MathDB
Problems
Contests
National and Regional Contests
Romania Contests
JBMO TST - Romania
2017 Junior Balkan Team Selection Tests - Romania
2
Real Number satisfying inequality
Real Number satisfying inequality
Source: JBMO TST 3 2017 P2
November 14, 2018
inequalities
Problem Statement
Given
x
1
,
x
2
,
.
.
.
,
x
n
x_1,x_2,...,x_n
x
1
,
x
2
,
...
,
x
n
real numbers, prove that there exists a real number
y
y
y
, such that,
{
y
−
x
1
}
+
{
y
−
x
2
}
+
.
.
.
+
{
y
−
x
n
}
≤
n
−
1
2
\{y-x_1\}+\{y-x_2\}+...+\{y-x_n\} \leq \frac{n-1}{2}
{
y
−
x
1
}
+
{
y
−
x
2
}
+
...
+
{
y
−
x
n
}
≤
2
n
−
1
Back to Problems
View on AoPS