Interesting Problems at Small Values

This post is based on the observation that, in a variety of fields (e.g. logic, computics, mathematics, physics), while certain classes of problems can be parameterized by some natural number $n$, it appears that the interesting problems―not so simple as to be trivial, but not so complex as to be unsolvable, undecidable, intractable, or nonexistent―always occur at small $n$. Below is a collection of such problems, describing at which $n$ they are interesting, and how so. A Summary First-order ...

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