MathDB

The number of convex m polygon

Source: Chinese National Olympiad 2009 P3

January 10, 2009

inductioncombinatorics proposedcombinatorics

Problem Statement

Given two integers

m,n

satisfying

4 < m < n.

Let A_{1}A_{2}\cdots A_{2n \plus{} 1} be a regular 2n\plus{}1 polygon. Denote by

P

the set of its vertices. Find the number of convex

m

polygon whose vertices belongs to

P

and exactly has two acute angles.