Connecting Points on a Circle
Source:
March 3, 2008
Problem Statement
Let be distinct points on a circle. Determine the number of possible configurations made by drawing a set of line segments connecting pairs of these points, such that: each is the endpoint of at most one segment and no two segments intersect. (The configuration with no edges drawn is allowed. An example of a valid configuration is shown below.)
[asy]unitsize(1cm);
pair[] P = new pair[8];
align[] A = {E, NE, N, NW, W, SW, S, SE};
for (int i = 0; i < 8; ++i) {
P = dir(45*i);
dot(P);
label("", P, A,fontsize(8pt));
}
draw(unitcircle);
draw(P[0]--P[1]);
draw(P[2]--P[4]);
draw(P[5]--P[6]);[/asy]