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average of sum of min and max of subsets of [2000]

Source: Moldova 2000 Grade 10 P3

April 26, 2021
combinatorics

Problem Statement

For every nonempty subset XX of M={1,2,…,2000}M=\{1,2,\ldots,2000\}, aXa_X denotes the sum of the minimum and maximum element of XX. Compute the arithmetic mean of the numbers aXa_X when XX goes over all nonempty subsets XX of MM.
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