CMO 2006 Problem 4
- Paper
- Answer
Consider a round-robin tournament with teams, where each team plays each other team exactly once. We say that three teams and , form a cycle triplet if beats beats , and beats . There are no ties.
(a) Determine the minimum number of cycle triplets possible.
(b) Determine the maximum number of cycle triplets possible.
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{n(n+1)(2 n+1)}{6}
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