A problem relating to small numbers: "Suppose we have a set of N natural numbers from 1 to 999...."

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kajamix

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Suppose we have a set of N natural numbers from 1 to 999.
We take m out of the N numbers at random and multiply them.
What is the smallest possible difference between two such products ?

We exclude the case when the two subsets of m numbers are identical (so difference is zero).
Also the N numbers can be sorted and ordered (is allowed) but not the products of m numbers - because there are too many.
 
kajamix said:
Suppose we have a set of N natural numbers from 1 to 999.
We take m out of the N numbers at random and multiply them.
What is the smallest possible difference between two such products ?

We exclude the case when the two subsets of m numbers are identical (so difference is zero).
Also the N numbers can be sorted and ordered (is allowed) but not the products of m numbers - because there are too many.
Click to expand...
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this problem
 
blamocur said:
Why does being sorted matter here?
Click to expand...

To <<Read before posting>> : If I make some partial progress in this, or find complete solution I will post.

Maybe it does.
If we know the minimum (Xmin), the maximun (Xmax) and the mean (<X>) maybe it helps.
As N approaches infinity we cannot even do that, but suppose N is not huge and we can.

Anyway assume it is the ordered set 1-2-3- .... -998-999. It amounts to the same thing.
 
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