What is the largest minlex minimal puzzle ?

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What is the largest minlex minimal puzzle ?

Postby coloin » Tue Apr 06, 2021 5:11 pm

Hot on the heels of What is the smallest minlex puzzle ?

Here is a minimal puzzle in its most lexographically minimal form
Code: Select all
........1.....2.3...456.7......789....3.....6.6..5..1..4.3..6..1......2.6....9.7.

Code: Select all
+---+---+---+
|...|...|..1|
|...|..2|.3.|
|..4|56.|7..|
+---+---+---+
|...|.78|9..|
|..3|...|..6|
|.6.|.5.|.1.|
+---+---+---+
|.4.|3..|6..|
|1..|...|.2.|
|6..|..9|.7.|
+---+---+---+


What is the largest valid minimal minlex puzzle that one can find ?

To date this is the largest posted ....
Code: Select all
+---+---+---+
|...|..1|..2|
|.34|...|.51|
|2.1|.3.|6..|
+---+---+---+
|...|17.|.8.|
|...|29.|..7|
|9..|..4|3..|
+---+---+---+
|..6|3..|.4.|
|.4.|6..|..3|
|18.|..2|5..|
+---+---+---+  29 clues
Last edited by coloin on Fri Apr 09, 2021 10:52 am, edited 2 times in total.
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Re: What is the largest minimal minlex puzzle ?

Postby Serg » Tue Apr 06, 2021 9:29 pm

Hi, coloin!
Here is one of Mladen's 39-clue minimal puzzles in minlex form:
.....1..2.12...34..35.42.61..7.2.....287.5.3435.4.8.27.6.1......81.564735....4.16
Code: Select all
+-----+-----+-----+
|. . .|. . 1|. . 2|
|. 1 2|. . .|3 4 .|
|. 3 5|. 4 2|. 6 1|
+-----+-----+-----+
|. . 7|. 2 .|. . .|
|. 2 8|7 . 5|. 3 4|
|3 5 .|4 . 8|. 2 7|
+-----+-----+-----+
|. 6 .|1 . .|. . .|
|. 8 1|. 5 6|4 7 3|
|5 . .|. . 4|. 1 6|
+-----+-----+-----+


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Re: What is the largest minimal minlex puzzle ?

Postby JPF » Tue Apr 06, 2021 9:41 pm

The thread you are refering to is about the Min[Lex(Puzzle)]
It happens that Min[Lex(Puzzle)] = Min[Minlex(Puzzle)]

From that, it would be more logical to study Max[Lex(Puzzle)] which is not equal to Max[Minlex(Puzzle)]

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Re: What is the largest minimal minlex puzzle ?

Postby coloin » Tue Apr 06, 2021 9:56 pm

Serg wrote:Hi, coloin!
Here is one of Mladen's 39-clue minimal puzzles in minlex form:
.....1..2.12...34..35.42.61..7.2.....287.5.3435.4.8.27.6.1......81.564735....4.16 ....

not a bad ploy .....i am sure it can be improved on though !
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Re: What is the largest minimal minlex puzzle ?

Postby coloin » Tue Apr 06, 2021 10:01 pm

JPF wrote:The thread you are refering to is about the Min[Lex(Puzzle)]
It happens that Min[Lex(Puzzle)] = Min[Minlex(Puzzle)]

From that, it would be more logical to study Max[Lex(Puzzle)] which is not equal to Max[Minlex(Puzzle)]

JPF


maybe ... but min lex puzzles are predominently used here..and there is a finite list of "2.55 × 10^25 non-essentially-equivalent minimal puzzles" for us to refer to !!! :!:
and presumably largest max lex puzzles will all start with 98765432.........

i will try to find an example ...

Code: Select all
+---+---+---+
|987|654|32.|
|653|72.|...|
|...|...|...|
+---+---+---+
|79.|8.5|6..|
|26.|4..|89.|
|...|...|...|
+---+---+---+
|5..|.6.|9..|
|...|..7|.4.|
|...|...|...|
+---+---+---+
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Re: What is the largest minimal minlex puzzle ?

