6

Part of 2019 New Zealand MO

Problems(1)

max of m(U) /|U|, U subset of V , set of vertices of regular 21-gon

Source: New Zealand MO 2019 Round 1 p6

V

be the set of vertices of a regular

21

-gon. Given a non-empty subset

U

V

m(U)

be the number of distinct lengths that occur between two distinct vertices in

U

. What is the maximum value of

\frac{m(U)}{|U|}

U

varies over all non-empty subsets of

V

combinatoricsRegular