## What is the largest minlex minimal puzzle ?

Everything about Sudoku that doesn't fit in one of the other sections

### What is the largest minlex minimal puzzle ?

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.
coloin

Posts: 2009
Joined: 05 May 2005

### Re: What is the largest minimal minlex puzzle ?

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
Serg
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### Re: What is the largest minimal minlex 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
JPF
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Location: Paris, France

### Re: What is the largest minimal minlex puzzle ?

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 !
coloin

Posts: 2009
Joined: 05 May 2005

### Re: What is the largest minimal minlex 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 !!!

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.||...|...|...|+---+---+---+`
coloin

Posts: 2009
Joined: 05 May 2005

### Re: What is the largest minimal minlex puzzle ?

Is Max Lex Luthor's brother?

Mathimagics
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### Re: What is the largest minlex minimal puzzle ?

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..|+---+---+---+`
coloin

Posts: 2009
Joined: 05 May 2005

### Re: What is the largest minlex minimal puzzle ?

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
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Location: Paris, France

### Re: What is the largest minlex minimal puzzle ?

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..........  coloin98765432.65423.............42.38.6..8937..2.............259.83........5..........  JPF`

JPF
JPF
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Location: Paris, France

### Re: What is the largest minlex minimal puzzle ?

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..........  coloin98765432.65423.............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..........  `

Hajime

Posts: 361
Joined: 20 April 2018
Location: Netherlands

### Re: What is the largest minlex minimal puzzle ?

The puzzles have to be minimal...

JPF
JPF
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Location: Paris, France

### Re: What is the largest minlex minimal puzzle ?

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..........  coloin98765432.65423.............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
Leren

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### Re: What is the largest minlex minimal puzzle ?

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..........  coloin98765432.65423.............42.38.6..8937..2.............259.83........5..........  JPF98764532.6543.....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

Posts: 2009
Joined: 05 May 2005

### Re: What is the largest minlex minimal puzzle ?

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
coloin

Posts: 2009
Joined: 05 May 2005

### Re: What is the largest minlex minimal puzzle ?

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..........  coloin98765432.65423.............42.38.6..8937..2.............259.83........5..........  JPF98764532.6543.....32.......89...3.........68.4...7....73.9..86.............7..4..  coloin298765432.6543.....32.......89..6..........75.5...3....2..9..57.............2...4.  JPF2`

Still looking for an effective way to tackle this problem!

JPF
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Location: Paris, France

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