Lamps on a 2014x2014 board
Source: Dutch IMO TST I Problem 5
July 17, 2014
combinatorics proposedcombinatorics
Problem Statement
On each of the squares of a -board a light bulb is put. Light bulbs can be either on or off. In the starting situation a number of the light bulbs is on. A move consists of choosing a row or column in which at least light bulbs are on and changing the state of all light bulbs in this row or column (from on to off or from off to on). Find the smallest non-negative integer such that from each starting situation there is a finite sequence of moves to a situation in which at most light bulbs are on.