MathDB

Every subset of size k has sum at most N/2

Source: USAMO 2006, Problem 2, proposed by Dick Gibbs

April 20, 2006

inequalitiesalgebracombinatorics

Problem Statement

For a given positive integer

k

find, in terms of

k

, the minimum value of

N

for which there is a set of

2k + 1

distinct positive integers that has sum greater than

N

but every subset of size

k

has sum at most

\tfrac{N}{2}.