2001 IMO Shortlist Problems/C1

Problem

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 $1 \le i < j < k \le 2001$ such that $a_j = a_i + 1$ and $a_k = a_j + 1$ . Considering all such sequences $A$ find the greatest value of $m$ .

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2001 IMO Shortlist Problems/C1

Problem

Solution