For questions about approaches and techniques for discovering a proof, as opposed to writing it down clearly (which involves (proof-writing)). Should not be used unless the focus is on the technique of the proof instead of the solution.

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Cauchy induction: are there examples of cases where choosing an integer other than $2$ is a better strategy?

Cauchy induction, sometimes called backwards induction, works as follows: show that $p(1)$ is true show that $p(n)$ implies $p(2n)$ (which inductively implies $p(2^n)$ is true) show that $p(n)$ ...