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Contests
National and Regional Contests
China Contests
China Team Selection Test
2020 China Team Selection Test
5
5
Part of
2020 China Team Selection Test
Problems
(1)
Easy inequality with integer variable
Source: China Additional TST for IMO 2020, P5
10/20/2020
Let
a
1
,
a
2
,
⋯
,
a
n
a_1,a_2,\cdots,a_n
a
1
,
a
2
,
⋯
,
a
n
be a permutation of
1
,
2
,
⋯
,
n
1,2,\cdots,n
1
,
2
,
⋯
,
n
. Among all possible permutations, find the minimum of
∑
i
=
1
n
min
{
a
i
,
2
i
−
1
}
.
\sum_{i=1}^n \min \{ a_i,2i-1 \}.
i
=
1
∑
n
min
{
a
i
,
2
i
−
1
}
.
inequalities
algebra