Friday, January 12, 2007

Multiplication Magic

Tonight, QB went out to her co-worker's going-away bash. I was just too tired to go out with her after a long, long day at work. So, here I am being bored and more or less unproductive.

To keep me busy, I have decided to share something I thought was pretty neat when I learned about it. I know that some of you out there have seen it before, but I still think it's pretty cool. Cool, until you see why it works, anyway.

So, start with any two whole numbers. Now, for the first number keep halving it until you end up with a value of 1. Note that you will always round down. For the second number, double it as often as the first number was halved.

As an example, say our numbers are 49 and 116.

 49 116 24 232 12 464 6 928 3 1856 1 3712

The next step now is to cross out the values in the right column if the value in the left column is even. Continuing with our example, here's what we get.

 49 116 24 232 12 464 6 928 3 1856 1 3712

Now, sum the values that remain in the right column. We have 116 + 1856 + 3712 = 5684, which is equivalent to the product of our two initial numbers (49 * 116 = 5684).

The reason the math works out this way is related to the binary number system (Decimal 49 = Binary 110001 = 2^5 + 2^4 + 2^0). Should be pretty obvious from here. Anyway, when I first saw this 'trick' I thought it was really neat. But, maybe it's because I'm easily amused. Ha ha.