Sunday, September 27, 2009

Eureka! My Very Own Magic Square(s)!

I was so proud about this.
Not too much now.

This post was supposed to be written and published at 6 AM.
But I had to go to the Sunday mass, so… there goes the excitement.

Anyway, let’s pretend that I am still very excited about this.

Yesterday, I saw Albrecht Durer’s magic square.
It was awesome.
For all of you who don’t know what a magic square is, well, it is simply a square with consecutive numbers on it.
The magic lies within the fact that the sum of each row, column, and diagonal are the same.
Albrecht Durer’s magic square, however, is more than that.


Not only does it have the usual properties of a magic square, it also has an equal sum of the numbers on its center square (which consists of four smaller squares), and all four quadrant squares.
Moreover, the number 1514 on the bottom row is actually the year the square was created.

Impressed, I decided to make my own.
After a gruesome long night, I was finally able to create what I think is a BETTER magic square.


Like any other magic squares, the sum of each row, column, and diagonal are the same.
But that’s only the half of it.
You will also find that the sum of EVERY four adjacent squares that form a larger square is the same.
Take any four squares that form a larger square you want, and the sum of the numbers will be the same.

UPDATE
From the initial square, I was also able to derive no less than 96 squares that follow the same rules (kinda takes away the value actually).
I divide them into three groups called batches.
For the sake of space, I'm only presenting one square per batch.

Batch 21-13/25-9
 2  16  5  11
13  3  10  8
12  6  15  1
 7   9   4  14

Batch 19-15/25-9
 7  14  1  12
 9   4  15  6
16  5  10  3
 2  11  8  13

Batch 18-16/25-9
 4   9   7  14
15  6  12  1
10  3  13  8
 5  16  2  11

But Albrecht Durer’s square has the production year on it, you might say.
Well, my squares are only 4 by 4, which means the largest number is 16. There’s no number 20 to create the year 2009.
But, as far as dates are concerned, here is the list of ALL possible dates you can get from my squares:
Batch 21-13/25-9
Apr 9/Sept 4, Aug 1/Jan 8, May 16, Dec 13, Jul 14, Oct 15, Feb 11/Nov 2, Jun 3/Mar 6, Jan 12/Dec 1, May 4/Apr 5, Aug 13, Sept 16, Jun 15, Nov 14, Mar 10/Oct 3, Jul 2/Feb 7.
Batch 19-15/25-9
Sept 16, Aug 11/Nov 8, Jun 3/Mar 6, Jan 14, Feb 7/Jul 2, Oct 5/May 10, Dec 13, Apr 15, Nov 14, Mar 16, Jan 8/Aug 1, Sept 6/Jun 9, May 4/Apr 5, Feb 13, Oct 15, Jul 12/Dec 7.
Batch 18-16/25-9
Oct 15, Feb 16, Jun 8/Aug 1, Sept 7/Jul 9, May 4/Apr 5, Mar 13, Nov 14, Jun 12/Dec 6, Sept 16, Aug 10/Oct 8, Jul 2/ Feb 7, Jan 15, Mar 6/Jun 3, Nov 5/May 11, Dec 13, Apr 14.

Hooray!
- The End –

Okay, now I’m going back to my mattress.

7 comments:

  1. okay..this is my comment..like Aron' said : GO STUDY!!!!
    It's H-... til ur neurology test!

    ReplyDelete
  2. I think i have a game in PSP for this "magic square" and there are a lot of square in that software..a puzzle kinda thing.

    he?neurology test? what neurology test? ....bwahahahaha

    ReplyDelete
  3. sudoku? it's different.

    blah. the re-registration has been opened for pediatrics you know, since they have their test on October 5.

    ReplyDelete
  4. he? not sudoku its 4x4 square with 4-5 squares filled with numbers somekind of a hint, and we're supposed to fill it like your magic box. i'll show it to you when i'm home.

    ReplyDelete