A number theory problem by divyansh tripathi

Consider a 20-sided convex polygon K, with vertices A1, A2, . . . , 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 while (A1A2, A4A5, A19A20) is not.)

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