2006 Canadian MO Problems/Problem 4

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Problem

Consider a round robin tournament with $2n+1$ teams, where two teams play exactly one match and there are no ties. We say that the teams $X$ , $Y$ , and $Z$ form a cycle triplet if $X$ beats $Y$ , $Y$ beats $Z$ , and $Z$ beats $X$ .

(a) Find the minimum number of cycle triplets possible.

(b) Find the maximum number of cycle triplets possible.

Solution

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2006 Canadian MO (Problems)
Preceded by Problem 3	1 • 2 • 3 • 4 • 5	Followed by Problem 5

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2006 Canadian MO Problems/Problem 4

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Problem

Solution

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