# RMO geometry problem

Geometry Level 4

Consider a 20-sided convex polygon K, with vertices A1,A2,A3.............A20 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, (A1A2, A4A5,A11A12) is an admissible triple but (A1A2, A4A5 ,A19A20) is not

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