Thursday, September 1, 2011

Magic squares

Have you ever heard of magic squares? These are squares with numbers in them, and if you add up the numbers in the columns or rows, they all add up to the same number.

In this example, all of the rows and columns add up to the number 15. There is a pretty simple pattern to use if you want to make one, although this pattern only works for boxes with an odd number of boxes in a row (3x3, 5x5, etc)

Read on to figure out how to make one after the jump. 

Here's how you can make one. There are two simple rules:
  1. Place the next number diagonally up and to the right
  2. If that space is filled, go down
I'll show you to explain:

Start with an empty box.

Put a "1" any where you want.

Put the "2" in the spot diagonally up and to the right. Do the same thing with the "3". (You have to imagine that the square kind of wraps around so that if you go off the side up appear on the other side.)

If we kept following the same pattern, we would have to put the "4" in the square where the "1" is. Since it's already occupied, you go down and put the "4" right below the "3". 

Then you go up and to the right again to place the "5". Continue following those two rules until you have filled in all the boxes, and there you have it! In a 3x3 square, you see that all the numbers add up to 15. I'm not sure how you do the trick where you can make a square that adds up to any number of your choosing.

Maybe that will be my next project...

I read about this a couple of months ago and I have tried to find the original source, but I can't seem to find it right now. However, I just refreshed myself on the rules by looking at Harvey Mudd College of Math's website.

Coincidentally, Harvey Mudd is the school that the mathemagician Arthur Benjamin teaches at. Katie, Lisa, and I saw him a few years ago at a show at BYU. It was pretty jawsome.

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