The sides of a $99$-gon are initially colored so that consecutive sides are red, blue, red, blue, $\,\ldots, \,$ red, blue, yellow. We make a sequence of modifications in the coloring, changing the color of one side at a time to one of the three given colors (red, blue, yellow), under the constraint that no two adjacent sides may be the same color. By making a sequence of such modifications, is it possible to arrive at the coloring in which consecutive sides are red, blue, red, blue, red, blue, $\, \ldots, \,$ red, yellow, blue?
Consider $\nu =$ the number of (yellow, red) pairs minus the number of (red, yellow) pairs in the configuration. $\nu=1$ for the initial configuration, and $\nu=-1$ for the desired configuration. The constraint on modifications effectively requires that when we make a modification of a side, its two neighboring sides should have the same color; thus modifications don't change $\nu$. Therefore passing from a $\nu=1$ configuration to a $\nu=-1$ one is impossible.