Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2018 3.2

Tags: algebra, inequalities, max



Let $a, b, c$, and $d$ be real numbers. The six sums of two numbers $x$ and $y$, different from the previous four, are $117$, $510$, $411$, $252$, in no particular order. Determine the maximum possible value of $x + y$.