KURSCHAK 1951

$ABCD$ is a square. $E$ is a point on the side $BC$ such that $BE =1/3 BC$ , and $F$ is a point on the ray $DC$ such that $CF =1/2 DC$ . Prove that the lines $AE$ and $BF$ intersect on the circumcircle of the square.

For which $m > 1$ is $(m -1)!$ divisible by $m$ ?

An open half-plane is the set of all points lying to one side of a line, but excluding the points on the line itself. If four open half-planes cover the plane, show that one can select three of them which still cover the plane.