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March 25th, 2017, 06:50 AM  #1 
Member Joined: Aug 2016 From: Used to be Earth Posts: 64 Thanks: 14  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? Regards 
March 25th, 2017, 01:38 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,653 Thanks: 840  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. 
March 25th, 2017, 03:53 PM  #3 
Member Joined: Aug 2016 From: Used to be Earth Posts: 64 Thanks: 14 
Just what I was looking for, thanks.


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