Magic Squares amuse more people than I'd've guessed!
One of the more amusing bits of my pollworking yesterday to me started around 1pm, while I was on the phone talking with jusdisguy, I heard the woman next to me (the other regular clerk) say to the student "Hey, you want to try a fun puzzle?". I could see that the woman had drawn a 3x3 grid, and was working at filling in the numbers, which she hadn't completed yet. I leaned over, and while I was talking, wrote down the 3x3 magic square. I ended my phone call, and she said "Wow, how did you do that?". I laughed and showed her the easy little pattern to make any odd-dimensioned magic square. She was really amazed! The student was also watching, fascinated too. Then FOR THE ENTIRE REST OF THE EVENING, these two played with magic squares, with the woman writing out all the odd ones up to 11, and the student writing out a 13 and a 25 magic square! I explained to them how to multiply the central number by the order of the square as a shortcut to find the square's sum, and they were amazed further. Me, I was very, very amazed that this little obscure bit of math trivia that I'd learned when I was maybe 10 years old (and somehow remembered all these years) suddenly popped up and became relevant and incredibly popular and amusing for an afternoon! Such unexpected fun!! The woman made a point to give me extra thanks at the end of the evening for the magic square info!
Funny part of that was before I went on my lunch break, I mentioned to them that you could make a 4x4 magic square with the numbers 15 and 14 in the two middle squares of the bottom row. I seemed to remember that there was some old painting that had this square in it, painted in 1514 (Whee, that's really true!). I said that I didn't know any pattern for even squares, though there might be some. Anyway, I left them to figure it out while I went for lunch. When I got back they hadn't figured it out, so I had to. Silly me! I'm lousy/slow at arithmetic, and so this had me doing lots of tiny sums. Luckily I made some good guesses about symmetry, using lots of pairs of numbers that added to 17 (to make sequences that added to 34), and managed to finish it reasonably quickly. Phew! Was fun, though, despite all that oh-so-hard arithmetic. ;)
I later found that there is a pattern for Magic Squares of order 4p ("doubly even"), and another "medjig method" for even squares.
UPDATE: Better explanations for even magic square patterns at Wolfram MathWorld.
Funny part of that was before I went on my lunch break, I mentioned to them that you could make a 4x4 magic square with the numbers 15 and 14 in the two middle squares of the bottom row. I seemed to remember that there was some old painting that had this square in it, painted in 1514 (Whee, that's really true!). I said that I didn't know any pattern for even squares, though there might be some. Anyway, I left them to figure it out while I went for lunch. When I got back they hadn't figured it out, so I had to. Silly me! I'm lousy/slow at arithmetic, and so this had me doing lots of tiny sums. Luckily I made some good guesses about symmetry, using lots of pairs of numbers that added to 17 (to make sequences that added to 34), and managed to finish it reasonably quickly. Phew! Was fun, though, despite all that oh-so-hard arithmetic. ;)
I later found that there is a pattern for Magic Squares of order 4p ("doubly even"), and another "medjig method" for even squares.
UPDATE: Better explanations for even magic square patterns at Wolfram MathWorld.