Lightning Bugs
Source: OMM 2007 5
July 19, 2014
combinatorics unsolvedcombinatorics
Problem Statement
In each square of a grid there is a lightning bug on or off. One move is to choose three consecutive squares, either horizontal or vertical, and change the lightning bugs in those squares from off to on or from on to off. Show if at the beginning there is one lighting bug on and the rest of them off, it is not possible to make some moves so that at the end they are all turned off.