Lights on a Board
Source: OMM 2010 2
July 15, 2014
analytic geometryinvariantinductioncombinatorics unsolvedcombinatorics
Problem Statement
In each cell of an board is a lightbulb. Initially, all of the lights are off. Each move consists of changing the state of all of the lights in a row or of all of the lights in a column (off lights are turned on and on lights are turned off).Show that if after a certain number of moves, at least one light is on, then at this moment at least lights are on.