Fun math algorithms

[David Hayden]

Subtraction without ever having to subtract from a 2-digit number. I actually came up with this in 5th grade.

12345
-9876
------

For the first digit, the normal method is to borrow from the 10's column and compute (10+5)-6 to get 9. Instead subtract the lower number from the upper (6-5=1) and then subtract the result from 10: (10-1=9)

More generally, if you must borrow to subtract a-b, instead of computing 10+a-b, compute b-a, then 10-(b-a)

For my little head, I could do the 2 easy subtractions faster and more accurately than the one subtraction from a 2-digit number. Hmm, maybe I invented RISC computing for humans in 1973!