Once you recognize the different variations, you solve a bunch of those problems to become more efficient at 'em.
Really, it's no different than solving certain calculus problems. If you've solved enough integrals that require certain substitutions and identities, you'll notice them right away - but of course, if you've never seen 'em before, the problems can become next to impossible - given a very limited time fame to solve them.
Sure - some candidates will be highly intelligent, notice intricate patterns right away, and solve them on the spot (in the same way they'd perform on IQ tests), but for the majority it's just discipline and preparation.
There's a reason people are following these ridiculous study guides, which involve hundreds to thousands of Leetcode/hackerrank/etc. questions. If you actually study the problems, and do them over and over again, you'll get there.
And by "just" doing that, you can indeed outclass the so-called elite candidates.