Problem

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

Tags: combinatorics, polygon, Polygons



Let $A_1 A_2...A_n$ be a convex $n$-gon. What’s the number of $m$-gons with vertices from $A_1,A_2,...,A_n$ such that between each two adjacent vertices of the $m$-gon there are at least $k$ vertices from the $n$-gon?