NL-NWO 1970

Four different points $A,B,C$ and $D$ lie in a plane. No three of these points lie on a single straight line. Describe the construction of a square $PQRS$ such that on each of the sides of $PQRS$ , or the extensions , lies one of the points $A, B, C$ and $D$ .

The equation $x^3 - x^2 + ax - 2^n = 0$ has three integer roots. Determine $a$ and $n$ .

$2n$ clubs want to play a league. Each club must play every other club exactly once. Each club is only allowed to play one game per day. Prove that the competition can be completed in $2n - 1$ days.