Hi internet! how ya gettin on?
People give out about maths. They hate it. They can't do it. It's too hard. It's stupid. Maths sux.
Well let me tell ya. I hate it and I cant do it and its too hard, but one thing's for sure.. it doesn't suc and it's pretty cool.
Will we show 'em a few reasons why internet? gowan we will sure.
Earlier I asked for some volunteered numbers, just so you know that i'm not using 'fixed' numbers, I had some lovely audience members spew some out. One came from the wonderful Emma Wade. It was 529. Now if we reverse this, we get 925. Subtracting the smaller from the larger, we get 396. Then we reverse this to get 693. Then finally we add this to it's predecessor to receive a solution of 1089.
What's so magical about that?
Well, lets try another number, donated by the fabliss Sarah Elaine. 417. Reverse to give 714. Subtract, 714 - 417 = 297. Reverse; 792 and add 792 + 297 and what do we get...
It's always 1089.
And this works for ANY 3 digit number, where the first and last differ by more than two.
Magnificent! Wonderous! Magical!
Well, not entirely..
Consider, 529. This can be written as 500 + 20 + 9. And any 3 digit number can be written in the form 100a + 10b + c. So let's, for handiness sake rename 529 as abc for the time being. Reverse abc to give cba. Then subtract, abc - cba = (100a + 10b + c) - (100c + 10b + a)
Ya still with me?
The bs cancel each other out and we're left with 99a - 99c.. or 99(a-c). Since the first and last digits differ by more than 2, a-c is either 2,3,4,5,6,7 or 8. So now we have that 99(a-c) is one of the following; 198, 297, 396, 495, 594, 693 or 792.
Any of these look familiar?
The final part is to add which ever one of these intermediary numbers to its reverse. So lets call our intermediary number def (which is 100d + 10e + f as before with abc) and add it to its reverse fed. Looking at the list of 7 possibilities for def we see that the middle number is always 9, and also, the first and last digits always add to give 9. i.e. d + f = 9. So, def + fed is 100d + 10e + f + 100f + 10e + d
or, 100(d+f) + 20e + d + f
which is (100 x 9) + (20 x 9) + 9
or, 900 + 180 + 9
And voila. 1089. The riddle is laid bare.
Anybody that has made it this far in the post should be commended. And well you should feel victorious in the fact that you can now see through the magic. If this is the case, you should come and do some sums with me and internet.
This post was brought to you by a quote (one i thought was quite nice. It's from a weird religious indian guy who tried to teach maths, he was a bit of a phoney but he said some nice things.)
To those who asked whether the method was maths or magic, he had a set reply: 'It is both. It is magic until you understand it; and it is mathematics thereafter.'