I recently polled a bunch of people at MIT asking them what the largest ordered set they have memorized all the elements of was, with conditions that the elements’ names must not be easily derivable from their indices and elements are not allowed to repeat (i.e. it’s not an ordered multiset). Most answers were in the 50-151 range. (I’m guessing you know why I bumped that 150 up to 151.)
I thought about the ordered sets that I’ve memorized and was frankly quite surprised the largest ordered set I’ve memorized is the elements (chemical elements; we have unfortunate wordspace collision with set elements here) 1-112 in atomic number order. (Also, surprising to me, I seem to be relatively unique in memorizing them in atomic number order; most other people who memorized the periodic table did so in Tom Lehrer order. I also knew the Tom Lehrer order at one point, but forgot it. Of course, thinking about it after the fact, memorizing the elements in Tom Lehrer order sounds like an exceedingly plausible path towards element set memorization.)
I also found out that I was a little off from getting all the MIT Buildings in lexicographic building number order. Had I gotten that, I would’ve have a slightly-over-150-size ordered set memorized, but more interestingly, that would’ve meant the largest ordered set I’ve memorized would’ve been one I’ve passively absorbed, that is, never intentionally set out to memorize.
The US States are a 50-element set that I’ve memorized in three different orders. It’s interesting that I’ve bothered to find three different orderings of the US States but never bothered to find an ordering for the countries of the world, that is, even though I’ve memorized all the members of that set, for most definitions of “country”, I don’t actually memorize an order to them.
One of my favorite responses that someone gave was the python3 builtins in alphabetical order. As an avid fan of python, I very much approve.