MathDB
Round-Robin Tournament

Source: 2012 AMC10B Problem #15

February 23, 2012
MATHCOUNTSAMC

Problem Statement

In a round-robin tournament with 66 teams, each team plays one game against each other team, and each game results in one team winning and one team losing. At the end of the tournament, the teams are ranked by the number of games won. What is the maximum number of teams that could be tied for the most wins at the end of the tournament?
<spanclass=latexbold>(A)</span> 2<spanclass=latexbold>(B)</span> 3<spanclass=latexbold>(C)</span> 4<spanclass=latexbold>(D)</span> 5<spanclass=latexbold>(E)</span> 6 <span class='latex-bold'>(A)</span>\ 2\qquad<span class='latex-bold'>(B)</span>\ 3\qquad<span class='latex-bold'>(C)</span>\ 4\qquad<span class='latex-bold'>(D)</span>\ 5\qquad<span class='latex-bold'>(E)</span>\ 6