Problem #PRU-64696

Problems Algebra and arithmetic Number theory. Divisibility Odd and even numbers Methods Pigeonhole principle Pigeonhole principle (other) Word problems Tables and tournaments Tournament tables

Problem

16 teams took part in a handball tournament where a victory was worth 2 points, a draw – 1 point and a defeat – 0 points. All teams scored a different number of points, and the team that ranked seventh, scored 21 points. Prove that the winning team drew at least once.