**IMO Team Selection Test Problems**

1993/Test 2/2.

Let *AB* and *CD* be distinct parallel chords of a circle and let *P* be a point on their common perpendicular bisector. The lines *AP* and *CP* meet the circle again at *Q* and *R* respectively. If *S* is the intersection of the lines *BR* and *QD*, prove that *PS* is parallel to *AB*.

1995/Test 2/6.

The King and the Queen invited *n* other married couples to the palace for a round-table dinner. In order that each person (including the King and the Queen) had a chance to sit beside every person except his/her spouse during the dinner, the King and the Queen decided to have a different sitting arrangement for each course of food served. Prove that they can achieve their purpose if *n* courses of food are served, but not fewer.

hede@pobox.org.sg