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Source: AMC 10B 2016 #22

February 21, 2016
AMCAMC 10AMC 10 BAMC 12 B2016 AMC 10B

Problem Statement

A set of teams held a round-robin tournament in which every team played every other team exactly once. Every team won 1010 games and lost 1010 games; there were no ties. How many sets of three teams {A,B,C}\{A, B, C\} were there in which AA beat BB, BB beat CC, and CC beat A?A?
<spanclass=′latex−bold′>(A)</span> 385<spanclass=′latex−bold′>(B)</span> 665<spanclass=′latex−bold′>(C)</span> 945<spanclass=′latex−bold′>(D)</span> 1140<spanclass=′latex−bold′>(E)</span> 1330<span class='latex-bold'>(A)</span>\ 385 \qquad <span class='latex-bold'>(B)</span>\ 665 \qquad <span class='latex-bold'>(C)</span>\ 945 \qquad <span class='latex-bold'>(D)</span>\ 1140 \qquad <span class='latex-bold'>(E)</span>\ 1330
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