Comments by "EebstertheGreat" (@EebstertheGreat) on "A Lifelong Mathematical Obsession" video.

  1. Shockingly, when I was a kid, I had exactly the same thoughts with tapping my fingers and developed exactly the same fidget. I would also go methodically through every single combination, before moving on to other tapping patterns, maybe tapping out rhythms, and then my mind wandering elsewhere. I don't have autism and don't fidget that much anymore, so I don't really do it as an adult, but it was something I did all the time as a kid in lower and middle school. And I never told anyone about it, because it never even occurred to me as something to mention. I also explored all possible sequences for n=5, and I paid special attention to the ones where you could get stuck. With only n=5 fingers, you don't get stuck very often. I also looked at n < 5, noticing that you can get stuck in the cases n=3 and n=4 and would always get stuck when n=2. As the number of fingers increased, it seemed like you got stuck less and less often, but I couldn't rule out that n=5 was somehow unique. When I explored n > 5 by adding one or more fingers from my left hand, I wasn't trying to count all the possible ways to do it correctly. I was mostly interested in how often you got stuck if you tapped at random. I had no method except picking fingers arbitrarily, like a really slow Monte Carlo simulation. At other times, particularly with n=6, I would try to include every single possible combination, though I didn't count them. It seemed like there was some obvious pattern that ought to present itself. Certainly the more fingers you add, the more often you get stuck (which is hardly surprising), but I couldn't figure out any pattern beyond that, so at some point I dropped the question. I had almost forgotten about it until I saw this video.
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