Monday, December 1, 2014
Lights forming a hexagon
Six lights are placed such that they form a regular hexagon. At each turn, we're allowed to do one of the following: 1. Toggle three consecutive lights 2. Toggle three lights that form an equilateral triangle 3. Toggle two diametrically opposite lights Prove or disprove, for any given starting configuration, we can turn off all the lights through a series of turns as described above.