Quant Interview Question #quant

Consider the infinite grid in the plane. Each integer grid point is colored using one of 100 colors with no restriction on how the colors are assigned. We want to find a rectangle whose four vertices are grid points and all have the same color. For example here, the four vertices of the highlighted rectangle are all the same color. The problem asks, does such a monochromatic rectangle necessarily exist for every possible coloring of the integer grid? Post your answers in comments.