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MathNet 2008-part-01 — 165 problems (EN–VI) Question 129

Math Olympiad Vault · MathNet 2008-part-01 — 165 problems (EN–VI)

Question 129

It is given the set $S = \{1, 2, 3, \dots, 3n\}$, where $n$ is a positive integer. $T$ is a subset of $S$ such that: for any $x, y, z \in T$ (where $x, y, z$ can be the same), $x+y+z \notin T$. Find the maximum value of the number of elements in such set.