# Even another problem...

• April 11th, 2008, 10:34 AM
thyristor
Even another problem...
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?
• April 11th, 2008, 10:42 AM
serpicojr
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.
• April 13th, 2008, 11:21 AM
thyristor
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?
• April 13th, 2008, 11:48 AM
serpicojr
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).
• April 14th, 2008, 07:15 AM
sunshinewarrior
Surely, if we're talking about natural numbers, the answer is one element each?
• April 14th, 2008, 08:56 AM
MagiMaster
I'm fairly certain that B has more elements. Compare 11135 and 11153 to 11155.
• April 14th, 2008, 09:04 AM
JaneBennet
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}
• April 14th, 2008, 10:24 AM
sunshinewarrior
Ah, but is ordering important? These are just the elements in the set aren't they?
• April 14th, 2008, 10:50 AM
JaneBennet
They are five-digit numbers, so 11135 (eleven thousand one hundred and thirty-five) ≠ 11153 (eleven thousand one hundred and fifty-three).
• April 14th, 2008, 01:13 PM
thyristor
That's right, set B contains twice as many elements as set A.