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Numbers Geekery

I was supposed to be reading A Storm of Swords (I have to catch my sister, and stay ahead of my wife…) but I caught up in thinking some more about a geeky bit of number play (aka what I think maths should be) that I started thinking about yesterday. So I thought I’d type it up and post it, because I think it’s neat. – Not that it necessarily has any point, or is original, or even especially clever; it’s just a fun neat pattern, and that’s what I like about maths: patterns and fun.

On a related note, I would suggest reading A Mathematician’s Lament by Paul Lockhart.

Anyway, what did I notice? (I’m glad you asked … or bothered to keep reading, at any rate).

The first thing I noticed was that if I subtracted the sum of 1 and 3 (i.e. 4) from 13, I got 9. Then I thought about other "teens", and found the same thing; e.g. 18 – (1 + 8) = 9. I thought that was pretty cool, and started wondering about other 2 digit numbers:

Pretty neat: if you take a two digit number, add the digits, and subtract that from the original number, you get a factor of 9. What factor of 9 do you get? Why, however many tens you had in the original number. I like that. So, what about 3 digit numbers?

So … you still get factors of 9, but no longer the number of tens in the original number. In fact, after some thought it became apparent that what you get is the highest factor of 9 that is less than the lowest number of that decade. That is, for 100-109, the highest multiple of 9 that is less than 100 is 99, or 11 x 9; for 200-209 the highest multiple of 9 that is lower than 200 is 198, or 22 x 9; for 360-369 the highest is 351 (39 x 9), and so on.

Heh – and it didn’t take much at all to work out that last multiple of 9: I simply subtracted (3 + 6) from 360 – being very sure the result would be a multiple of nine.

Fail. Once I started looking at the higher 200s I found that my "highest multiple of 9" idea was wrong. Clearly wrong. Maybe I shouldn’t have been surprised, as it didn’t seem especially easy to explain, nor elegant. Rather what seems to be the rule, is that the factor of nine is found with the hundreds and tens columns: the hundreds becomes tens, and then adding the digits in the hundreds and tens columns gives the ones for the factor. Gawd that sounds messy. Example then:

No easier to explain, perhaps, but it "feels" to me to be more elegant.

So. Fun with numbers. I said earlier that it might not have any point – but in a way that’s the point: it’s just fun, and it doesn’t need to have any sort of application.

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