Let n be a fixed positive integer. The points A1, A2, …, A2n are on a straight line. Color each point blue or red according to the following procedure: draw n pairwise disjoint circumferences, each with diameter AiAj for some i=j and such that every point Ak belongs to exactly one circumference. Points in the same circumference must be of the same color.
Determine the number of ways of coloring these 2n points when we vary the n circumferences and the distribution of the colors. inductioncombinatorics unsolvedcombinatorics