2014 minus 35: Things you didn’t even care whether or not you knew

Posted: 27 November 2013 in skills
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Somewhere in the boxes I possess which contain the books I don’t actually have up on the bookshelves is a book entitled The Dictionary Of Misinformation. It’s a cracking book based upon the simple principle that most trivia books tell you things that, in the title of this entry, you didn’t know you didn’t know.

However, this book takes a decidedly different tack, by debunking loads of things you know… that are flat out false. Old wives tales, misquotes and the like, every incorrect item is taken seriously and the common fallacy is, for want of a better description, destroyed.

Music hath charms to soothe the savage beast? Quite possibly, but the quote actually refers to the savage breast, and it’s has, not hath. (It’s from… no, not from Shakespeare, but from William Congreve’s 1697 play The Mourning Bride, Act 1, Scene 1.)

Surely there’s no-one who still thinks the ‘wherefore’ in “wherefore art thou, Romeo?” means where? Well, yes, there surely are.

Urban myths don’t escape – the authors are merciless in describing the belief that a drowning man surfaces three times as the rubbish it is. Similarly, while they acknowledge that some people have amusingly appropriate surnames, they obliterate the concept of nominative determinism with some relish.

So, the book seems to address the idea of things you knew, but were wrong, and trivia books by the hundred tell you things you didn’t know you didn’t know, and there are more than a few volumes addressing the things you knew you didn’t know. (They’re in the non-fiction section of the library.)

You know, every so often on my blog I ask you to teach me something, to show (or tell) me something that you know about that I probably don’t. And I’ve been rewarded by lessons on cornering at speed, on how to judge wine, how to light a photograph correctly.

But I’ve never returned the favour, so what follows is something that you may have known, may not have known or might never have even thought about.

mathfun1How to tell if a number is divisible by any number between 2 and 12

I had a great maths teacher at school. He understood that to get kids interested in maths as a subject, he had to make it interesting as a subject. And to that end, he taught his class what he called the ‘tricks of the trade’.

So, for example, he taught us how to discover whether any number was divisible by any number between 2 and 12.

Some of them are, you’ll see, obvious; some of them make sense, and one or two you’ll have to trust me on until you test them out and find out they work

2: duh, the number’s even

3: if the number’s digits sum to a number divisible by 3, the number itself is divisible by 3.

4: If the last two digits of the number are divisible by 4, the whole number is. (Remember this, I’ll come back to it.)

5: the number ends in 5 or 0.

6: if the number’s even and the number’s digits sum to a number divisible by 3, the number itself is divisible by 6. (Makes sense, doesn’t it, but most people never combine them…)

7: hmm, he didn’t teach us this one.

8: If the last three digits of the number are divisible by 8, the whole number is.

(A slight bit of explanation here: Notice anything? If the last digit is divisible by 2, the whole number is; if the last two digits are divisisble by 4, the whole number is; if the last three digits of the number are divisible by 8, the whole number is. That’s because 2, 4 and 8 are 2 to the power of 1, 2 and 3 respectively, and the similar powers of 10, i.e. 10, 100 and 1000 are, respectively divisible by 2, 4 and 8. OK, explanation over.)

9: if the number’s digits sum to a number divisible by 9, the number itself is divisible by 9.

10: the number ends in a 0.

11. If the sum of every other digit, starting with the first, is either equal to the sum of every other digit starting with the second, or the difference is exactly divisible by 11, then the number is evenly divisible by 11. It sounds complicated, but it really isn’t, I promise. Couple of examples to show you what I mean.

Try 13,057. That’s 13,057. Add the bolded numbers, and then the non-bolded. So 1+0+7 = 8. Subtract the non-bolded (3+5 = 8), and you get 8 – 8 = 0, therefore it should divide evenly by 11. And indeed it does: 13,057 divided by 11 = 1,187.

Take 92,807. The bolded (9+8+7) sum to 24; The non-bolded (2+0) sum to 2. So… 24 – 2 = 22, which is divisible by 11. Therefore the ‘big’ number should divide evenly by 11. And it does: 92,807 divided by 11 = 8,437.

12: Another combination one; if the number’s digits sum to a number divisible by 3, and the last two digits of the number are divisible by 4, the whole number is exactly divisible by 12.

Nice and easy, eh? Well, easy-ish, I’ll grant you. All the numbers from 2 to 12. All the numbers from… hold it, I hear you shout. What about 7? You skipped over that one pretty bloody quickly, didn’t you, budgie?

Truth is, he didn’t teach us how to quickly find if a number was divisible by seven. I even told my lad Philip, when teaching him those same tricks, that there wasn’t a quick way.

Well, I was wrong, and it took me until well into my 40’s (25 years after I learned the rest of them) to discover an incredibly easy way… I have no idea why it works, but it does.

Take the number’s final digit and double it. Subtract that from the rest of the digits and if you end up with a number divisible by 7, you’re home and dry.

Take the number 364. Double the final digit and you get 8. Subtract that from the first two digits: 36 – 8 = 28. And what do you know? 28 is divisible by 7, so 364 is exactly divisible by 7.

903? 90 minus 6 [3 doubled] = 84, so 903 is divisible by 7.

Look, I told you I didn’t know why it works, but it does.

So, who’s still awake now? Anyone? Anyone?

Ah.

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Comments
  1. […] Long time ago, I posted here about arithmetic, specifically How to tell if a number is divisible by any number between 2 and 12. […]

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