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Dear Mitch,

I have two questions, and I'm hoping you'll answer both of them.  First, do you know the way that people can look at a really long number, like 111,123,792,432, and in just a few seconds without using a calculator they can tell you if it's divisible by 3?

(Some guy did it the other day with the serial number on a dollar bill at a business lunch and we were all impressed.)

My second question pertains to this new "mystery person". At first I got the impression she was going to be giving advice and techniques that students can use to overcome their fear of math (their "math anxiety") and their test anxiety, giving real ways to help our daughter relax when she gets worked up over tests, but so far all I see is this new person doing is something you call "numerology", which, to be honest, seems to be quite a change from the down-to-earth kinds of things you've done in the past (and the reason my wife and daughter and I have frequently checked in to see what kinds of questions you were answering that week), so if you could answer the one about how to tell if a big number is divisible by 3, just by looking at it, and then clarify the kinds of things your new staff member will be concentrating on, I'd really appreciate it.

Your fan,

Mr. G.B.

(Speaking for the rest of my family as well as a number of my daughter's classmates who also visit your website for your SAT tips.)


Dear Mr. G. B.,

Of course I'd be more than happy to answer both of your questions. First, the one regarding the quick testing of a number in one's head to see if it is divisible by 3.  It's a simple trick.  You simply add up all the digits, and if their sum is divisible by 3, then the whole number is divisible by 3.  To use the number you gave as an example, 111, 123, 792, 432 -- when you add 1 + 1 + 1 + 1 + 2 + 3 + 7 + 9 + 2 + 4 + 3 + 2, you get 36.  And 36  is evenly divisible by 3, which means that 3 goes into 36 exactly (12 times), leaving no remainder.  (3 x 12 = 36).

So, that long number (111,123,792,432) is divisible by 3.  In another post, soon, I will explain why this works, but what I think is more interesting to note here is that there are other divisibility rules ("tricks"), and, in fact, there is at least one such method for each and every number from 1-10 (even though a lot of books seem to say there is no trick for 7).  Those books are wrong; there is a way to check for 7.  Also, in addition to the relatively easy ways to check to see if a number is divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, there are relatively easy ways to check a number to see if it is divisible by PLENTY of much bigger numbers).  And since we've had a number of requests for them since we began, three years and a couple of weeks ago, I have decided to include them in posts within the next few weeks.

Regarding our new "mystery guest"/team-member, you bring up a very good point.  I did originally present her as someone who would help me cover the area of "math anxiety" and overall "test phobia", which are the specialties I believe will benefit this website the most. So. . . long story short, after several in-depth discussions, we arrived at what I believe is the perfect solution to the fact that her other passion, numerology, is something that is indeed very different from our typical 'Question & Answer' range of topics:  From this point forward she will be working on this website SOLELY on the topics of overcoming anxiety around the learning of math and the taking of standardized tests, and she has JUST launched her own blog that will be devoted primarily to numerology and will be tailored to give that passion and expertise of hers its own forum, to answer questions pertaining to that subject and where she will have the space and audience worthy of the study's in-depth development in all its complexity. On this website,, this could have proved a challenge. In the VERY near future, I will post this "mystery person's" blog address, so that readers interested in learning more about the ancient practice of numerology will know where to go to satisfy their appetite.  (Having known this woman for some time, I myself am excited to visit her blog and learn as she shares her wealth of knowledge and experience on a subject that, truthfully, is one on which I am a novice).  Oh, and by then I will reveal her identity!

I hope you found this interesting as well as informative.

Mathematically yours,