3

Part of 1999 Junior Balkan MO

Problems(1)

1999 points in the interior of a square S

Source: JBMO 1999, Problem 3

S

be a square with the side length 20 and let

M

be the set of points formed with the vertices of

S

and another 1999 points lying inside

S

. Prove that there exists a triangle with vertices in

M

and with area at most equal with

\frac 1{10}

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