Periodic Table. Caveat: I remember very little of the logical backing for the periodic table (part of why I wondered how pure memorization would work). There are groupings in the periodic table, but I don’t think it’s possible to deduce any possible forgotten element name or (especially) abbreviation if you don’t recall it yourself. Still, it’s a fair point, if there was a way to remember the table without memorization that would be all of (i-iii). Your point about multiplication tables is this in a nutshell, I think. From this point already though, you can kind of feel that the more “memorization required” some given content is, the less “intellectually valuable” it is. This alludes to your second question, addressed below.