This Is An Infinite Sudoku(?)

wustvn · Posted: Sun Aug 31, 2008 12:33 pm Post subject: This Is An Infinite Sudoku(?)

Hi to all of you guys, I’m new here…
Basically, I just wonder how to make an algorithm to scramble numbers 0-9 in m rows x n columns, where m & n can be infinite, to be looked “cryptographically random”, which if it is seen by every four columns, there will be at least one number repeated, not just to the next four columns, but also to the next row. Sometimes this may not happen indeed.
Can somebody help me about this?
Thank you very much for your attentions.

Best regards,
Steven Wu
Bali - Indonesia

m_b_metcalf

wustvn · Posted: Mon Sep 01, 2008 1:34 pm Post subject:

Hi m_b_metcalf, nice to meet you...
Thx for your suggestion. Can it result like this table? This table actually has 284 columns and infinite rows, but here I give you the example with 100 rows x 20 columns. The file named puzle.pdf. I can't attach the file here, but I also can't put link yet to point to the file hosting service, where I put it.
Thank you very much for your attention.

m_b_metcalf · Posted: Mon Sep 01, 2008 2:15 pm Post subject:

wustvn · Posted: Tue Sep 02, 2008 12:42 pm Post subject:

Ok Mike (can I call you Mike? Just call me Steven).
As I do, I bet you've never seen an infinite sudoku, haven't you? Smile

Thx for your attention.

wustvn · Posted: Wed Sep 10, 2008 1:00 pm Post subject:

I put a table at Mediafire.com (a file hosting service) name puzle.pdf:
http://www.mediafire.com/?sharekey=c7ba82a6b7006656d2db6fb9a8902bda

A friend of mine gave me this table actually with 350 rows x 284 columns, which every cell contains of a single number from 0-9. Then by finding its patterns, he asked me to fill in the columns 1-20 for the rows 351,352,etc (meanwhile, ignore the columns 21-284 to make it simpler). I just can't find its patterns, that's why I need your help guys...

I just found by myself that THIS IS THE MAGIC OF THIS TABLE: no matter how you arrange the order of each four columns, there will be at least one number repeated, not just to the next four columns [(x-4,y) to (x+4,y)], but also to the next row [(x,y-1) to (x,y+1)]. Sometimes this may not happen indeed.

Take rows 1-2 as example. Let’s say columns 1-4 as section A, columns 5-8 as section B, columns 9-12 as section C, columns 13-16 as section D, columns 17-20 as section E.
The numbers that repeated to the next row (row 1 to row 2):
5,6 in section A ; 8 in section B ; 7,3,8 in section C ; 9 in section D ; 4 in section E.
The numbers that repeated to the next four columns (section):
Row 1:
No numbers from section A to section B.
7,8 from section B to section C.
No numbers from section C to section D.
6 from section D to section E.
Row 2:
4,3 from section A to section B.
8,3 from section B to section C.
No numbers from section C to section D.
9 from section D to section E.
Now you can try by changing the order of section from A-B-C-D-E to A-C-E-B-D or A-D-B-E-C or A-E-D-C-B or B-C-D-E-A.

Lately, I also found that this occurs on the opposite way too, if it is seen by every four rows.
Take columns 1-2 as example. Let’s say rows 1-4 as section A, rows 5-8 as section B, rows 9-12 as section C, etc.
The numbers that repeated to the next column (column 1 to column 2):
0,4 in section A ; 3 in section B ; no number in section C.
The numbers that repeated to the next four rows (section):
Column 1:
3 from section A to section B.
1 from section B to section C.
Column 2:
5 from section A to section B.
3 from section B to section C.
Now you can try by changing the order of section from A-B-C to A-C-B or B-A-C.

So please help me guys finding its patterns to fill in the columns 1-20 for the rows 351,352,etc.
Thx.