Checking your work

Multiple distinct paths toward a conclusion are a good thing.  Travel the second or third one (after you've followed the first to its conclusion) and you gain confidence in the validity of a proposition.  We learned this in math, but it is a lesson that applies more broadly.

When I was in elementary school and we learned arithmetic, a big deal was made about the difference between what our parents were taught - carry the one - and what we were instructed to do - exchange the ten for ten ones.  You have a feeling that they're on a different verse but are still singing the same song as back then.  

Of course, the best tune on this score was given to us by Tom Lehrer. 

Now, that actually is not the answer that I had in mind, because the book that I got this problem out of wants you to do it in base eight. But don't panic! Base eight is just like base ten really - if you're missing two fingers! Shall we have a go at it? Hang on...  (The full lyric is here.) 

The Faulty Logic of the 'Math Wars' - NYTimes.com via kwout