Do the Math
If you can convert your problem into a math problem, then you have done two things: (1) you have simplified the problem and (2) you have brought the full power of mathematics to bear on your problem. Translating a problem into a mathematical one is called mathematical modeling. Once a math model is chosen (which means that certain specific assumptions are made), there are centuries of mathematical techniques that can be used to answer your question. In this way, you tap the brains of mathematicians who have already solved your problem.