Someone showed me that oh, lo, these many years ago; a truly nifty and quick error-finder.
"Casting out nines". Yeah, it's a very old technique; I'd be willing to bet it appeared in Fibonacci's Liber Abaci, which was the first extended discussion of decimal notation to appear in Europe, in 1202. I give that a good bit of attention in my history of math class; the possibility of simple error-checking techniques was one of the major benefits of the switchover to decimal notation.
Re: Nine!
"Casting out nines". Yeah, it's a very old technique; I'd be willing to bet it appeared in Fibonacci's Liber Abaci, which was the first extended discussion of decimal notation to appear in Europe, in 1202. I give that a good bit of attention in my history of math class; the possibility of simple error-checking techniques was one of the major benefits of the switchover to decimal notation.