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Problems
Contests
National and Regional Contests
Iran Contests
Iran MO (2nd Round)
1996 Iran MO (2nd round)
4
4
Part of
1996 Iran MO (2nd round)
Problems
(1)
Blue and red points lie on a line [Iran Second Round 1996]
Source:
11/25/2010
Let
n
n
n
blue points
A
i
A_i
A
i
and
n
n
n
red points
B
i
(
i
=
1
,
2
,
…
,
n
)
B_i \ (i = 1, 2, \ldots , n)
B
i
(
i
=
1
,
2
,
…
,
n
)
be situated on a line. Prove that
∑
i
,
j
A
i
B
j
≥
∑
i
<
j
A
i
A
j
+
∑
i
<
j
B
i
B
j
.
\sum_{i,j} A_i B_j \geq \sum_{i<j} A_iA_j + \sum_{i<j} B_iB_j.
i
,
j
∑
A
i
B
j
≥
i
<
j
∑
A
i
A
j
+
i
<
j
∑
B
i
B
j
.
inequalities
combinatorics proposed
combinatorics