\textcolor{red}{11^2 - 31^2}: memorized the squares via direct association:
- 18^2 is 324 because 8x3=24
- 19^2 is 361 because if you rotate 19 by 180° you get 61
- 21^2 is 441 because 21 is 12 backwards (12^2=144)
\textcolor{green}{32^2 - 99^2}: memorized by pairing 2-digit P with 3 digit image
- 97^2 = 9409 Bill Clinton with a purse (940) filled with balloons (9*)
- 85^2 = 7225 Vladimir Lenin (85) with a cannon (722) shooting tea cups (5*)
*the shapes are just in case I blank, but the rule is that 0, 1, 5, and 6 always end in squares with 0, 1, 5, and 6; respectively. Same goes for 10 compliments, so 1 and 9 is the same, 6 and 4 is the same. The missing 2 and 8 are both 4, “mnemonic because” 2x4=8. 3 and 7 are both 9, but everybody knows 3² is 9.
I have a set of seven memory palaces for year codes when I do calendar calculation. These seven uniquely hold all Ps (as in PAO) from 00 - 99. Since there are no 3-digit images in these palaces yet, there is no confusion adding an image to each P.
I’m pretty solid on both after one week, but I’m going to add 3-digit images for the rest of them and prefix them with a 0, so 18 from above will receive 032 (not 32 nor 324). That’s just because switching systems is slowing me down. This way there is no need to determine first if the number is greater than 31 or not.
At the moment I’m faster on a few with mnemonics but still slower on others. I have to control myself to not calculate and use the mnemonics. Things ending in 0 are pretty bad, because they are already known from the single digit squares; 50^2=2,500 because 5^2=25.
The worst are powers of 2 though 16^2=256; 32^2=1,024; 64^2=4,096; etc. I just see those before I can even calculate or use mnemonics, so those I’ll skip.
I’ll update you next week!
ps: congrats on your progress even if you were “busy and being lazy” 