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MathNet 2007-part-03 — 185 problems (EN–VI) Question 121

Math Olympiad Vault · MathNet 2007-part-03 — 185 problems (EN–VI)

Question 121

Let $S$ denote the set of all triples $(i, j, k)$ of positive integers where $i + j + k = 17$. Compute
$$
\sum_{(i, j, k) \in S} i j k.
$$