July 7–July 14, 2009

Problem

n points are given on the circumference of a circle, and the chords determined by them are drawn. Suppose no three chords have a common point. How many triangles are formed all of whose vertices lie inside the circle? For example, in the picture below, n = 6 and there is one such triangle.

Solution

here

List of solvers

Huy Hoang-Nguyen, Matthew Inouye (undergrad); Patrick C. Tam (Berkeley grad); Peiyush Jain, Mike Goodman, Qiyuan Wei, Lloyd Sakazaki, Yo Tu (outside).

Patrick Tam wins the prize!