IMO 2008 Shortlist C5
Let S = {x1,x2,...,xk+} be a (k + )-element set of real numbers contained in the interval [0,1]; k and are positive inte...
Category: Combinatorics
Problem
Let S = {x1,x2,...,xk+} be a (k + )-element set of real numbers contained in the
interval [0,1]; k and are positive integers. A k-element subset A ⊂ S is called nice if k X xi∈A xi −
X
xj∈S\A
xj ≤
k + 2k
.
Prove that the number of nice subsets is at least
k + k +
k
.