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CMO 2017 P3

Source: Canadian Mathematical Olympiad 2017

March 31, 2017
combinatoricsSetsAveragemedian

Problem Statement

Define SnS_n as the set 1,2,⋯ ,n{1,2,\cdots,n}. A non-empty subset TnT_n of SnS_n is called balancedbalanced if the average of the elements of TnT_n is equal to the median of TnT_n. Prove that, for all nn, the number of balanced subsets TnT_n is odd.
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