Posts Tagged ‘numbers’

2017 minus 26: Numbers

Posted: 6 December 2016 in 2017 minus
Tags: ,

One of the questions I used to ask, when I was interviewing people for the finance department I used to run, was… “why finance? Why accountancy?”

There were plenty of ‘good’ answers – this wasn’t one of those ‘impossible to answer’ questions, nor a ‘there’s only one right answer’ question. Genuinely, there were loads of good answers and I got some of them when I asked it. Some were the kind of answers you’d expect, some… not so much.

I think my favourite was the young lady who said she entered the profession to spite an ex-boyfriend who’d constantly belittled her and – when they split up – had mocked her for an opportunity she’d had at her company: to cover for someone in her company’s finance department on maternity leave. She took the proffered opportunity, and found she loved the work.

Then there was the interviewee who told me he’d chosen accountancy because he’d fancied the woman who’d come to his careers day at school, had temped during the summer at an accountancy firm, and again, found he enjoyed the work.

The best answer, though, the one that pleased me most, was when someone said they’d always felt comfortable with numbers. I could teach them the methodologies of accountancy and the rules and regs, but yeah, they had to feel supremely comfortable with numbers. (Much as my younger brother used to say, he could teach anyone to cut a head of hair, but only someone who felt very comfortable with the idea of changing someone’s appearance stood a chance of success as a hairdresser.)

I said above there’s no ‘right answer’ to the question. You might have inferred from that that ‘there’s no or wriog answer to the question’. But you’d have been wrong. Oh boy were there some wrong answers and I heard all of them. But The Wrong Answer was, and remained throughout my career, “I was always good at maths”.

It was a bad answer for so, so many reasons. For a start, they never meant they were good at maths; they meant they were good at arithmetic. To say they’re the same is like claiming that speaking is the same as making a speech. Or being able to write is the same as being a writer. Sure, the latter involve the former, but it’s a small part.

Besides which, I had a calculator and a spreadsheet to be good at arithmetic. (Never forget that a computer is just a pocket calculator with a jumped up attitude.)

But, I hear you cry, when they said they were good at maths, they meant they felt comfortable with numbers. Really? Then why didn’t they say that? No, what they usually – almost invariably – meant by “I’m good at maths” is that they got good exam results on their maths exams.

Every person I took on to work for me either in an accountancy practice or in a finance department who’d said they ‘were comfortable with numbers’, or who’d said ‘numbers always made sense to me’ turned out to be a good hire.

Me? I’ve been out of accountancy now for some time. I still like numbers. I still like playing games with numbers, solving number problems often, though not always, logic problems involving numbers, sometimes just solving those “Are you smarter than an [insert age] year old?” online puzzles.

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

But here’s some odd things involving numbers you might not have known:

  • A pizza that has radius “z” and height “a” has volume Pi × z × z × a.
  • In a room of just 23 people there’s a 50% chance that two people have the same birthday. It’s called The Birthday Problem, presumably because you now have to buy birthday presents you didn’t previously realise you had to.
  • a) Choose a four digit number (the only condition is that it has at least two different digits)  b) Arrange the digits of the four digit number in descending then ascending order  c) Subtract the smaller number from the bigger one d) Repeat. Do it enough times you always end up with 6174, Kaprekar’s Constant.
  • Forty is the only number whose letters are in alphabetical order.

Look, numbers are just weird. Well, some of them are, anyway.

And finally, random numbers aren’t that random. For various reasons, they tend to follow the distribution as below. It’s the first thing auditors look for when they think expenses have been faked. The tax man, and the SEC are also very aware of it… In a given list of numbers representing anything from stock prices to city populations to the heights of buildings to the lengths of rivers, about 30 percent of the numbers will begin with the digit 1. Fewer of them will begin with 2, even fewer with 3, and so on, until only one number in twenty will begin with a 9. The bigger the data set, and the more orders of magnitude it spans, the more strongly this pattern emerges.


This post is part of a series of blog entries, counting down to 1st January 2017. You can see other posts in the run by clicking here.

A number of things

Posted: 29 October 2011 in personal, skills
Tags: , ,

Skip this if you’re not fascinated by numbers.

I’m serious – this subject has been known to have a more soporific effect than laudanum.

OK, still with me?

I was talking with (isn’t that a great way of being polite, instead of saying “I was having a small argument with…”?) a friend last night about something and as part of it, said I’d prove that 1 = 2, and proceeded to so so, but more about that in a moment.

But it started me thinking about mathematics and the tricks those of who have a grasp of it use. Of course, I use mathematics and arithmetic synonymously, and they’re not the same, at all. But forgive me for using them this way, just this once? Thanks.

Now, 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.

It remains a mystery to me how everyone doesn’t know this, but:

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.

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.

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.

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. Try 13,057. 1+0+7 = 3+5, therefore it should divide evenly by 11. And indeed it does: 13,057 ÷ 11 = 1,187. Take 92,807. (9+8+7) – (2+0) = 22, therefore it should divide evenly by 11. And it does: 92,807 ÷ 11 = 8,437.

12: 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.

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

Well, I was wrong, and it took me until the age of 40 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 it was boring; don’t say I didn’t warn you. Be grateful, I could have taught you a quick way of working out the two-digit cube root of any number between 1,000 and 970,299.

Anyway, that proof.

I have no doubt that some of you will spot the flaw in this fairly quickly, but it’s genuinely astonishing to me how many people don’t.

(1) Let a = b

(2) Multiply both sides by b… ab = b²

(3) Subtract a² from both sides… ab – a² = b² – a²

(4) Factorise… a (b – a) = (b + a)(b – a)

(5) Divide both sides by (b – a)… a = b + a

(6) Since a = b… a = 2a

(7) Divide by a… 1 = 2

Ta-da!

Yeah – I know, but be fair, I said there was a flaw…