Solving with Python and numpy

I believe it is worth spending some effort to sharpen my programming skills independently of any application.  A good path is provided by toptal and by Codility : the challenges are mathematical problems that can be programmed in several languages, and I choose Python and numpy. What follows is the one that kept me busy for almost ONE WEEK. I would like to do some of those challenges as a warm up exercise, and then register with Toptal for any business opportunity that requires programming skills.