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Romania Junior TST 2021 Day 2 P2

Source:

June 6, 2021
number theorySubsetsromaniaRomanian TST

Problem Statement

For any non-empty subset XX of M={1,2,3,...,2021}M=\{1,2,3,...,2021\}, let aXa_X be the sum of the greatest and smallest elements of XX. Determine the arithmetic mean of all the values of aXa_X, as XX covers all the non-empty subsets of MM.
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