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Korea National Olympiad
2012 Korea National Olympiad
3
Maximum value in permutations
Maximum value in permutations
Source: Korea National 2012 Problem 7
August 19, 2012
induction
inequalities
inequalities proposed
Problem Statement
Let
{
a
1
,
a
2
,
⋯
,
a
10
}
=
{
1
,
2
,
⋯
,
10
}
\{ a_1 , a_2 , \cdots, a_{10} \} = \{ 1, 2, \cdots , 10 \}
{
a
1
,
a
2
,
⋯
,
a
10
}
=
{
1
,
2
,
⋯
,
10
}
. Find the maximum value of
∑
n
=
1
10
(
n
a
n
2
−
n
2
a
n
)
\sum_{n=1}^{10}(na_n ^2 - n^2 a_n )
n
=
1
∑
10
(
n
a
n
2
−
n
2
a
n
)
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