Canonicalizing all Sudokus

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Canonicalizing all Sudokus

Postby Tomoka » Thu Apr 06, 2017 6:16 pm

I was wondering if we can canonicalize all Sudokus. If we can't do all of them, then let's start the first 10, and then show the last one as a symbolic "closure".

The canonicalization is based grids, then Sudokus that fit the grid. Digits ordered from 1 through 9. For each grid, Sudokus are ordered from fewest clues to most clues. For Sudokus with the same number of clues, clues are ordered based on positions of the clues; from top to bottom, then left to right. Again, digits are ordered from 1 through 9, and canonicalized based on the numbers in the top row first, and then in cells from left to right. I notice this Sudoku by Rico Alan (rotated and rows re-ordered compared to how he posted it):

Code: Select all
1234.....
.....3456
.........
2345.....
.....4567
.........
3456.....
.....5678
.........

Based on the proposed canonicalizing scheme, can we say that this is the first Sudoku? If not, then what is the first Sudoku? Also, how many more Sudoku's will there be in the complete list?
Tomoka
 
Posts: 6
Joined: 06 April 2017

Re: Canonicalizing all Sudokus

Postby coloin » Fri Apr 07, 2017 10:07 pm

Code: Select all
+---+---+---+
|123|4..|...|
|...|..1|234|
|...|...|...|
+---+---+---+
|582|7..|...|
|...|..3|549|
|...|...|...|
+---+---+---+
|759|8..|...|
|...|..4|671|
|...|...|...|
+---+---+---+


This may not be what you are looking for - but as ever its never straightforward - but this is a lexographically less - but by no means the least.
I guess there may be over 10 million [ maybe a whole lot more] ED puzzles [min and non min] with this pattern

this one is looking toward the end [ all bands are the largest minimum] but can be morphed smaller...]
Code: Select all
+---+---+---+
|123|4..|...|
|...|..5|671|
|...|...|...|
+---+---+---+
|987|6..|...|
|...|..4|327|
|...|...|...|
+---+---+---+
|479|8..|...|
|...|..1|539|
|...|...|...|
+---+---+---+
coloin
 
Posts: 1638
Joined: 05 May 2005

Re: Canonicalizing all Sudokus

Postby Tomoka » Fri Apr 07, 2017 10:43 pm

I checked your first one but not your second one. I just realized that neither your Sudoko nor mine is close to the front of the list because they aren't even from the first grid. (Grids are canonicalized before the puzzles of the grid). So to be early in the list, it has to be a Sudoku from this grid (I think):
Code: Select all
123456789
456789123
789123456
234567891
567891234
891234567
345678912
678912345
912345678

Both your Sudoku and mine are good (maybe within the top 1%) but I think we can do much better. There's lots of Sudokus. 8-)
Tomoka
 
Posts: 6
Joined: 06 April 2017


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