Consider an n x n chessboard, where each square is arbitrarily chosen to be either black or white. Your goal is to make all squares in the chessboard white. At each step, you are allowed to "switch" a square, but each switch will toggle not only the particular square being switched, but also the 4 squares that are adjacent to it: Two vertically up and down and two horizontally up and down the square being switched. Note : At corners only 4/3 squares are toggled, while at the center all 5 squares are toggled.
Show how you can make the entire chessboard white.
Solution: Posted by JDGM in comments! Very academic solution to a very interesting problem! :) Thanks