I am currently trying to understand the architecture of various proofs of results in additive analytic number theory. In particular, I am studying the proof that every large odd integer is the sum of three primes. In the exposition I’m reading the author, K. Soundararajan, begins by making some guesses on the order of various quantities using arithmetic combinatorics. I want to learn this method and I'm looking for easier, toy problems, where I can practice this approach.