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Why is Box 1 filled in?

 
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Adak

Joined: 27 Feb 2008
Posts: 87
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PostPosted: Tue Jan 13, 2009 11:26 pm    Post subject: Why is Box 1 filled in? Reply with quote

I've seen a lot of canonical or normalized grids, shown with the top left box already filled in:
Code:

---*
123|
456|
789|

Papers about Sudoku grids, and normalizing them, also show this; Jarvis and Russell, among others.

Yet when I look at Gordon's 17's, etc., he has his grids in row minimized order, and the top left hand box is nearly all zero's. This makes sense to me, since now we're basically referring to the grid, as though it were a huge 81 number integer.

Then, is the first box being filled more for illustration purposes? Something to help the author show how the grids can be canonicalized easier?
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daj95376

Joined: 05 Feb 2006
Posts: 349
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PostPosted: Wed Jan 14, 2009 3:49 pm    Post subject: Reply with quote

There is more than one way to create a canonicalized/normalized solution. Here's the one currently in use ... along with the former.

Code:
===== ===== ===== ===== Min-Lex Grids

            Base                        Minimum                       Maximum
 +-----------------------+     +-----------------------+     +-----------------------+
 | 1 2 3 | 4 5 6 | 7 8 9 |     | 1 2 3 | 4 5 6 | 7 8 9 |     | 1 2 3 | 4 5 6 | 7 8 9 |
 | 4 5 . | . . . | . . . |     | 4 5 6 | 7 8 9 | 1 2 3 |     | 4 5 7 | 8 9 3 | 6 1 2 |
 | . . . | . . . | . . . |     | 7 8 9 | 1 2 3 | 4 5 6 |     | 9 8 6 | 2 1 7 | 3 5 4 |
 |-------+-------+-------|     |-------+-------+-------|     |-------+-------+-------|
 | 2 . . | . . . | . . . |     | 2 3 1 | 5 6 4 | 8 9 7 |     | 2 7 4 | 5 3 8 | 1 9 6 |
 | . . . | . . . | . . . |     | 5 6 4 | 8 9 7 | 2 3 1 |     | 5 3 1 | 9 6 4 | 8 2 7 |
 | . . . | . . . | . . . |     | 8 9 7 | 2 3 1 | 5 6 4 |     | 6 9 8 | 7 2 1 | 4 3 5 |
 |-------+-------+-------|     |-------+-------+-------|     |-------+-------+-------|
 | . . . | . . . | . . . |     | 3 1 2 | 6 4 5 | 9 7 8 |     | 3 4 2 | 6 8 5 | 9 7 1 |
 | . . . | . . . | . . . |     | 6 4 5 | 9 7 8 | 3 1 2 |     | 7 1 5 | 3 4 9 | 2 6 8 |
 | . . . | . . . | . . . |     | 9 7 8 | 3 1 2 | 6 4 5 |     | 8 6 9 | 1 7 2 | 5 4 3 |
 +-----------------------+     +-----------------------+     +-----------------------+
______________________________________________________________________________________

             Old
 +-----------------------+
 | 1 2 3 | 4 . . | . . . |
 | 4 5 6 | . . . | . . . |
 | 7 8 9 | . . . | 4 . . |
 |-------+-------+-------|
 | . . . | . . 4 | . . . |
 | . . 4 | . . . | . . . |
 | . . . | . . . | . . 4 |
 |-------+-------+-------|
 | . . . | . 4 . | . . . |
 | . 4 . | . . . | . . . |
 | . . . | . . . | . 4 . |
 +-----------------------+
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