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IMO 2001 — Complete Shortlist Question 7

IMO Shortlist · IMO 2001 — Complete Shortlist

Question 7

Let $ A = (a_1, a_2, \ldots, a_{2001}) $ be a sequence of positive integers. Let m be the number of 3-element subsequences $ (a_i, a_j, a_k) $ with $ 1 \leq i \lt j \lt k \leq 2001 $, such that $ a_j = a_i + 1 $ and $ a_k = a_j + 1 $. Considering all such sequences A, find the greatest value of m.