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Combinatorics from Iran TST

Source: Iranian TST 2018, third exam day 2, problem 5

April 19, 2018
combinatoricsIranIranian TST

Problem Statement

2n−12n-1 distinct positive real numbers with sum SS are given. Prove that there are at least (2n−2n−1)\binom {2n-2}{n-1} different ways to choose nn numbers among them such that their sum is at least S2\frac {S}{2}.
Proposed by Amirhossein Gorzi
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