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2010 Iran MO (2nd Round)
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(1)
Iran National Math Olympiad-Day 1-Problem 2
Source:
4/30/2010
There are
n
n
n
points in the page such that no three of them are collinear.Prove that number of triangles that vertices of them are chosen from these
n
n
n
points and area of them is 1,is not greater than
2
3
(
n
2
−
n
)
\frac23(n^2-n)
3
2
(
n
2
−
n
)
.
geometry
combinatorics
counting question