Hi KV!
Analysing the problem and breaking it down into smaller chunks comes to mind.
System analysts do that, and you can do it too, provided, you don't get into coding mode as soon as you have a keyboard in front of you.
Your reference to pen and paper is a very good one.
It will take some time to run even with an optimised code, but I had run one similar to this in only 53 hours over seventy odd thousand races, yes RACES not horses.
Good luck with it.