So I'm trying to solve this problem.
We are given an image ( a two dimensional matrix ). The image is all white except for some red dots. We are given the list of the red dots ( (X,Y) pairs ). The red dots have an even geographic distribution across the image :-)
We are given a list of locations where we can place some blue dots. This list has N elements ( (X,Y) pairs ).
The problem is to place M blue dots ( M < N ) in such a way that : the blue dots are geographically distributed across the image ( let's say 25% in the upper left side , 25% in the upper right side etc....) , as far away as possible from the red dots , as far away as possible from each other.
How would I go about finding the best possible M out of N ? Does this problem have a mathematical solution or do I just have to get all possible combinations and see which one is best ?