Try to arrange the numbers 1-9 in a 3 by 3 grid such that each row, column, and diagonal adds up to 15.

A Magic Square is a set of integers arranged in a square matrix. The numbers in each column, row, and diagonal add up to the same sum. Magic squares have been around for a long time probably dating back over 3000 years. Many believe they were derived from the oldest known number mystery, the legend of Lo Shu from a book entitled Yih King discovered in China. The word Lo means "river" and Shu means "books" and the legend has it that the solution to appeasing the river god after a great flood with the right number of sacrifices was a symbol for the number 15 engraved on the shell of a turtle. In 1514 Albrecht Durer, an engraver from Nuremberg, Germany created an engraving he called Melancholia that included a magic square. Durer later went on to write a practical book on geometry. American Benjamin Franklin, in addition to being a great statesman and inventor, also enjoyed working with magic squares and came up with an intriguing 8 x 8 arrangement. He probably burned the candles for ,any long evenings figuring out that complex puzzle--but then, he didn't have television and the Internet to take up his time.

816 357 492

got it

Do the same thing, in three dimensions, such that any planar section is a magic square.

_______ __42___ 1 17 24 15 19 8 26 6 10 23 3 16 7 14 21 12 25 5 18 22 2 10 9 13 4 11 27 In a 3 dimensional magic square it isn't possible to get single plane diagonals, but you'll notice that the triagonals work fine! This is a good one, filled with all sorts of weird numerological coincidences. I wonder if anyone can point out a couple of them?

By the way, I was working on a base4 magic cube today, and realized that a PERFECT cube is possible for a base8 configuration, but I don't have that much free time to sit around doing this. It is impossible to have a perfect base3 or base4 magic cube because you cant get the diagonals to work properly on their individual planes, therefore making the individual magic squares imperfect (Triagonals work). I'll probably finish my base4 magic cube tomorrow. Oh Boy! Now I'm going to get high and watch "City of Lost Children". It looks very depressing!!

____130_____ 60 37 12 21 13 20 61 36 56 41 8 25 1 32 49 48 7 26 55 42 50 47 2 31 11 22 59 38 62 35 14 19 57 40 9 24 16 17 64 33 53 44 5 28 4 29 52 45 6 27 54 43 51 46 3 30 10 23 58 39 63 34 15 18 This is an imperfect magic cube based on a constant of 130. Again, notice that the diagonals dont work on the individual layers, but quatragonally (?) they work fine. This took me almost 13 hours of constant work. I have no idea why I did it. After I proofed it, I found an IDENTICAL magic square in one of my books. I'm feeling a little bitter, because I felt like it should have been mine. I hate That someone got to it before me. On top of it all, I have a monstrous headache, and am very paranoid. Seeing patterns like this can be very disturbing. There is no bright side.

You obviously have way to much time on your hands. Well at least you're not using it in one of the "anti-" movements.

Christopher, it's really neat that you came up with that yourself. I have discovered that manipulating numbers gives me a high and I can do it for hours without noting the passage of time. Is it the same way with you? Did you watch "the City of Lost Children" yet? It's one of my favorites.

m'kay. Try magic hypercubes now. Start with a 4 dimensional 3x3x3x3. Any 3d cross section must be a magic cube.

What would that look like, graphically? (Also, do I sound like an idiot in the post above?)

Antigone, I'll have to get back to you on this one. I'm still trying to get over my last one. Watcher, I really do not have enough time at all!Currently, I'm involved in no fewer than 3 money making projects (network and computer consultancy), but always make time to "feed my head". The biggest time waster for me is the internet. I am incredibly wired, and have computer access 24x7; DSL at home, and a wireless laptop. If I didn't need connection for my work, I would probably find that I had MUCH more free time, and MUCH less money. I'm an incredible multi-tasker; I can waste time while paying the bills. Spider, I am indeed the same way. When I do intensive math, especially relating to prime numbers, I can lose myself for days on end. Unfortunately, I find that I tend to get paranoid, seeing *patterns* and incredible coincidences. It makes me too weird to be around, because I just want to talk about them, and no one understands me. I don't have any friends that are mathematically inclined, and while I find the subject fascinating, its generally a big turn off for the folks at large. I DID see City of Lost Children, and really enjoyed it. It had amazing production values, and was really quite well done. My favorite aspect of it was "Le Pieuvre (The Octopus)", the siamese twin sisters. Their faces were very disturbing to me...Very menacing. They almost always had a gentle smile, and twinkling eyes, while saying the most terrible things. I loved the dichotomy. I've been looking for a good picture of them to use as wallpaper on my laptop, but haven't found the right one yet. Heres one picture that I found, for those of you who want to see them: http://www.geocities.com/Hollywood/Academy/1351/children/octopus.jpg

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