MathDB

sum of differences of largest to smallest of subsets of {1,2,...,n}

Source: Mathematics Regional Olympiad of Mexico Center Zone 2009 P6

November 10, 2021

combinatorics

Problem Statement

For each subset

A

\{1,2, \dots, n \}

, let

M_A

be the difference between the largest of the elements of

A

and the smallest of the elements of

A

. Finds the sum of all values of

M_A

when all possible subsets

A

\{1,2, \dots, n \}

are considered.