MathDB

Consider a

20

-sided convex polygon

K

, with vertices

A_1, A_2,...,A_{20}

in that order. Find the number of ways in which three sides of

K

can be chosen so that every pair among them has at least two sides of

K

between them. (For example

(A_1A_2, A_4A_5, A_{11}A_{12})

is an admissible triple while

(A_1A_2, A_4A_5, A_{19}A_{20})

is not.

Problem Statement