China TST 1997 football teams
Source: China TST 1997, problem 2
May 22, 2005
combinatorics unsolvedcombinatorics
Problem Statement
There are football teams in a round-robin competition where every 2 teams meet once. The winner of each match receives 3 points while the loser receives 0 points. In the case of a draw, both teams receive 1 point each. Let be as follows: 2 \leq k \leq n \minus{} 1. At least how many points must a certain team get in the competition so as to ensure that there are at most k \minus{} 1 teams whose scores are not less than that particular team's score?