MathDB
The Team Tournament

Source: 2019 AMC 8 #19

November 19, 2019

Problem Statement

In a tournament there are six teams that play each other twice. A team earns 3 points for a win, 1 point for a draw, and 0 points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for each of the top three teams?
<spanclass=latexbold>(A)</span>22<spanclass=latexbold>(B)</span>23<spanclass=latexbold>(C)</span>24<spanclass=latexbold>(D)</span>26<spanclass=latexbold>(E)</span>30<span class='latex-bold'>(A) </span>22\qquad<span class='latex-bold'>(B) </span>23\qquad<span class='latex-bold'>(C) </span>24\qquad<span class='latex-bold'>(D) </span>26\qquad<span class='latex-bold'>(E) </span>30