The New Sudoku Players' Forum

[coloin]

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

[Serg]

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|
+-----+-----+-----+

Serg

[JPF]

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

[coloin]

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 !

[coloin]

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.|
|...|...|...|
+---+---+---+


[Mathimagics]

Is Max Lex Luthor's brother?

[coloin]

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..|
+---+---+---+


[JPF]

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

JPF

[JPF]

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

[Hajime]

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.......... 


[JPF]

The puzzles have to be minimal...

JPF

[Leren]

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

[coloin]

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

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
,

[coloin]

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

[JPF]

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!

JPF