MathDB

Putnam 2006 B2

Source:

December 4, 2006

Putnaminequalitiespigeonhole principlecollege contests

Problem Statement

Prove that, for every set

X=\{x_{1},x_{2},\dots,x_{n}\}

n

real numbers, there exists a non-empty subset

S

X

and an integer

m

such that

\left|m+\sum_{s\in S}s\right|\le\frac1{n+1}