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MathNet 2022-part-02 — 197 problems (EN–VI) Question 20

Math Olympiad Vault · MathNet 2022-part-02 — 197 problems (EN–VI)

Question 20

Mari chooses five distinct positive integers not greater than $2021$. From these five numbers, it must be possible to choose two numbers with sum $1919$ in two different ways. Likewise, from these five numbers, it must be possible to choose two numbers with sum $2929$ in two different ways. Find all possibilities of which five numbers Mari may choose.