Well it’s kinda nice to know that we’ve just had the 3000th visitor to the blog site. I’ve not had Rupert Murdoch itching to buy the site from me (nor perhaps more importantly from KG!) as yet but traffic’s developing which is great – thank you folks. Keep telling the odd mate about the site and I’ll keep writing about you in my memories. I’ve got a thing about numbers as it happens: I like big ones (Tate Online access figures used to give me the horn every month). I guess being a man that’s a given right? But I really, really like quirky numbers/arithmetic. Odd ball Paul, I know. Can’t help it. I was never great at maths at school but I’ve always been numerate and I love the preciseness, symmetry and the sheer serendipity in number occurrence, balance and sequencing.
Consider this, a couple of weeks ago I woke up, came downstairs, checked the clock in the kitchen and it was almost 10 past 8. Nothing too significant in that except that for some reason I instantly realised it was 08:08 on the 08/08. Pity it was 2007 but hey, to me it seemed numerically special. Later the same day I happened to glance down at the car’s milometer (actually kilometer, if there is such a thing) to see it was registering exactly 78,000 kms. I love that random moment of numerical preciseness. You’ll probably be thinking I ought to have bought a lottery ticket there and then but it’s not the same thing. Anyway I did and it didn’t work. Harumph.
It’s the delight of the accidental surprise which I enjoy. When I was at BT I had a fuel card as part of my package so, of course, I was less-obsessed about landing the fuel cost on the precise amount of £xx-00, as you tend to be when you’re paying cash. Actually that often seems bizarre when I think about it, as I usually spend a long minute or so nudging the gauge, fractions of 1p at a time towards landing the overall fuel price at exactly £38-00, only to go into to the petrol station and buy a paper and Mars bar and thus destroy the preciseness of the total spend. Men eh.
But with the fuel card I consciously turned away from the meter reading and studied the girl at the next pump or something equally distracting until the automatic shut-off clicked in on the petrol feed. Then I’d look up and check the price reading. 5 times in my life it landed precisely on a full pounds amount ie £45-00 or whatever. That was 100 glorious points, gold star and a magical day, on my imaginary petrol game (this is meant as an in -car ent feature but that’s about all it is – sad I know). £45-01 would count as 1 point; whereas £44-99 was 99 points. I didn’t actually keep a score – honestly – it was just some mental fun with numbers between my filling up and paying/signing. You can tell I did a lot a miles a year if I regarded this as mildly amusing entertainment.
Actually travelling with Mike R was always hugely more enjoyable than travelling alone; whether it was listening to Phillip Hodson talking about women’s intimate issues on the old 5 live or counting the apple pie packets in the back of his car/ the elbow routine/the parabola (personal jokes, sorry) or getting to Old Trafford in 2hrs 25 mins from Buckingham. But mostly it was me and the car and my numbers (or car names) of course.
Do you know there is a mathematical concept known as weird numbers? I might not be able to explain this so well but any number has its divisors – the numbers which divide into it. 50 for example has 1, 2, 5, 10, 25 and of course 50. 50 is not weird. A ‘weird’ number has divisors (excluding the same number as itself) which in total add up to more than the number itself but none of its constituent numbers can arithmetically be made to add up to the original number. Take the number 12. Its divisors are 1,2,3,4,and 6. They add up to more than 12 in total but 2 x 6 or 3 x 4 = 12 so it’s not weird. Still with me? The first weird number is 70. After that it goes 836, 4030, 5830 and so on. Also, there are no odd numbers below something really huge but they do exist. Is that not weird?
There are all sorts of other goombah numbers – though that isn’t a mathematical term so far as I know. Take 1729. Innocuous, simple and dull? This mathematical lulu happens to be the smallest number that is the sum of two cubes in two different ways ie 12 to the power 3 + 1 to the power 3 or 10 to the power 3 + 9 to the power 3. Who on earth discovered that and don’t you find it irresistible? Technically I think they call it an ‘interesting’ number. To me it’s frigging fascinating.
There are of course simpler examples of arithmetic charm. One of the earliest short cuts I learned was to multiply any number by 10 by adding a ‘0’ to the original multiplying number (there’s bound to be a term for that which I don’t know). That must be one of the original arithmetic tricks kids must learn but i’m always amazed that so few know the sister trick which is about x 11. Pick any 2 digit number like 27, where the sum of the two is less than 10, and the answer to x 11 is to add the numbers together and inserting the sum of the two betwixt them. So that 27 x 11 = 297. It always works. 11 x 63 = 693.
But my personal favourite is the no. 9. It’s just a magical number number for sequencing. For example multiply any number by 9 and the digits of the answer must always add up to 9. So that 1 x 9 = 9, 2 x 9 = 18 (and 1 + 8 = 9), 3 x 9 = 27 (and 2 + 7 = 9) and so on. But here’s another truism; you can probably work out in your head the answer to multiplying any number by any combination of 9’s. No? Well take 45 x 999. Take the number of 9’s and add the same number of 0’s to the multiplying number – 45000. Subtract the total of the 9’s = 27. So that 45000 – 27 = 44973. There’s your answer.
Too simple for you, take a look at this sequence?
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 1111 and so on. Wacky eh?
This isn’t strictly a 9 sequence but I still like it:
3 x 37 = 111 (constituents of which = 3)
6 x 37 = 222 (ditto 6)
9 x 37 = 333 (ditto 9)
12 x 37 = 444 (ditto 12)
15 x 37 = 555 (ditto 15) and so on….
Back to 9’s. What’s the highest number you can write with just 3 digits? 999? Wrong. Struggling? It’s could be 9 to the power 99. But others would say it’s 9 to the power 9 to the power 9 which is equivalent to 9 to the power 387420489. And that’s pretty big. Having said that I’ve seen mathematical argument saying this is not the biggest but I got a bit lost by the symbology thereafter.
Let’s get this back to simpler stuff. How to tell a reluctant person’s age arithmetically by some simple probes. Ask them to muliply the first digit of their age x 5. Add 3 and then double it. Tell them to add the second digit and ask them to confirm the total. Whatever it is, minus 6 for their precise age. Never fails.
Here’s a final thought about numbers and spelling sent to me by Vish. The letters a,b,c and d are very common right? Well the letter d appears nowhere in any number before 100. Incredibly, the letter a appears nowhere before 1000. Unbelievably the letter b appears nowhere before 1000,000,000 (billion) whilst the letter c appears nowhere in our numbering sequence at all.
You go do the math