KURSCHAK 1958

Given any six points in the plane, no three collinear, show that we can always find three which form an obtuse-angled triangle with one angle at least $120^o$ .

Show that if $m$ and $n$ are integers such that $m^2 + mn + n^2$ is divisible by $9$ , then they must both be divisible by $3$ .

The hexagon $ABCDEF$ is convex and opposite sides are parallel. Show that the triangles $ACE$ and $BDF$ have equal area