The two StackOverflow questions are:

http://stackoverflow.com/questions/38478754/how-to-interpolate-between-n-colors-by-a-fractional-contribution-for-each-color

http://stackoverflow.com/questions/38479403/how-to-find-the-fractional-weighting-of-n-colors-which-contribute-to-a-known-col

Notes.

It may be useful to think firstly of just one dimension such as Red and ignore the other two, this can simplify the problem.

Feel free to use any Java or Scala library you need to use to get the job done. If there is a library which can do the maths for you then use it.

You may need to use Gradle or Ant or Maven to build and run. I assume you can make that work.

If there are multiple values for the solution of a problem then maybe one way to solve it is to return a function which can tell if a RGB is within the solution space. So your method could return a method, a Function<>. Also return one solution.