Consider a sport in which teams can score two types of goals, worth either 3 points or 7 points. For example, Team Vikings might (theoretically speaking) score 32 points by accumulating, in...

Consider a sport in which teams can score two types of goals, worth either 3 points or 7 points. For example, Team Vikings might (theoretically speaking) score 32 points by accumulating, in succession, 3, 7, 3, 7, 3, 3, 3, and 3 points. Find the smallest possible n0 such that, for any n ≥ n0, a team can score exactly n points in a game. Prove your answer correct by strong induction.