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4

Part of 2006 Canada National Olympiad

Problems(1)

round-robin tournament with $2n+1$ teams

Source: Canadian Mathematical Olympiad 2006, problem 4

1/28/2007
Consider a round-robin tournament with 2n+12n+1 teams, where each team plays each other team exactly one. We say that three teams X,YX,Y and ZZ, form a cycle triplet if XX beats YY, YY beats ZZ and ZZ beats XX. There are no ties. a)Determine the minimum number of cycle triplets possible. b)Determine the maximum number of cycle triplets possible.
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