2009 Belgians handshaking
Source: Flanders Math Olympiad 2009 p1
December 24, 2022
combinatorics
Problem Statement
In an attempt to beat the Belgian handshake record come on exactly Belgians together in a large sports hall. Among them are Nathalie and thomas. During this event, everyone shakes hands with everyone exactly once other attendees. Afterwards, Nathalie says: “I have exactly times as many Flemish people shaken hands as people from Brussels.” Thomas replies with “I have exactly times as much Walloons and Brussels people shook hands”. From which region does Nathalie come and from which region comes Thomas?