MathDB

2n

(

n\ge 2

) teams took part in the football league matches and there were

2n-1

matchweeks. In each matchweek each team played one match. Any two teams met with each other during the matches in exactly one game. Moreover, in each match one team was the host and the second was a guest. Say a team is traveling, if in any two consecutive matchweeks it was once a host and once a guest. Prove that there are at most two traveling teams.

Problem Statement