Trachtenberg System for Rapid Mental Calculation (en.wikipedia.org)

The multiplication by 3 seems quite more complicated than just multiplying digits by 3 and carrying over the rest.

I always thought this was a neat trick:

http://www.archimedes-lab.org/Maths2_Multiplication.html

This seems, at a high level, similar to the various mental arithmetic tricks/pnemonics from India, commonly known as “Vedic Mathematics”. e.g. https://www.quora.com/What-are-some-of-the-best-Vedic-math-t...

I came across this book in the 1960s and remember working through the different algorithms. The only one I remember now is multiplication by 11. More generally, I was not reluctant to do mental arithmetic in school, especially for approximations and sanity checks.