Finding what numbers added together equal 2 sums

[bowers2000]

I had a quick question for the math/excel experts on here.

I have 10 numbers. Call it 1,2,3,4,5,6,7,8,9,10.

If you add 4 of the numbers (2+4+8+10) you get 24. If you add the other six remaining numbers (1+3+5+6+7+9) you get 31.

I need a way to figure out which numbers added together equal the sum. So in this example. I would only have the list of the 10 available numbers and the two sums. 24 and 31. I would know that 4 of them added together equal 1 sum and 6 together equal another sum. I need to find out which ones added to together produce the sum.

The numbers will not be sequential like they are in the example above.

I will always have the 2 sums. The total of the 2 sums (55) and the numbers that can be added to get to those totals. I just won't know which ones were used in which total.

Any suggestion on how to use solver and constraints or some other method to figure this out? I'm at a loss.

 

[VoG]

This may help you http://www.tushar-mehta.com/excel/templates/match_values/index.html

 

[bowers2000]

Thanks for the response. It is similar to what I want but I can't get it to work. I tried the basic problem I posted. (i.e. data set 1-10) Target value 24.

It did find me three numbers that equal 24. (7+8+9). I wanted 4 numbers though. So I set-up an additional contraint in the solver. I added a CountIf statement to count numbers selected. I set a constraint = 4.

When I tried that it failed to produce any answers.

Suggestions? Am I using it wrong?

 

[bowers2000]

Nevermind. I got it to work. The sample set data the user was giving me was bad. The solver worked great. Thanks a million.