MEMO 2007 ekipno problem 6
Dodao/la:
arhiva28. travnja 2012. For a set
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
of five points in the plane, no three of them being collinear, let
![s(P)](/media/m/f/5/2/f5265221172b317e4b3e6c4b613901a7.png)
be the numbers of acute triangles formed by vertices in
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
.
Find the maximum value of
![s(P)](/media/m/f/5/2/f5265221172b317e4b3e6c4b613901a7.png)
over all such sets
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
.
%V0
For a set $P$ of five points in the plane, no three of them being collinear, let $s(P)$ be the numbers of acute triangles formed by vertices in $P$.
Find the maximum value of $s(P)$ over all such sets $P$.
Izvor: Srednjoeuropska matematička olimpijada 2007, ekipno natjecanje, problem 6