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Thread: mathematical induction

  1. #1
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    mathematical induction

    Show that any amount of postage of at least 12 cents can be made using 3 cent and 7 cent stamps?

    I tried a couple of numbers of 12 and greater:

    P(12) is true. 12 = 3 + 3 + 3 + 3.
    P(13) is true. 13 = 7 + 3 + 3.
    P(14) is true. 14 = 7 + 7.
    P(15) is true. 15 = 3 + 3 + 3 + 3 + 3.
    P(16) is true. 16 = 3 + 3 + 3 + 7
    P(17) is true. 17 = 7 + 7 + 3
    P(18) is true. 18 = 3 + 3 + 3 + 3 + 3 +3
    P(19) is true. 19 = 3 + 3 + 3 + 7 + 3


    ??

    Any help would be appreciated
    Last edited by relyt; Apr 13th 2009 at 09:15 PM.
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  2. #2
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    Quote Originally Posted by relyt View Post
    Show that any amount of postage of at least 12 cents can be made using 3 cent and 7 cent stamps?

    I tried a couple of numbers of 12 and greater:

    P(12) is true. 12 = 3 + 3 + 3 + 3.
    P(13) is true. 13 = 7 + 3 + 3.
    P(14) is true. 14 = 7 + 7.
    P(15) is true. 15 = 3 + 3 + 3 + 3 + 3.
    P(16) is true. 16 = 3 + 3 + 3 + 7
    P(17) is true. 17 = 7 + 7 + 3
    P(18) is true. 18 = 3 + 3 + 3 + 3 + 3 +3
    P(19) is true. 19 = 3 + 3 + 3 + 7 + 3


    and I can see that you can form postage of x + 1 by using postage of x - 3 plus an additional 3 cent stamp....but how do I show this to solve the problem?

    Any help would be appreciated
    You're trying to prove that any integer, p, greater than 11 can be written as  p = 3n+7m , where n and m are natural numbers.
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  3. #3
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    I'm lost I guess...back to the books

    Ugh...I'm really struggling with this one. Any additional help would be appreciated
    Last edited by mr fantastic; Apr 13th 2009 at 09:30 PM. Reason: Merged posts
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