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Sum set diameters: try to do it with the least calculation!

Source: Brazilian Math Olympiad, 2002

November 15, 2005

combinatorics unsolvedcombinatorics

Problem Statement

For any non-empty subset

A

\{1, 2, \ldots , n\}

define

f(A)

as the largest element of

A

minus the smallest element of

A

. Find

\sum f(A)

where the sum is taken over all non-empty subsets of

\{1, 2, \ldots , n\}