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Turkey NMO 2006 1st Round - P24 (Combinatorics)

Source:

February 2, 2013

Problem Statement

In a handball tournament with nn teams, each team played against other teams exactly once. In each game, the winner got 22 points, the loser got 00 point, and each team got 11 point if there was a tie. After the tournament ended, each team had different score than the others, and the last team defeated the first three teams. What is the least possible value of nn?
<spanclass=latexbold>(A)</span> 8<spanclass=latexbold>(B)</span> 9<spanclass=latexbold>(C)</span> 10<spanclass=latexbold>(D)</span> 12<spanclass=latexbold>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 8 \qquad<span class='latex-bold'>(B)</span>\ 9 \qquad<span class='latex-bold'>(C)</span>\ 10 \qquad<span class='latex-bold'>(D)</span>\ 12 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}