Postby Mathimagics » Wed Apr 07, 2021 3:04 am

Is Max Lex Luthor's brother? :?:
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Re: What is the largest minlex minimal puzzle ?

Postby coloin » Wed Apr 07, 2021 8:38 pm

Hmmm was that his name ?

Update ... but maybe further to go ...

Code: Select all
.....1..2.12...34..35.42.61..7.2.....287.5.3435.4.8.27.6.1......81.564735....4.16 serg
.....1..2.34....512.1.3.6.....17..8....29...79....43....63...4..4.6....318...25.. coloin2

Code: Select all
+---+---+---+
|...|..1|..2|
|.34|...|.51|
|2.1|.3.|6..|
+---+---+---+
|...|17.|.8.|
|...|29.|..7|
|9..|..4|3..|
+---+---+---+
|..6|3..|.4.|
|.4.|6..|..3|
|18.|..2|5..|
+---+---+---+
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Re: What is the largest minlex minimal puzzle ?

Postby JPF » Wed Apr 14, 2021 9:56 am

here is a good one:
Code: Select all
+---+---+---+
|..1|..2|..3|
|.4.|.5.|.6.|
|7..|8..|9..|
+---+---+---+
|..2|.6.|7..|
|.5.|9..|..1|
|8..|..3|.4.|
+---+---+---+
|..6|1..|.8.|
|.9.|..4|2..|
|3..|.7.|1.5|
+---+---+---+

It's not mine... Mauricio posted it in 2007.
I just (re)discovered this thread On the minimum and maximum minlex minimal sudokus
Code: Select all
.....1..2.12...34..35.42.61..7.2.....287.5.3435.4.8.27.6.1......81.564735....4.16 serg/dobrichev
.....1..2.34....512.1.3.6.....17..8....29...79....43....63...4..4.6....318...25.. coloin2
..1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7.1.5 Mauricio

He gave also the same Min(MinLex) as coloin's here

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Re: What is the largest minlex minimal puzzle ?

Postby JPF » Wed Apr 14, 2021 8:15 pm

Now, about the largest Lex puzzle, here is a new one:
Code: Select all
+---+---+---+
|987|654|32.|
|654|23.|...|
|...|...|...|
+---+---+---+
|42.|38.|6..|
|893|7..|2..|
|...|...|...|
+---+---+---+
|..2|59.|83.|
|...|...|.5.|
|...|...|...|
+---+---+---+

Code: Select all
98765432.65372.............79.8.56..26.4..89..........5...6.9.......7.4..........  coloin
98765432.65423.............42.38.6..8937..2.............259.83........5..........  JPF

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Re: What is the largest minlex minimal puzzle ?

Postby Hajime » Wed Apr 14, 2021 8:41 pm

JPF wrote:Now, about the largest Lex puzzle, here is a new one:
Code: Select all
+---+---+---+
|987|654|32.|
|654|23.|...|
|...|...|...|
+---+---+---+
|42.|38.|6..|
|893|7..|2..|
|...|...|...|
+---+---+---+
|..2|59.|83.|
|...|...|.5.|
|...|...|...|
+---+---+---+

Code: Select all
98765432.65372.............79.8.56..26.4..89..........5...6.9.......7.4..........  coloin
98765432.65423.............42.38.6..8937..2.............259.83........5..........  JPF

JPF

Is this larger? The first dot changed to 1 ?
Code: Select all
98765432165423.............42.38.6..8937..2.............259.83........5.......... 
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Re: What is the largest minlex minimal puzzle ?

Postby JPF » Wed Apr 14, 2021 9:02 pm

The puzzles have to be minimal...

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Re: What is the largest minlex minimal puzzle ?

Postby Leren » Wed Apr 14, 2021 9:12 pm

Hajime wrote : Is this larger? The first dot changed to 1 ?

Code: Select all
98765432.65372.............79.8.56..26.4..89..........5...6.9.......7.4..........  coloin
98765432.65423.............42.38.6..8937..2.............259.83........5..........  JPF
           ^

Not that this my topic, but JPF's looks larger to me, because the two puzzles are the same up to cell 11 and then differ in cell 12, where JPF has 4 vs coloin 3. Leren
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Re: What is the largest minlex minimal puzzle ?

