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March 25th, 2017, 05:50 AM   #1
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Is this part of combinatorics?

Hi

I need your help to figure the following out. Thanks in advance.

So, let’s say I’m given 10 elements (numbers, for example) and I need to select 3 of these elements (the order doesn’t matter, and I can select the same element more than once) to obtain a fixed result.

So for example, among 10 numbers, I have to pick 3 numbers, then add them together (so the first number + the second one + the third one) to obtain a given constant K. The question then becomes, how many combinations of 3 numbers can I make to obtain the constant K?

How do I model this problem? And is there a straightforward way of generalizing the problem to any number of total elements and any number of selected elements?

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March 25th, 2017, 12:38 PM   #2
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The subset sum problem is essentially what you have here. You are using multisets rather than sets in that elements can be repeated.

I'm not seeing any closed form solution for the problem, just algorithms.
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March 25th, 2017, 02:53 PM   #3
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Just what I was looking for, thanks.
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