# Is It Shapeist To Disallow Triangles?

Discrete Mathematics Level pending

In a round-robin tournament involving $$n$$ football teams, each of the $$n$$ teams played exactly one game against each of the other teams. Each game may end in a win, loss or draw. It happened that each team won exactly three games and also there were not three teams $$A$$, $$B$$, $$C$$ such that $$A$$ beat $$B$$, $$B$$ beat $$C$$ and $$C$$ beat $$A$$. For how many values of $$n$$ in the set $$\{4,5,6,\ldots, 100\}$$ is this situation possible?

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