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Putnam
2006 Putnam
B2
B2
Part of
2006 Putnam
Problems
(1)
Putnam 2006 B2
Source:
12/4/2006
Prove that, for every set
X
=
{
x
1
,
x
2
,
…
,
x
n
}
X=\{x_{1},x_{2},\dots,x_{n}\}
X
=
{
x
1
,
x
2
,
…
,
x
n
}
of
n
n
n
real numbers, there exists a non-empty subset
S
S
S
of
X
X
X
and an integer
m
m
m
such that
∣
m
+
∑
s
∈
S
s
∣
≤
1
n
+
1
\left|m+\sum_{s\in S}s\right|\le\frac1{n+1}
m
+
s
∈
S
∑
s
≤
n
+
1
1
Putnam
inequalities
pigeonhole principle
college contests