They are seated around a table
Source: IMO LongList 1988, Singapore 1, Problem 68 of ILL
November 3, 2005
geometrygeometric transformationrotationgraph theorycombinatorics unsolvedcombinatorics
Problem Statement
In a group of people, each one knows exactly three others. They are seated around a table. We say that the seating is if everyone knows the two sitting by their sides. Show that, if there is a perfect seating for the group, then there is always another perfect seating which cannot be obtained from by rotation or reflection.