9.7

Part of 2010 All-Russian Olympiad Regional Round

Problems(1)

acquaintances among 7 people, round table

Source: Russian Regional Olympiad 2010 9.7

In a company of seven people, any six can sit at a round table so that every two neighbors turn out to be acquaintances. Prove that the whole company can be seated at a round table so that every two neighbors turn out to be acquaintances.