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Thread: Postage Stamps Problem?

  1. #1
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    Postage Stamps Problem?

    You have an unlimited supply of 5 cent stamps and 11 cent stamps. What is the greatest amount of postage you cannot make by using the stamps?
    1.When will it work?(What numbers)
    2.What's the pattern?
    3.Why does it work?

    I know it's 39 cents but I don't really know the pattern and steps to get there?
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  2. #2
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    Re: Postage Stamps Problem?

    Quote Originally Posted by kikhakplz View Post
    You have an unlimited supply of 5 cent stamps and 11 cent stamps. What is the greatest amount of postage you cannot make by using the stamps?
    1.When will it work?(What numbers)
    2.What's the pattern?
    3.Why does it work?
    I know it's 39 cents but I don't really know the pattern and steps to get there?
    I will not simply give answers. I think that to do is to learn.
    Basically you want to look at $5m+11n$ where $m~\&~n$ are non-negative integers.
    So list the sums less than $40$. Here is a start: $5,~10,~11,~15,~16\cdots$ Show each is made-up.
    Then show how $40\text{ to }50$ can each be made.
    When you do that work, then you are ready to ask why.
    Thanks from kikhakplz
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    Re: Postage Stamps Problem?

    40 = 8 x 5
    41 = 1 x 11 + 6 x 5
    42 = 2 x 11 + 4 x 5
    43 = 3 x 11 + 2 x 5
    44 = 4 x 11 + 0 x 5
    45 = 9 x 5
    46 = 41 as above + 5
    47 = 42 as bove + 5
    and so on

    Does that count as the pattern?
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    Re: Postage Stamps Problem?

    So all numbers above 39 can be represented by 5x + 11y correct?
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    Re: Postage Stamps Problem?

    Quote Originally Posted by kikhakplz View Post
    So all numbers above 39 can be represented by 5x + 11y correct?
    Why is that the case? Show us, $73=5m+11n$ What are $m~\&~n~?$
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    Re: Postage Stamps Problem?

    Quote Originally Posted by Plato View Post
    Why is that the case? Show us, $73=5m+11n$ What are $m~\&~n~?$
    So I subtracted 73 by 33 to make the number divisible by 5, and I get 5->(73-33)/5=8 11->(73-5x8)/11=3
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    Re: Postage Stamps Problem?

    Quote Originally Posted by Plato View Post
    Why is that the case? Show us, $73=5m+11n$ What are $m~\&~n~?$
    I realized that I just need to make the number greater than 44 be divisible by 5 then I will be able to find out.
    That number can be subtracted by 11, 22, 33 ,44 ,0 right?

    How do I put this into the pattern?
    Last edited by kikhakplz; Nov 9th 2017 at 06:41 PM.
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    Re: Postage Stamps Problem?

    Quote Originally Posted by Plato View Post
    I will not simply give answers. I think that to do is to learn.
    Basically you want to look at $5m+11n$ where $m~\&~n$ are non-negative integers.
    So list the sums less than $40$. Here is a start: $5,~10,~11,~15,~16\cdots$ Show each is made-up.
    Then show how $40\text{ to }50$ can each be made.
    When you do that work, then you are ready to ask why.

    I see, so for part one it works with 5x + 11y
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    Re: Postage Stamps Problem?

    Quote Originally Posted by kikhakplz View Post
    I realized that I just need to make the number greater than 44 be divisible by 5 then I will be able to find out. That number can be subtracted by 11, 22, 33 ,44 ,0 right? How do I put this into the pattern?
    Take $98\\87\\76\\65$
    There we have it. We have a multiple of five, $65$.
    So $98=3(11)+13(5)$
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    Re: Postage Stamps Problem?

    Quote Originally Posted by Plato View Post
    Take $98\\87\\76\\65$
    There we have it. We have a multiple of five, $65$.
    So $98=3(11)+13(5)$
    for 87 (87-22)/5=13=#of 5

    # of 11=(87-13x5/)11=2
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    Re: Postage Stamps Problem?

    Quote Originally Posted by kikhakplz View Post
    for 87 (87-22)/5=13=#of 5

    # of 11=(87-13x5/)11=2
    Look, I do not know how you think. I hope that you do not expect a quick way to get it.
    I think about a programmer: Say the number is K.
    Now count the number of subtractions of $11$ from the K until you have a multiple of five.
    Now say that the count is $j$ That is $K-(11)\cdot j =5\cdot n$

    Then put it together: $K= 5\cdot n + 11\cdot j$
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    Re: Postage Stamps Problem?

    Solved
    Last edited by kikhakplz; Nov 9th 2017 at 09:22 PM.
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    Re: Postage Stamps Problem?

    Solved
    Last edited by kikhakplz; Nov 9th 2017 at 09:22 PM.
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    Re: Postage Stamps Problem?

    Solved
    Last edited by kikhakplz; Nov 9th 2017 at 09:19 PM.
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    Re: Postage Stamps Problem?

    Solved
    Last edited by kikhakplz; Nov 9th 2017 at 09:22 PM.
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