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Math Help - 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 exact postage you cannot make by using these stamps?
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  2. #2
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    It is infinity.
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  3. #3
    Newbie Cooler's Avatar
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    Actually no

    Actually you could make infinity.

    I beleive it is 39 cents.

    It makes sense to me but I'm having a hard time demonstrating why.
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  4. #4
    Newbie Matrix's Avatar
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    can you please explain?
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  5. #5
    Site Founder MathMan's Avatar
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    Quote Originally Posted by Dantown
    You have an unlimited supply of 5 cent stamps and 11 cent stamps. What is the greatest amount of exact postage you cannot make by using these stamps?
    You cannot make or can make??
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  6. #6
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    I see now..

    If you have N, and keep decreasing N by 11. If N is large enough, eventually you will get a 0 or 5 in the ending digit. However, if N is just small enough, you cannot decrease N enough times to get to a 0 or 5 in the ending digit.
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  7. #7
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    Clarification

    To Clarify . . .

    The question is with an unlimited supply of 5 and 11 cent stamps what is the highest postage amount you cannot make exactly using a combination of stamps.

    for example I cannot make 39 cents out of 5 and 11 cent stamps as Cooler suggests. But I could make 40, 41, 42 etc.

    40 = 5+5+5+5+5+5+5+5
    41 = 11+5+5+5+5+5+5
    42 = 11+11+5+5+5+5

    can anyone prove it?

    I guess we have to start with P = 5*x + 11*y where x and y are integers.
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  8. #8
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    For now we know 39 cents postage is the largest that you cannot make. You can prove that you can make any larger than 39. I can already think of:
    40: by 5
    41: minus 11, by 5
    42: minus 22, by 5
    43: minus 33, by 5
    44: by 11
    45: by 5
    46: minus 11, by 5
    47: minus 22, by 5
    48: minus 33, by 5
    49: minus 44, by 5

    Any postage above 49 cents:
    For any A: a positive integer > 4,
    A*10+0: by 5
    A*10+1: minus 11, then divisible by 5
    A*10+2: minus 22, then divisible by 5
    A*10+3: minus 33, then divisible by 5
    A*10+4: minus 44, then divisible by 5
    A*10+5: by 5
    A*10+6: minus 11, then divisible by 5
    A*10+7: minus 22, then divisible by 5
    A*10+8: minus 33, then divisible by 5
    A*10+9: minus 44, then divisible by 5


    Postages greater than 44 are automatically covered because they can be subtracted by 0, 11, 22, 33, or 44, and will then be divisible by 5.
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