My friend aced the mathematics final. Not due to my intervention, I’d say; my friend only remembered one question on the exam being much like anything we had discussed recently. Though it was very like one of those, a question about the probability of putting together a committee with none, one, two, or more than two members of particular subgroups. And that one we didn’t even work through; I just confirmed my friend’s guess about what calculation to do. Which is good since that particular calculation is a tedious one that I didn’t want to do. No, my friend aced it by working steadily through the whole term. And yes, asking me for tutoring a couple times, but that’s all right. Small, steady work adds up, in mathematics as with so much else.
Meanwhile may I draw your attention over to my humor blog where last night I posted a bit of silliness about number divisibility. Because I can’t help myself, it does include a “quick” test for whether a number could be divided by 21. It’s in the same spirit as tests for whether a number can be divided by 3 or 9 (add the digits add see whether that sum’s divisible by 3 or 9) or 11 (add or subtract digits, in alternate form, and see whether that sum is divisible by 11). The process I give is correct, which is not to say that anyone would ever use it. Even if they did they’d be better off testing for divisibility by both 3 and 7. And I don’t think I’d use an add-the-digits scheme for 7 either.