IMO Shortlist 1994 problem C7
Dodao/la:
arhiva2. travnja 2012. Let
![n > 2](/media/m/0/0/c/00c70c7584115c4a2b5b99d993eedf40.png)
. Show that there is a set of
![2^n - 1](/media/m/3/6/8/368d10e8ec7984984aeaca1729252368.png)
points in the plane, no three collinear such that no
![2n](/media/m/d/2/d/d2da874dc9bc356be9468cdbd57fbfdf.png)
form a convex
![2n](/media/m/d/2/d/d2da874dc9bc356be9468cdbd57fbfdf.png)
-gon.
%V0
Let $n > 2$. Show that there is a set of $2^n - 1$ points in the plane, no three collinear such that no $2n$ form a convex $2n$-gon.
Izvor: Međunarodna matematička olimpijada, shortlist 1994