Each side of a regular octagon is colored blue or yellow. In each step, the sides are simultaneously recolored as follows: if the two neighbors of a side have different colors, the side will be recolored blue, otherwise it will be recolored yellow. Show that after a finite number of moves all sides will be colored yellow. What is the least value of the number N of moves that always lead to all sides being yellow? Coloringoctagoncombinatorics