AMC 10 Step by Step
2016 AMC 10BProblem 22P21-25~6 minPrint

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?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.