MathDB

4.

Part of 2014 Poland - Second Round

Problems(1)

Traveling teams

Source: Poland 2014 - Second Round P4

7/28/2019
2n2n (n≥2n\ge 2) teams took part in the football league matches and there were 2n−12n-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.
combinatorics