The New Sudoku Players' Forum

[coloin]

And of course we need to be careful in our definitions

1.Puzzle from the minlex grid solution
2.Puzzle in min lex format
3.Puzzle in minlex pattern format and also minlex

1.and 2. can be used by transforming programs to identify a particular puzle from another
Of note most of the time 2 and 3, coincide but not always.

Coined by JPF in this thread

4.A MinLex puzzle is a MinLex subgrid having only one MinLex grid solution.

We are defining grid solutions with ever reducing data input it seems

[JPF]

Withdrawn.

[Mathimagics]

Maybe this solution, one of 229,603,014, is near:

Code: Select all

  1  2  3  4  5  6  7  8  9
  4  5  6  7  9  8  1  2  3
  9  7  8  1  2  3  4  5  6
  2  3  1  5  6  4  9  7  8
  5  9  4  8  3  7  2  6  1
  6  8  7  2  1  9  5  3  4
  3  4  2  9  8  5  6  1  7
  7  6  5  3  4  1  8  9  2
  8  1  9  6  7  2  3  4  5

So sorry, but no, not very near at all ...

I was hoping that JPF might confirm the 7-clue puzzle's validity first, before posting the solution, but I guess I should really make it available now.

By the way, my solver reports (eventually) that, somewhat astonishingly, 6 of those 7 clues are removable, giving valid 6-clue puzzles.

I asked it to try and remove 2 at a time, but it has been churning away for a couple of hours with no response ...

Solution: Show

Code: Select all

 +-------+-------+-------+
 | 1 2 3 | 4 5 6 | 7 8 9 |
 | 4 5 7 | 8 9 3 | 6 1 2 |
 | 9 8 6 | 2 1 7 | 3 5 4 |
 +-------+-------+-------+
 | 2 7 4 | 5 3 8 | 1 9 6 |
 | 5 3 1 | 9 6 4 | 8 2 7 |
 | 6 9 8 | 7 2 1 | 4 3 5 |
 +-------+-------+-------+
 | 3 4 2 | 6 8 5 | 9 7 1 |
 | 7 1 5 | 3 4 9 | 2 6 8 |
 | 8 6 9 | 1 7 2 | 5 4 3 |
 +-------+-------+-------+
123456789457893612986217354274538196531964827698721435342685971715349268869172543

[Band = 416, grid #1]  ED catalog index #5472730538    !! Note !!


[JPF]

Congratulations Mathimagics!
I'am still checking that this solution is unique... but the way I'm doing it is awfully slow.

JPF

[coloin]

I had an inkling that it might be band the 416/416/416 solution grid !

[JPF]

I had an inkling that it might be band the 416/416/416 solution grid !

yes, it is the maximum Minlex grid ; see here

edit : it is the unique solution, checked.

JPF

[Mathimagics]

1-clue puzzles

Band 416 is the only grid with 1-clue puzzles. There are 5 cells with values that do NOT occur in any other ED (Minlex) grid, so there are 5 puzzles with unique solutions for just the 1 clue:

Code: Select all

 r2c4 = 8
 r2c5 = 9
 r2c6 = 3
 r7c5 = 8
 r8c6 = 9


Interestingly, the first 3 are a complete mini-row (r2c456).

The penny finally dropped that it would be much quicker (given that I suspected 1-clue existence) to scan the ED catalog (23 minutes) counting cell/value occurrences.

I'm now working on a 2-clue scan, hopefully that will offer more band variety ...

[coloin]

A little bit similarly Here
was a stab at representing each minlexgrid with the minimum of data ie here it was a 53 string with 11 clues. And the first band was band 29 - coded in box 8 and box 6

Code: Select all

+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|.35|...|9..|
|6.1|5..|...|
|...|...|...|
+---+---+---+
|...|...|.1.|
|57.|...|...|
|...|..2|..3|
+---+---+---+

but am sure it could be done even more efficiently as you have done !

But I think is not quite one of those SudokuMLG Mellow Yellow puzzles !!

[dobrichev]

[Offtopic joke withdrawn]

[Mathimagics]

[Ditto]

[JPF]

Offtopic, deleted

[Mathimagics]

Personally, I'm happy with JPF's original description, "Minlex Puzzles", but as coloin has pointed out, this is already in use as a term meaning "puzzles in minlex form".

Perhaps, then, a suffix form, eg SudokuM, just as we now commonly use SudokuP, SudokuX, SudokuJ ... etc, might be a good idea?

[Mathimagics]

Since there is no obvious method for testing an incomplete grid for the minlex property, a solver for this puzzle type has to "filter" the solutions obtained from a normal solver, testing each solution for being in minlex form.

• Since this testing is will inevitably involve many, many, calls to the grid minlex function, I strongly advise to use Michael Deverin's Minlex code

• The solver should check, at any point where setting a cell completes row 2 and/or row 3, that the solution matches one of the known bands.

• The solver should check, when setting cells in column 1, the obvious inequalities (r4 < r5 < r6, etc)

• Another improvement is to apply global eliminations. Below I list the results of a scan over the ED catalog, identifying (non-trivial) cases of cell/value pairs that never occur. I think that this list is valid and complete ...

Cheers
MM

Eliminations: Show

Code: Select all

 cn12   r2c4        -9
 cn13   r2c5     -1237
 cn14   r2c6     -1278
 cn21   r3c4       -89
 cn22   r3c5       -89
 cn23   r3c6       -89
 cn25   r3c8        -3
 cn26   r3c9        -3
 cn31   r4c5        -8
 cn32   r4c6        -9
 cn36   r5c1        -9
 cn40   r5c5        -8
 cn41   r5c6        -9
 cn45   r6c1        -3
 cn49   r6c5        -8
 cn50   r6c6        -9
 cn54   r7c1       -89
 cn59   r7c6        -9
 cn63   r8c1       -39
 cn67   r8c5        -8
 cn72   r9c1       -35
 cn76   r9c5        -8
 cn77   r9c6        -9


[ EDIT ] added {r7c6 -9} which had somehow escaped from the list

[JPF]

SudokuM is fine to me

JPF

[dobrichev]

A solver for this puzzle can loop over the minlex grid catalogue represented as 81*9 compressed bitmap indexes. Circularly looping over cells with givens would give each iteration a chance for big leap over an index which has first matching value far ahead.
Of course first indexes will be all-zero or all-one and useless. Compression of the indexes is the real magic in such approach.

Another approach is to compose a pencilmark puzzle taking into account the allowed values for the top cells. Plus a final filter whether the solution is a minlex grid.

Replacing the requirement from Minlex to Anchor5 puzzles takes advantage of 18 static givens, more than Minlex.

... if I wasn't busy with other tasks ...