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Contests
National and Regional Contests
China Contests
China Team Selection Test
2019 China Team Selection Test
3
2019 China TST 2 Day 1 Q3
2019 China TST 2 Day 1 Q3
Source: Mar , 2019
March 11, 2019
inequalities
China
China TST
Problem Statement
Let
n
n
n
be a given even number,
a
1
,
a
2
,
⋯
,
a
n
a_1,a_2,\cdots,a_n
a
1
,
a
2
,
⋯
,
a
n
be non-negative real numbers such that
a
1
+
a
2
+
⋯
+
a
n
=
1.
a_1+a_2+\cdots+a_n=1.
a
1
+
a
2
+
⋯
+
a
n
=
1.
Find the maximum possible value of
∑
1
≤
i
<
j
≤
n
min
{
(
i
−
j
)
2
,
(
n
+
i
−
j
)
2
}
a
i
a
j
.
\sum_{1\le i<j\le n}\min\{(i-j)^2,(n+i-j)^2\}a_ia_j .
∑
1
≤
i
<
j
≤
n
min
{(
i
−
j
)
2
,
(
n
+
i
−
j
)
2
}
a
i
a
j
.
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