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Re: number of ways to add and multiply numbers
Posted:
Aug 16, 2007 1:33 AM


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>k2)[sum(j=0>n)C(j,i)]
Where C(k,i) is the binomial coefficient C(k,i)=k!(i!*(ki)!) 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 k1 operands between them but the > ordering is strange and I don't know how to describe it. > > Any ideas? > > Thanks, > Jon



