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max of x+y given sums with 6 sums with 4 numbers

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

September 20, 2021
algebrainequalitiesmax

Problem Statement

Let a,b,ca, b, c, and dd be real numbers. The six sums of two numbers xx and yy, different from the previous four, are 117117, 510510, 411411, 252252, in no particular order. Determine the maximum possible value of x+yx + y.
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