The rope question is more of a Fermi question[1]. Not that they aren't commonly called [2] puzzlers, but I think the distinction is useful. Fermis are about estimating, and that's an actual skill - innumeracy[3] is real.
What I would call puzzle problems usually involve some trick to getting the answer. If you can't figure out the trick, you're stumped. If you know the trick, you barely have to think to crank out the answer. Optimally solving the example in the article is one of those.
They weren't widely banned because they were too novel and charming. They were banned because "time to aha!" in any given instance doesn't tell you much about how someone solves problems. Also, because the bulk of the work at most jobs doesn't really resemble seeking "aha moments," these questions tend to select for people who thrive most on doing something other than the job at hand.
To me it definitely seems to be in the puzzler category based on those descriptions. The trick is realizing it's "just" asking you to solve the well known formula for radius to circumference, 2*pi*r=c, for c=6 would give r≈1 while you can ignore the rest of the information worded to trick you into thinking it's a complicated problem which would require a fancy solution. Of course if you're not dealing with geometry every day of your adult life it's more likely it leads to seeing what your general thought process is, such as "I'll fall back to Fermi Estimation to get a ballpark going".
What I would call puzzle problems usually involve some trick to getting the answer. If you can't figure out the trick, you're stumped. If you know the trick, you barely have to think to crank out the answer. Optimally solving the example in the article is one of those.
They weren't widely banned because they were too novel and charming. They were banned because "time to aha!" in any given instance doesn't tell you much about how someone solves problems. Also, because the bulk of the work at most jobs doesn't really resemble seeking "aha moments," these questions tend to select for people who thrive most on doing something other than the job at hand.
[1] https://en.wikipedia.org/wiki/Fermi_problem
[2] https://blog.codinghorror.com/the-hardest-interview-puzzle-q...
[3] https://innumeracy.net/category/estimation/