Thread: 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?

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.

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?

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^-s in ζ⁵(s), the 5th power of the Riemann zeta functions. The number of elements in set B is the coefficient on 15^-s in ζ⁵(s).

Surely, if we're talking about natural numbers, the answer is one element each?

I'm fairly certain that B has more elements. Compare 11135 and 11153 to 11155.

According to how I interpret the question, I make it A has ⁵C₂ = 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}

Ah, but is ordering important? These are just the elements in the set aren't they?

They are five-digit numbers, so 11135 (eleven thousand one hundred and thirty-five) ≠ 11153 (eleven thousand one hundred and fifty-three).

That's right, set B contains twice as many elements as set A.