There was a nice little curiosity on the Guardian puzzle page yesterday. To follow it, just pull out a calculator. The Windows calculator will do fine, and I'm sure other operating systems have something similar. You'll notice that the numbers 1-9 are arranged like this.
4 5 6
1 2 3
Take any rectangle within that grid of 3 by 3, and count round the corners clockwise. You can have 1452, 1782, 1463, 1793, 2563, 2893, 4785, 4796 or 5896. You can also start at any point, so instead of 1452 you could have say 5214. You could even, if you were so minded, go anticlockwise, and have 5412.
Any number spelt out by this method will be divisible by 11. This is why.
If you take any number which can be divided by 11 and add the odd placed digits (the first, third, fifth digit, and so on) and the even placed digits (second, fourth, sixth ...), you get two separate numbers. These two numbers may be the same, but even if they aren't, the difference will always be 11.
Take 4521, for instance. 4 + 2 and 5 + 1 both equal 6, so you know 4521 can be divided by 11. In fact, it gives you 411. With 2948, 2 + 4 = 6 and 9 + 8 = 17. 17 - 6 = 11, so again you know 2948 can be divided by 11, this time to give 268.
With a rectangle of digits on the calculator, the second digit will always be 1, 2, 3 or 6 higher or lower than the second, depending on whether you're jumping one or two rows or columns. Whichever it is, the third digit and fourth digit will always have the opposite relationship. For instance, with 1452, 1 to 4 is plus 3, while 5 to 2 is minus 3. Therefore, the first digit plus the third will always equal the second digit plus the fourth. Therefore, the number will always divide by 11.
Which amused half of you, and bored the rest. Whatever I write about, I will always be putting some of you off. Which brings me neatly back to the football.
I was all set to write about something else, really I was. As with any great tragedy, there's a mourning period, and then you get back to your life. Unfortunately, in my life every second Saturday is spent at Ashton Gate, which meant I spent yesterday watching my team being outclassed in the mud and rain, struggling to find any attacking creativity and defending like dorks, and losing at home. It was just too much like Wednesday to be borne. Now I'm back where I started. Or not. Yes, lo and behold, Leeds have just lost 1-0 at Cheltenham. Yes, that's Cheltenham, the well known football powerhouse, originators of total football and catenaccio. Now I'm actually even sulkier than I was in the first place, which means you've got more football writing to come.
Except that football is shit. I've seen the light, and from now on, I'm going to watch Saturday afternoon ballet. Not that it will help. Inevitably, whichever ballet troupe I choose will be constantly outshone by the visiting ballet team, with their pliés, entrechasses and deft flicks into the penalty area while my cutprice Baryshnikovs just hoof it up to the big tall ballerina at the front, and - no, I think that will have to do. I really can't go on.
Still, there is a silver lining. My friend Simon assures me that I write better when my teams are losing. Apparently, when they're doing well I'm all smarmy towards them, but when they're rubbish the vitriol dripping off the keyboard takes it to a higher level. He also suggested that when I'm writing about sport, the objectivity and precise reasoning that I value when writing about science or philosophy may be slightly less in evidence. I can't imagine what he means.
So there it is. As the old line has it, I have to suffer for my art, and now it's your turn.
