Sandy asked in 科學及數學數學 · 10 years ago

Math Problem

Suppose that you have at your disposal arbitrarily many 4-cent stamps and 7-cent stamps. What are all the different postage you can pay? Show in particular that you can pay all postage greater than 17 cents.

3 Answers

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  • 10 years ago
    Favorite Answer

    設想您有可以任您處置、足夠多張的4分錢郵票與7分錢郵票,

    您總共可以組合出哪些不同郵資?尤其是證明您能組合出所有18元以上的郵資

    對於任意正整數郵資,有下列4個恆等式

    4n=4*n + 7*0

    4n+1=4*(n-5) + 7*3

    4n+2=4*(n-3) + 7*2

    4n+3=4*(n-1) + 7*1

    但4分錢郵票的張數不能為負,

    所以1 ,5 ,9 ,13 ,17 ,2 ,6 ,10 ,3無法組合,其他任意正整數郵資都可以,

    亦即18元以上的郵資都可以(因為不可以者最大是17)。

  • 10 years ago

    to:吧八

    就算翻譯成中文你也不會懂

  • 10 years ago

    請你翻成中文

    please speak Chinese

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