Postby coloin » Wed Apr 14, 2021 10:38 pm

JPF wrote:Mauricio posted it in 2007.
I just (re)discovered this thread On the minimum and maximum minlex minimal sudokus

Wow he did well so long ago - and no gridchecker !
and
Maurico wrote:Finding the minimum minlex sudoku should be easier than finding the maximum


Ive been working on that one ! [in anticipation] and i think he was right ... i gave up on the diagonal 27 clue with 3 clues per row and all different clues in the bands - but that was a good find.

I did struggle for a long time to get the minlex 123456789 in the first band.

But with 30 clues there are many greater albeit not as perfect
Code: Select all
+---+---+---+
|..1|..2|..3|
|.4.|.5.|.6.|
|7..|8..|9..|
+---+---+---+
|..2|.7.|1.9|
|.9.|..8|2..|
|4..|2..|.3.|
+---+---+---+
|..4|5..|.9.|
|5..|.84|..6|
|83.|..7|5..|
+---+---+---+

Code: Select all
.....1..2.12...34..35.42.61..7.2.....287.5.3435.4.8.27.6.1......81.564735....4.16 serg/dobrichev
.....1..2.34....512.1.3.6.....17..8....29...79....43....63...4..4.6....318...25.. coloin2
..1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7.1.5 Mauricio
..1..2..3.4..5..6.7..8..9....2.7.1.9.9...82..4..2...3...45...9.5...84..683...75.. coloin3


I dont know how we will know when we have achieved the maximum puzzle - but perhaps I am close with my other efforts !

It is possibly easier with the non min lex max puzzle though as the initial clues are cast and cant be changed or improved on - as in
Code: Select all
+---+---+---+
|987|645|32.|
|654|3..|...|
|32.|...|...|
+---+---+---+
|89.|..3|...|
|...|...|68.|
|4..|.7.|...|
+---+---+---+
|73.|9..|86.|
|...|...|...|
|...|7..|4..|
+---+---+---+

Code: Select all
98765432.65372.............79.8.56..26.4..89..........5...6.9.......7.4..........  coloin
98765432.65423.............42.38.6..8937..2.............259.83........5..........  JPF
98764532.6543.....32.......89...3.........68.4...7....73.9..86.............7..4..  coloin2

but still can be improved


Will comment on the minimum puzzle in the other thread
,
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Re: What is the largest minlex minimal puzzle ?

Postby coloin » Thu Apr 15, 2021 6:39 am

Code: Select all
..1..2..3.4..5..6.7..8..9....2.7.1.9.9...82..4..2...3...45...9.5...84..683...75.. coloin3                   
..1..2..3.2.18..6.98.7..2....5.7.43.3..8..5...1...5..9..45...9.1...2...6.7...83.. morphed more minlex coloin3

Although something isnt quite right with my min lexing software !! [gsf's sudoku-64 -f%#mc and the latest version of gridchecker subcanon...] maybe this is that bug that holdout mentioned !!!....

And Mauricio's puzzle looks very good indeed!!!

Hmmm
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Re: What is the largest minlex minimal puzzle ?

Postby JPF » Thu Apr 15, 2021 5:54 pm

Code: Select all
+---+---+---+
|987|654|32.|
|654|3..|...|
|32.|...|...|
+---+---+---+
|89.|.6.|...|
|...|...|75.|
|5..|.3.|...|
+---+---+---+
|2..|9..|57.|
|...|...|...|
|...|2..|.4.|
+---+---+---+

Code: Select all
98765432.65372.............79.8.56..26.4..89..........5...6.9.......7.4..........  coloin
98765432.65423.............42.38.6..8937..2.............259.83........5..........  JPF
98764532.6543.....32.......89...3.........68.4...7....73.9..86.............7..4..  coloin2
98765432.6543.....32.......89..6..........75.5...3....2..9..57.............2...4.  JPF2

Still looking for an effective way to tackle this problem!

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