From The American Mathematical Monthly, Volume 117, Number 7 (August – September 2010)

11520. Proposed by Peter Ash, Cambridge Math Learning, Bedford MA. Let n and k be integers

with 1 ≤ ≤k n and let A be a set of n real numbers. For i with 1 ≤ ≤i n , let i

S be the set of all

subsets of A with i elements, and let max( )σ∈

=∑i

i s Ss . Express the kth smallest element of A as

a linear combination of 0 , ,σ σ�n.

[Note. There is a typo on the last line. 0σ should (of course) be 1σ ].