IMO 1988 LL SIN73

In a group of n people each one knows exactly three others. They

IMO 1988 LL SIN73

Origin: SIN

Problem

In a group of n people each one knows exactly three others. They are seated around a table. We say that the seating is perfect if everyone knows the two sitting by their sides. Show that if there is a perfect seating S for the group, then there is always another perfect seating that cannot be obtained from S by rotation or reflection.