Quite a lot of people run across the Trachtenberg system at one point or another and think its rather novel; along with the story behind it.

When working with it, it is actually rather limited compared to other systems that were around the same time.

There is a far better and more robust system that has been reprinted several times, which was aggregated in a book more recently, called "The Cosmic Calculator", this is a three volume series for teaching mental math to kids, based on the ancient Vedas teachings, also called Vedic Mathematics.

It is at least 20 years old, I still have my copies that I received in 2001 as a gift, Amazon says it was published in 2019 which is incorrect; it is far older.

It was often used alongside activities where you would memorize (via flashcards) the common complements for 9 and 10 to the point of instant recall/association.

The digit sums are somewhat lacking, although understandable considering that the fundamentals of abstract math and group theory were still being explored at the time of publication. (i.e. digit sums <> cyclic groups).

You can find a link here. For reference, the copies I received in 2001 are identical to the displayed version below. There is also a Instructors Manual (a 4th book) which came with the set.

https://www.amazon.com/Cosmic-Calculator-Course-Mathematics-...

Now there's a coincidence - just watched Gifted https://www.imdb.com/title/tt4481414/ last night, quite enjoyed it. This system is featured. Also of note, Terence Tao is credited as "technical advisor: mathematics"