Proof of a variation and particular case of the Postage Stamp problem, using strong induction.

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Question: Help proving this by induction?
Consider a sport in which teams can score two types of goals, worth either 3 points or 7 points. For example, Team Miners 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.

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Answered By:

Adam F.
Physics Tutor
More information: www.wyzant.com/Tutors/GA/Suwanee/7648364/?utm_sour…

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Written Explanation:

First, find the number we think n0 should be, which it turns out is 12. Next show three base cases so that we can always refer back three steps. That means n=12, 13, 14.Next, using strong induction, let n ›= 14 and assume everything from 12 to n satisfies the claim. Using this, show the claim is true for n+1 by splitting off a 3, and rearranging terms.
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