Splitting a number over several ranges

I am trying to split a number into smaller numbers that fit predefined ranges and I can't seem to get the algorithm right. I am using C#.

Example

Split 20 into three numbers where the numbers have to fit the following ranges: 1-3, 3-10, and 0-15. Final numbers could look like this: 1,5,14 or 2,3,15

Another example could be to split 100 into four numbers that fit the following ranges: 0-10, 0-10, 0-40, 0-40. The result would naturally be 10,10,40,40. Splitting 90 on the same ranges could result 5,8,38,39 etc.

Can you kick me in the right direction?

(no, it's not a homework, it's for a personal project)