More than 5 teams are playing football
Source: China TST 1998, problem 2
May 22, 2005
combinatorics unsolvedcombinatorics
Problem Statement
football teams participate in a round-robin tournament. For every game played, the winner receives 3 points, the loser receives 0 points, and in the event of a draw, both teams receive 1 point. The third-from-bottom team has fewer points than all the teams ranked before it, and more points than the last 2 teams; it won more games than all the teams before it, but fewer games than the 2 teams behind it. Find the smallest possible .