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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