MathDB

Let

n

be a fixed positive integer. The points

A_1

A_2

\ldots

A_{2n}

are on a straight line. Color each point blue or red according to the following procedure: draw

n

pairwise disjoint circumferences, each with diameter

A_iA_j

for some

i \neq j

and such that every point

A_k

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.

Problem Statement