08 November, 2006

Somewhat annoying

It is somewhat annoying to spend several days on a problem, conclude that it is impossible, finally use the internet, and see that I am correct and it is impossible. I have spent the past few days trying to construct a magic cube. A magic cube is a three dimensional model of something like this:

816
357
492


Notice that every row, column, and diagonal adds up to 15. Also note that every number from 1 to 9 is used once and only once. This is called a magic square, and I spent a part of my childhood being fascinated by them. I think the largest magic square I ever created was a 15x15 one. Everything added up to 1,695.

Anyway, a week ago it occurred to me that magic cubes should exist. So I set to work trying to come up with a 3x3x3 magic cube. Today, I began using intelligence instead of guesswork. I actually used an augmented matrix, and figured out that the centre entry in every single square absolutely had to be 14. This would mean 7 entries that were 14, which is flat-out against the rules. However, I had actually used math to prove it, so I felt there was no reason to work more at the problem. So I looked on the internet, and it turns out the smallest possible magic cube is 5x5x5.

I guess it is good that I was right, but still. I don't want to be right, I just want a magic cube that is 3x3x3. I mean, 5x5x5 is ridiculous and not as impressive. One reason I did not show you my 15x15 square is because it is not impressive. You waste too much time doing addition to appreciate the beauty of any one much larger than 3. I mean, look at this 5x5 one:

17241815
23571416
46132022
101219213
11182529


It is cool maybe, but only after squinting at it for a while. It really is too bad that there can't be a 3x3x3 magic cube. What a shame.

2 comments:

Anonymous said...

every time I read one of your math entries, I want to kill myself because you might as well be speaking Like, Lativan mixed with French as far as I can tell.

Matthew A LaChance said...

I mean, you don't have to read my math entries. I guess I secretly hope that someone reads my math entries and understands them, but I have not seen evidence of this.