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Problem 5 of Fourth round - m-gons in an n-gon with a certain property

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

December 15, 2019
combinatoricspolygonPolygons

Problem Statement

Let A1A2...AnA_1 A_2...A_n be a convex nn-gon. What’s the number of mm-gons with vertices from A1,A2,...,AnA_1,A_2,...,A_n such that between each two adjacent vertices of the mm-gon there are at least kk vertices from the nn-gon?
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