This time we have a
counting, or combinatorics problem.
On a circle, pick an even number of distinct points and pair them up to draw
chords.
How many ways can this be done for 3, 4, or (bonus question) any number of
chords?
Consider two ways equivalent if the points can be pushed around the circle to
transform
one into another without any point crossing another. Consider two ways
different
if the chords intersect in a different number of ways. The two ways for the
2 chord case are
pictured. Three ways for the 3 chord case are pictured.
Harder question: what
if all the points do not have to be distinct?
Send your solution to sedwards@spsu.edu,
or by snail mail to Steve Edwards in the Math
Department. The names of the first solvers will be posted here.