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Topic: number of ways to add and multiply numbers
Replies: 2   Last Post: Aug 16, 2007 1:51 AM

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stephane.frion@gmail.com

Posts: 14
Registered: 8/15/07
Re: number of ways to add and multiply numbers
Posted: Aug 16, 2007 1:33 AM
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I have an idea , I just wondered if i don't double count sometimes .
I consider k>2 components ( two operators + or * ) The number of
operations is N :

N = 2*sum(i=0->k)C(k,i) + sum(i=0->k-2)[sum(j=0->n)C(j,i)]

Where C(k,i) is the binomial coefficient C(k,i)=k!(i!*(k-i)!)
First term count the + or * only , the second term count the
permutation of * ( + are induite this way )

Hope this is good

SF
-----------------------------------------------------------------------
**Apology if I'm wrong, It's only by trying that you can make mistakes
***


On Aug 15, 9:38 pm, "Jon Slaughter" <Jon_Slaugh...@Hotmail.com> wrote:
> does anyone know the unique symbolic(and not computation) way to count the
> number of ways to add and multiply numbers from a set?
>
> That is, say I'm given 1 and 2 then I can do
>
> 1
> 2
> 1+2
> 1*2
>
> for 1,2,3
>
> 1
> 2
> 3


> 1+2
> 1+3
> 2+3
> 1+2+3
> 1*2
> 1*3
> 2*3


> 1*2+3
> 1+2*3
> 1*3+2
> 1*2*3
>
> (I think thats every one but I thought from previous work that there should
> be 15)
>
> (1+3*2 is not in the set because the operations are commutative(its already
> there in the form of 1+2*3)
>
> Actually the problem comes from trying to count the number of combinations
> of putting elements in a electrical network such as resistors.
>
> Say I have a pile of n resistors then how many ways can I form different
> "networks" from them that result in unique results. Actually the problem is
> more general and one must treat each resistor as unique and that unique
> results do not relate to the electrical characteristics.
>
> Basically you can form parallel or series networks recursively and there is
> a reduction in some cases in that if two elements are in series then there
> order doesn't matter(for my application) or if they are in parallel. But in
> some cases the order does matter because it cannot be reordered like the
> example with 1*3+2
>
> which would be
>
> ---1---
> ----| |----2----
> ---3---
>
> except for things like 2+1*3, 2+3*1, 3*1+2.
>
> notice that for k elements there is k-1 operands between them but the
> ordering is strange and I don't know how to describe it.
>
> Any ideas?
>
> Thanks,
> Jon






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