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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1996 Moldova Team Selection Test
9
nice inequality
nice inequality
Source:
September 3, 2010
inequalities
function
Problem Statement
Let
x
1
,
x
2
,
.
.
.
,
x
n
∈
[
0
;
1
]
x_1,x_2,...,x_n \in [0;1]
x
1
,
x
2
,
...
,
x
n
∈
[
0
;
1
]
prove that
x
1
(
1
−
x
2
)
+
x
2
(
1
−
x
3
)
+
.
.
.
+
x
n
−
1
(
1
−
x
n
)
+
x
n
(
1
−
x
1
)
≤
[
n
2
]
x_1(1-x_2)+x_2(1-x_3)+...+x_{n-1}(1-x_n)+x_n(1-x_1) \leq [\frac{n}{2}]
x
1
(
1
−
x
2
)
+
x
2
(
1
−
x
3
)
+
...
+
x
n
−
1
(
1
−
x
n
)
+
x
n
(
1
−
x
1
)
≤
[
2
n
]
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