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Thread: Even another problem...

  1. #1 Even another problem... 
    Forum Masters Degree thyristor's Avatar
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    We have two sets, A and B.
    Both contain numbers ABCDE (i.e. with five numbers).
    The product of A,B,C,D and E in A is 25.
    Thr product of A,B,C,D and E in B is 15.
    Which set contains the largest amount of numbers, and how many more?


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  3. #2  
    Forum Professor serpicojr's Avatar
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    You should restate this, because it's really confusing as stated. You should never use the same letter to mean two different things in a problem. Also, I don't know what you mean, "Both contain numbers ABCDE (i.e. with five numbers)." My first interpretation was that each set contained 5 numbers, but this doesn't make sense because you ask which set is larger. My next thought was that you mean that each contains a five-digit number of numbers, but this situation is too ambiguous for there to be a unique solution to your problem. I don't know what else you could mean, so you're going to have to try again.


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  4. #3  
    Forum Masters Degree thyristor's Avatar
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    Sorry, if I confused you. Since I'm not English I don't know all the terms in mathematics. I mean that the sets A and B both contain only five digit-elements which are natural numbers.
    Set A contains only five digit-elements where the product of the digits is 25.
    Set B contains only five-digit elements where the product of the digits is 15.
    Which set consists of the largest amount of elements?
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  5. #4  
    Forum Professor serpicojr's Avatar
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    I get it now. I'll let others take a stab first.

    Actually, let me give you a real oblique answer: the number of elements in set A is the coefficient on 25<sup>-s</sup> in ζ<sup>5</sup>(s), the 5th power of the Riemann zeta functions. The number of elements in set B is the coefficient on 15<sup>-s</sup> in ζ<sup>5</sup>(s).
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  6. #5  
    Forum Professor sunshinewarrior's Avatar
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    Surely, if we're talking about natural numbers, the answer is one element each?
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  7. #6  
    Forum Radioactive Isotope MagiMaster's Avatar
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    I'm fairly certain that B has more elements. Compare 11135 and 11153 to 11155.
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  8. #7  
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    According to how I interpret the question, I make it A has <sup>5</sup>C<sub>2</sub> = 10 members while B has 5 × 4 = 20 elements.

    A = {11155, 11515, 11551, 15115, 15151, 15511, 51115, 51151, 51511, 55111}

    B = {11135, 11153, 11315, 11351, 11513, 11531, 13115, 13151, 13511, 15113, 15131, 15311, 31115, 31151, 31511, 35111, 51113, 51131, 51311, 53111}
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  9. #8  
    Forum Professor sunshinewarrior's Avatar
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    Ah, but is ordering important? These are just the elements in the set aren't they?
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  10. #9  
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    They are five-digit numbers, so 11135 (eleven thousand one hundred and thirty-five) ≠ 11153 (eleven thousand one hundred and fifty-three).
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  11. #10  
    Forum Masters Degree thyristor's Avatar
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    That's right, set B contains twice as many elements as set A.
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