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Subsets with either odd and even sums of elements

Source: Polish Second Round 2001

March 6, 2012

combinatorics proposedcombinatorics

Problem Statement

For a positive integer

n

, let

A_n

and

B_n

be the families of

n

-element subsets of

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

with respectively even and odd sums of elements. Compute

|A_n|-|B_n|