooses an occupied sector, removes its marker and then switches each of the two adjacent sectors from occupied to empty or vice-versa. Starting with a single occupied sector, for which is it possible to end up with all empty sectors after finitely many steps?