I have been talking with my math teacher (I am only 14), about doing math and magic, and he showed me a three by three magic square. I said that this worked the same way as a 5X5 square works, and then I realized that actually all odd numbered squares will work with the same method. I just wanted to know whether any of you know the equation that is needed to start the square?
Thanks,
Owen

I'm not sure if this is the same magic square feat that you're talking about, but in the book 101 Easy-to-Do Magic Tricks by Bill Tarr, he talks about doing simple magic squares.

His method works with any X by X magic square where X is odd. He doesn't so much use an equation. He places a 1, then places a 2, then 3, 4, and so on, according to certain rules, until all the squares are filled.

Daniel,

Scott has some excellent suggestions.

You're correct, if you know how to do a 5x5 magic square using the "diagonally up to the right" method, then all odd magic squares are the same. Your starting number always goes in the center of the top row. If N is the number of rows in the square, and S is your starting number, then the sum of each row will be [(N squared+2S-1)/2] x N. (This looks more complicated than it really is: you're just taking the average of your first and last number, then multiplying by the number of rows.)

If you already know what you want the final sum to equal (the sum needs to be divisible by N if it's going to be a consecutive magic square with whole numbers) and you want to figure out what number to start with then:

Let F= final sum, and N = number of rows, then the first number should be [(2F/N)+1-N squared]/2. Again, this is simpler than it looks since N squared is simply the total number of boxes in the square.

Hope this helps. If you need more, you can PM me.

Jack Shalom

Owen, have a look at the following page on my own website: http://www.markfarrar.co.uk/msqodd01.htm.