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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 1:51 AM
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On Aug 15, 10:33 pm, stephane.fr...@gmail.com wrote:
> 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- Hide quoted text -

>
> - Show quoted text -


well i ve just realise the second term is wrong .
You should read
N = 2*sum(i=0->k)C(k,i) + sum(i=1->k-2)[sum(j=3->n)C(j,i)]




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