# Sum it up!

Algebra Level 5

Let $T = \{5, 8, 11, 14, \ldots, 47, 50\}$ and let $S$ be the sum of $3$ pairwise distinct integers chosen from $T$. How many distinct possible values are there for $S$?

Details and assumptions

3 integers are pairwise distinct if no two of them are equal.

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