Sounds like a fun math excercise: For any trademark of color T(represented as a vector in RGB colorspace), the chance that a brand using color C can be success

Sounds like a fun math excercise: For any trademark of color T(represented as a vector in RGB colorspace), the chance that a brand using color C can be successfully sued is equal to 1-k*||T-C||, where k is lesser than 1 divided by the maximum distance between any two points in RGB colorspace. Find the minimum number of trademarks needed so that for any color the chance of successfully suing is greater than or equal to P.