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in set of 21 real numbers sum of any 10 is less than sum of rest 11

Source: North Macedonian Mathematical Olympiad 1999 p1

February 12, 2020
Sumalgebrapositivecombinatorics

Problem Statement

In a set of 2121 real numbers, the sum of any 1010 numbers is less than the sum of the remaining 1111 numbers. Prove that all the numbers are positive.
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