The idea is that you can also just add up the digits of a number to &#x27;cast out nines&#x27; (during this calculation you can also ignore any pair of digits that adds up to 9).<p>By the way, you can combine this with &#x27;casting out tens&#x27;, then you&#x27;ll know if your result is accurate mod 90 (which is even less likely than it being accurate mod 10 or mod 9, if you&#x27;ve made a mistake).